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<h1 id="162">16.2 一起参与创作<a class="headerlink" href="#162" title="Permanent link">¶</a></h1>
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<p>所有<a href="https://github.com/krahets/hello-algo/graphs/contributors">撰稿人</a>的 GitHub ID 将被展示在本书的仓库主页上，以感谢他们对开源社区的无私奉献。</p>
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<p>所有<a href="https://github.com/krahets/hello-algo/graphs/contributors">撰稿人</a>的 GitHub ID 将被展示在本书的仓库主页上，以感谢他们对开源社区的无私奉献。</p>
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<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a>docker-compose<span class="w"> </span>down
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<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a>docker-compose<span class="w"> </span>down
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<h1 id="16">第 16 章 附录<a class="headerlink" href="#16" title="Permanent link">¶</a></h1>
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<h1 id="16">第 16 章 附录<a class="headerlink" href="#16" title="Permanent link">¶</a></h1>
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<li><a href="https://www.hello-algo.com/chapter_appendix/contribution/">16.2 一起参与创作</a></li>
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<h1 id="161">16.1 编程环境安装<a class="headerlink" href="#161" title="Permanent link">¶</a></h1>
|
<h1 id="161">16.1 编程环境安装<a class="headerlink" href="#161" title="Permanent link">¶</a></h1>
|
||||||
<h3 id="1-vscode">1. VSCode<a class="headerlink" href="#1-vscode" title="Permanent link">¶</a></h3>
|
<h3 id="1-vscode">1. VSCode<a class="headerlink" href="#1-vscode" title="Permanent link">¶</a></h3>
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||||||
<p>本书推荐使用开源轻量的 VSCode 作为本地 IDE ，下载并安装 <a href="https://code.visualstudio.com/">VSCode</a> 。</p>
|
<p>本书推荐使用开源轻量的 VSCode 作为本地 IDE ，下载并安装 <a href="https://code.visualstudio.com/">VSCode</a> 。</p>
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|||||||
<li>在 VSCode 的插件市场中搜索 <code>rust</code> ，安装 <a href="https://marketplace.visualstudio.com/items?itemName=rust-lang.rust-analyzer">rust-analyzer</a> 。</li>
|
<li>在 VSCode 的插件市场中搜索 <code>rust</code> ，安装 <a href="https://marketplace.visualstudio.com/items?itemName=rust-lang.rust-analyzer">rust-analyzer</a> 。</li>
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||||||
<h1 id="41">4.1 数组<a class="headerlink" href="#41" title="Permanent link">¶</a></h1>
|
<h1 id="41">4.1 数组<a class="headerlink" href="#41" title="Permanent link">¶</a></h1>
|
||||||
<p>「数组 array」是一种线性数据结构，其将相同类型元素存储在连续的内存空间中。我们将元素在数组中的位置称为该元素的「索引 index」。图 4-1 展示了数组的主要术语和概念。</p>
|
<p>「数组 array」是一种线性数据结构，其将相同类型元素存储在连续的内存空间中。我们将元素在数组中的位置称为该元素的「索引 index」。图 4-1 展示了数组的主要术语和概念。</p>
|
||||||
<p><img alt="数组定义与存储方式" src="../array.assets/array_definition.png" /></p>
|
<p><img alt="数组定义与存储方式" src="../array.assets/array_definition.png" /></p>
|
||||||
@@ -4618,11 +4650,73 @@
|
|||||||
<li><strong>数据结构实现</strong>：数组可以用于实现栈、队列、哈希表、堆、图等数据结构。例如，图的邻接矩阵表示实际上是一个二维数组。</li>
|
<li><strong>数据结构实现</strong>：数组可以用于实现栈、队列、哈希表、堆、图等数据结构。例如，图的邻接矩阵表示实际上是一个二维数组。</li>
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<h1 id="42">4.2 链表<a class="headerlink" href="#42" title="Permanent link">¶</a></h1>
|
<h1 id="42">4.2 链表<a class="headerlink" href="#42" title="Permanent link">¶</a></h1>
|
||||||
<p>内存空间是所有程序的公共资源，在一个复杂的系统运行环境下，空闲的内存空间可能散落在内存各处。我们知道，存储数组的内存空间必须是连续的，而当数组非常大时，内存可能无法提供如此大的连续空间。此时链表的灵活性优势就体现出来了。</p>
|
<p>内存空间是所有程序的公共资源，在一个复杂的系统运行环境下，空闲的内存空间可能散落在内存各处。我们知道，存储数组的内存空间必须是连续的，而当数组非常大时，内存可能无法提供如此大的连续空间。此时链表的灵活性优势就体现出来了。</p>
|
||||||
<p>「链表 linked list」是一种线性数据结构，其中的每个元素都是一个节点对象，各个节点通过“引用”相连接。引用记录了下一个节点的内存地址，通过它可以从当前节点访问到下一个节点。</p>
|
<p>「链表 linked list」是一种线性数据结构，其中的每个元素都是一个节点对象，各个节点通过“引用”相连接。引用记录了下一个节点的内存地址，通过它可以从当前节点访问到下一个节点。</p>
|
||||||
@@ -3571,8 +3603,8 @@
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|||||||
<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span> <span class="nc">ListNode</span><span class="p">:</span>
|
<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span> <span class="nc">ListNode</span><span class="p">:</span>
|
||||||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w"> </span><span class="sd">"""链表节点类"""</span>
|
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w"> </span><span class="sd">"""链表节点类"""</span>
|
||||||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||||||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">val</span> <span class="c1"># 节点值</span>
|
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">val</span> <span class="c1"># 节点值</span>
|
||||||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="bp">self</span><span class="o">.</span><span class="n">next</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">ListNode</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 指向下一节点的引用</span>
|
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="bp">self</span><span class="o">.</span><span class="n">next</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 指向下一节点的引用</span>
|
||||||
</code></pre></div>
|
</code></pre></div>
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</div>
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@@ -4572,9 +4604,9 @@
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|||||||
<div class="highlight"><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="k">class</span> <span class="nc">ListNode</span><span class="p">:</span>
|
<div class="highlight"><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="k">class</span> <span class="nc">ListNode</span><span class="p">:</span>
|
||||||
<a id="__codelineno-72-2" name="__codelineno-72-2" href="#__codelineno-72-2"></a><span class="w"> </span><span class="sd">"""双向链表节点类"""</span>
|
<a id="__codelineno-72-2" name="__codelineno-72-2" href="#__codelineno-72-2"></a><span class="w"> </span><span class="sd">"""双向链表节点类"""</span>
|
||||||
<a id="__codelineno-72-3" name="__codelineno-72-3" href="#__codelineno-72-3"></a> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
<a id="__codelineno-72-3" name="__codelineno-72-3" href="#__codelineno-72-3"></a> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||||||
<a id="__codelineno-72-4" name="__codelineno-72-4" href="#__codelineno-72-4"></a> <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">val</span> <span class="c1"># 节点值</span>
|
<a id="__codelineno-72-4" name="__codelineno-72-4" href="#__codelineno-72-4"></a> <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">val</span> <span class="c1"># 节点值</span>
|
||||||
<a id="__codelineno-72-5" name="__codelineno-72-5" href="#__codelineno-72-5"></a> <span class="bp">self</span><span class="o">.</span><span class="n">next</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">ListNode</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 指向后继节点的引用</span>
|
<a id="__codelineno-72-5" name="__codelineno-72-5" href="#__codelineno-72-5"></a> <span class="bp">self</span><span class="o">.</span><span class="n">next</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 指向后继节点的引用</span>
|
||||||
<a id="__codelineno-72-6" name="__codelineno-72-6" href="#__codelineno-72-6"></a> <span class="bp">self</span><span class="o">.</span><span class="n">prev</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">ListNode</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 指向前驱节点的引用</span>
|
<a id="__codelineno-72-6" name="__codelineno-72-6" href="#__codelineno-72-6"></a> <span class="bp">self</span><span class="o">.</span><span class="n">prev</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 指向前驱节点的引用</span>
|
||||||
</code></pre></div>
|
</code></pre></div>
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||||||
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||||||
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||||||
@@ -4765,11 +4797,73 @@
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|||||||
<li><strong>数据缓冲区</strong>：在某些数据缓冲区的实现中，也可能会使用到循环链表。比如在音频、视频播放器中，数据流可能会被分成多个缓冲块并放入一个循环链表，以便实现无缝播放。</li>
|
<li><strong>数据缓冲区</strong>：在某些数据缓冲区的实现中，也可能会使用到循环链表。比如在音频、视频播放器中，数据流可能会被分成多个缓冲块并放入一个循环链表，以便实现无缝播放。</li>
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||||||
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||||||
<p><strong>数组长度不可变导致实用性降低</strong>。在实际中，我们可能事先无法确定需要存储多少数据，这使数组长度的选择变得困难。若长度过小，需要在持续添加数据时频繁扩容数组；若长度过大，则会造成内存空间的浪费。</p>
|
<p><strong>数组长度不可变导致实用性降低</strong>。在实际中，我们可能事先无法确定需要存储多少数据，这使数组长度的选择变得困难。若长度过小，需要在持续添加数据时频繁扩容数组；若长度过大，则会造成内存空间的浪费。</p>
|
||||||
<p>为解决此问题，出现了一种被称为「动态数组 dynamic array」的数据结构，即长度可变的数组，也常被称为「列表 list」。列表基于数组实现，继承了数组的优点，并且可以在程序运行过程中动态扩容。我们可以在列表中自由地添加元素，而无须担心超过容量限制。</p>
|
<p>为解决此问题，出现了一种被称为「动态数组 dynamic array」的数据结构，即长度可变的数组，也常被称为「列表 list」。列表基于数组实现，继承了数组的优点，并且可以在程序运行过程中动态扩容。我们可以在列表中自由地添加元素，而无须担心超过容量限制。</p>
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_backtracking/backtracking_algorithm.md" title="编辑此页" class="md-content__button md-icon">
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<h1 id="131">13.1 回溯算法<a class="headerlink" href="#131" title="Permanent link">¶</a></h1>
|
<h1 id="131">13.1 回溯算法<a class="headerlink" href="#131" title="Permanent link">¶</a></h1>
|
||||||
<p>「回溯算法 backtracking algorithm」是一种通过穷举来解决问题的方法，它的核心思想是从一个初始状态出发，暴力搜索所有可能的解决方案，当遇到正确的解则将其记录，直到找到解或者尝试了所有可能的选择都无法找到解为止。</p>
|
<p>「回溯算法 backtracking algorithm」是一种通过穷举来解决问题的方法，它的核心思想是从一个初始状态出发，暴力搜索所有可能的解决方案，当遇到正确的解则将其记录，直到找到解或者尝试了所有可能的选择都无法找到解为止。</p>
|
||||||
<p>回溯算法通常采用“深度优先搜索”来遍历解空间。在二叉树章节中，我们提到前序、中序和后序遍历都属于深度优先搜索。接下来，我们利用前序遍历构造一个回溯问题，逐步了解回溯算法的工作原理。</p>
|
<p>回溯算法通常采用“深度优先搜索”来遍历解空间。在二叉树章节中，我们提到前序、中序和后序遍历都属于深度优先搜索。接下来，我们利用前序遍历构造一个回溯问题，逐步了解回溯算法的工作原理。</p>
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<li>最大团问题是图论中的一个经典问题，可用贪心等启发式算法来解决。</li>
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<li>最大团问题是图论中的一个经典问题，可用贪心等启发式算法来解决。</li>
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_backtracking/index.md" title="编辑此页" class="md-content__button md-icon">
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<h1 id="13">第 13 章 回溯<a class="headerlink" href="#13" title="Permanent link">¶</a></h1>
|
<h1 id="13">第 13 章 回溯<a class="headerlink" href="#13" title="Permanent link">¶</a></h1>
|
||||||
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<li><a href="https://www.hello-algo.com/chapter_backtracking/summary/">13.5 小结</a></li>
|
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<h1 id="134-n">13.4 N 皇后问题<a class="headerlink" href="#134-n" title="Permanent link">¶</a></h1>
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<h1 id="134-n">13.4 N 皇后问题<a class="headerlink" href="#134-n" title="Permanent link">¶</a></h1>
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<p>逐行放置 <span class="arithmatex">\(n\)</span> 次，考虑列约束，则从第一行到最后一行分别有 <span class="arithmatex">\(n\)</span>、<span class="arithmatex">\(n-1\)</span>、<span class="arithmatex">\(\dots\)</span>、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(1\)</span> 个选择，<strong>因此时间复杂度为 <span class="arithmatex">\(O(n!)\)</span></strong> 。实际上，根据对角线约束的剪枝也能够大幅地缩小搜索空间，因而搜索效率往往优于以上时间复杂度。</p>
|
<p>逐行放置 <span class="arithmatex">\(n\)</span> 次，考虑列约束，则从第一行到最后一行分别有 <span class="arithmatex">\(n\)</span>、<span class="arithmatex">\(n-1\)</span>、<span class="arithmatex">\(\dots\)</span>、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(1\)</span> 个选择，<strong>因此时间复杂度为 <span class="arithmatex">\(O(n!)\)</span></strong> 。实际上，根据对角线约束的剪枝也能够大幅地缩小搜索空间，因而搜索效率往往优于以上时间复杂度。</p>
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<p>数组 <code>state</code> 使用 <span class="arithmatex">\(O(n^2)\)</span> 空间，数组 <code>cols</code>、<code>diags1</code> 和 <code>diags2</code> 皆使用 <span class="arithmatex">\(O(n)\)</span> 空间。最大递归深度为 <span class="arithmatex">\(n\)</span> ，使用 <span class="arithmatex">\(O(n)\)</span> 栈帧空间。因此，<strong>空间复杂度为 <span class="arithmatex">\(O(n^2)\)</span></strong> 。</p>
|
<p>数组 <code>state</code> 使用 <span class="arithmatex">\(O(n^2)\)</span> 空间，数组 <code>cols</code>、<code>diags1</code> 和 <code>diags2</code> 皆使用 <span class="arithmatex">\(O(n)\)</span> 空间。最大递归深度为 <span class="arithmatex">\(n\)</span> ，使用 <span class="arithmatex">\(O(n)\)</span> 栈帧空间。因此，<strong>空间复杂度为 <span class="arithmatex">\(O(n^2)\)</span></strong> 。</p>
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<h1 id="132">13.2 全排列问题<a class="headerlink" href="#132" title="Permanent link">¶</a></h1>
|
<h1 id="132">13.2 全排列问题<a class="headerlink" href="#132" title="Permanent link">¶</a></h1>
|
||||||
<p>全排列问题是回溯算法的一个典型应用。它的定义是在给定一个集合（如一个数组或字符串）的情况下，找出这个集合中元素的所有可能的排列。</p>
|
<p>全排列问题是回溯算法的一个典型应用。它的定义是在给定一个集合（如一个数组或字符串）的情况下，找出这个集合中元素的所有可能的排列。</p>
|
||||||
<p>表 13-2 列举了几个示例数据，包括输入数组和对应的所有排列。</p>
|
<p>表 13-2 列举了几个示例数据，包括输入数组和对应的所有排列。</p>
|
||||||
@@ -4394,11 +4426,73 @@
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|||||||
<p><img alt="两种剪枝条件的作用范围" src="../permutations_problem.assets/permutations_ii_pruning_summary.png" /></p>
|
<p><img alt="两种剪枝条件的作用范围" src="../permutations_problem.assets/permutations_ii_pruning_summary.png" /></p>
|
||||||
<p align="center"> 图 13-9 两种剪枝条件的作用范围 </p>
|
<p align="center"> 图 13-9 两种剪枝条件的作用范围 </p>
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<h1 id="133">13.3 子集和问题<a class="headerlink" href="#133" title="Permanent link">¶</a></h1>
|
<h1 id="133">13.3 子集和问题<a class="headerlink" href="#133" title="Permanent link">¶</a></h1>
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<h2 id="1331">13.3.1 无重复元素的情况<a class="headerlink" href="#1331" title="Permanent link">¶</a></h2>
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<h1 id="135">13.5 小结<a class="headerlink" href="#135" title="Permanent link">¶</a></h1>
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<h1 id="135">13.5 小结<a class="headerlink" href="#135" title="Permanent link">¶</a></h1>
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||||||
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deal in the Software without restriction, including without limitation the
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all copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
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|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_computational_complexity/index.md" title="编辑此页" class="md-content__button md-icon">
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_computational_complexity/index.md" title="编辑此页" class="md-content__button md-icon">
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||||||
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|
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|
||||||
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||||||
|
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|
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|
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<h1 id="2">第 2 章 复杂度分析<a class="headerlink" href="#2" title="Permanent link">¶</a></h1>
|
<h1 id="2">第 2 章 复杂度分析<a class="headerlink" href="#2" title="Permanent link">¶</a></h1>
|
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||||||
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|
||||||
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|
|||||||
<li><a href="https://www.hello-algo.com/chapter_computational_complexity/summary/">2.5 小结</a></li>
|
<li><a href="https://www.hello-algo.com/chapter_computational_complexity/summary/">2.5 小结</a></li>
|
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<h1 id="22">2.2 迭代与递归<a class="headerlink" href="#22" title="Permanent link">¶</a></h1>
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<h1 id="22">2.2 迭代与递归<a class="headerlink" href="#22" title="Permanent link">¶</a></h1>
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||||||
<p>在数据结构与算法中，重复执行某个任务是很常见的，其与算法的复杂度密切相关。而要重复执行某个任务，我们通常会选用两种基本的程序结构：迭代和递归。</p>
|
<p>在数据结构与算法中，重复执行某个任务是很常见的，其与算法的复杂度密切相关。而要重复执行某个任务，我们通常会选用两种基本的程序结构：迭代和递归。</p>
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<h2 id="221">2.2.1 迭代<a class="headerlink" href="#221" title="Permanent link">¶</a></h2>
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<p>总之，<strong>选择迭代还是递归取决于特定问题的性质</strong>。在编程实践中，权衡两者的优劣并根据情境选择合适的方法是至关重要的。</p>
|
<p>总之，<strong>选择迭代还是递归取决于特定问题的性质</strong>。在编程实践中，权衡两者的优劣并根据情境选择合适的方法是至关重要的。</p>
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<h1 id="21">2.1 算法效率评估<a class="headerlink" href="#21" title="Permanent link">¶</a></h1>
|
<h1 id="21">2.1 算法效率评估<a class="headerlink" href="#21" title="Permanent link">¶</a></h1>
|
||||||
<p>在算法设计中，我们先后追求以下两个层面的目标。</p>
|
<p>在算法设计中，我们先后追求以下两个层面的目标。</p>
|
||||||
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|||||||
<p>复杂度是个数学概念，对于初学者可能比较抽象，学习难度相对较高。从这个角度看，复杂度分析可能不太适合作为最先介绍的内容。然而，当我们讨论某个数据结构或算法的特点时，难以避免要分析其运行速度和空间使用情况。</p>
|
<p>复杂度是个数学概念，对于初学者可能比较抽象，学习难度相对较高。从这个角度看，复杂度分析可能不太适合作为最先介绍的内容。然而，当我们讨论某个数据结构或算法的特点时，难以避免要分析其运行速度和空间使用情况。</p>
|
||||||
<p>综上所述，建议你在深入学习数据结构与算法之前，<strong>先对复杂度分析建立初步的了解，以便能够完成简单算法的复杂度分析</strong>。</p>
|
<p>综上所述，建议你在深入学习数据结构与算法之前，<strong>先对复杂度分析建立初步的了解，以便能够完成简单算法的复杂度分析</strong>。</p>
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<h1 id="24">2.4 空间复杂度<a class="headerlink" href="#24" title="Permanent link">¶</a></h1>
|
<h1 id="24">2.4 空间复杂度<a class="headerlink" href="#24" title="Permanent link">¶</a></h1>
|
||||||
<p>「空间复杂度 space complexity」用于衡量算法占用内存空间随着数据量变大时的增长趋势。这个概念与时间复杂度非常类似，只需将“运行时间”替换为“占用内存空间”。</p>
|
<p>「空间复杂度 space complexity」用于衡量算法占用内存空间随着数据量变大时的增长趋势。这个概念与时间复杂度非常类似，只需将“运行时间”替换为“占用内存空间”。</p>
|
||||||
<h2 id="241">2.4.1 算法相关空间<a class="headerlink" href="#241" title="Permanent link">¶</a></h2>
|
<h2 id="241">2.4.1 算法相关空间<a class="headerlink" href="#241" title="Permanent link">¶</a></h2>
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||||||
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|
|||||||
<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span> <span class="nc">Node</span><span class="p">:</span>
|
<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span> <span class="nc">Node</span><span class="p">:</span>
|
||||||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w"> </span><span class="sd">"""类"""</span>
|
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w"> </span><span class="sd">"""类"""</span>
|
||||||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||||||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">x</span> <span class="c1"># 节点值</span>
|
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">x</span> <span class="c1"># 节点值</span>
|
||||||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="bp">self</span><span class="o">.</span><span class="n">next</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">Node</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 指向下一节点的引用</span>
|
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="bp">self</span><span class="o">.</span><span class="n">next</span><span class="p">:</span> <span class="n">Node</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 指向下一节点的引用</span>
|
||||||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>
|
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||||||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="k">def</span> <span class="nf">function</span><span class="p">()</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="k">def</span> <span class="nf">function</span><span class="p">()</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||||||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="w"> </span><span class="sd">"""函数"""</span>
|
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="w"> </span><span class="sd">"""函数"""</span>
|
||||||
@@ -5366,11 +5398,73 @@ O(1) < O(\log n) < O(n) < O(n^2) < O(2^n) \newline
|
|||||||
<p><strong>降低时间复杂度通常需要以提升空间复杂度为代价，反之亦然</strong>。我们将牺牲内存空间来提升算法运行速度的思路称为“以空间换时间”；反之，则称为“以时间换空间”。</p>
|
<p><strong>降低时间复杂度通常需要以提升空间复杂度为代价，反之亦然</strong>。我们将牺牲内存空间来提升算法运行速度的思路称为“以空间换时间”；反之，则称为“以时间换空间”。</p>
|
||||||
<p>选择哪种思路取决于我们更看重哪个方面。在大多数情况下，时间比空间更宝贵，因此“以空间换时间”通常是更常用的策略。当然，在数据量很大的情况下，控制空间复杂度也是非常重要的。</p>
|
<p>选择哪种思路取决于我们更看重哪个方面。在大多数情况下，时间比空间更宝贵，因此“以空间换时间”通常是更常用的策略。当然，在数据量很大的情况下，控制空间复杂度也是非常重要的。</p>
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<h1 id="25">2.5 小结<a class="headerlink" href="#25" title="Permanent link">¶</a></h1>
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<h1 id="25">2.5 小结<a class="headerlink" href="#25" title="Permanent link">¶</a></h1>
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<p>在实际中，因为我们通常不知道每个方法的“常数项”复杂度是多少，所以一般无法仅凭复杂度来选择 <span class="arithmatex">\(n = 8\)</span> 之下的最优解法。但对于 <span class="arithmatex">\(n = 8^5\)</span> 就很好选了，这时增长趋势已经占主导了。</p>
|
<p>在实际中，因为我们通常不知道每个方法的“常数项”复杂度是多少，所以一般无法仅凭复杂度来选择 <span class="arithmatex">\(n = 8\)</span> 之下的最优解法。但对于 <span class="arithmatex">\(n = 8^5\)</span> 就很好选了，这时增长趋势已经占主导了。</p>
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<h1 id="23">2.3 时间复杂度<a class="headerlink" href="#23" title="Permanent link">¶</a></h1>
|
<h1 id="23">2.3 时间复杂度<a class="headerlink" href="#23" title="Permanent link">¶</a></h1>
|
||||||
<p>运行时间可以直观且准确地反映算法的效率。如果我们想要准确预估一段代码的运行时间，应该如何操作呢？</p>
|
<p>运行时间可以直观且准确地反映算法的效率。如果我们想要准确预估一段代码的运行时间，应该如何操作呢？</p>
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|
|||||||
<p>可能由于 <span class="arithmatex">\(O\)</span> 符号过于朗朗上口，我们常常使用它来表示平均时间复杂度。但从严格意义上看，这种做法并不规范。在本书和其他资料中，若遇到类似“平均时间复杂度 <span class="arithmatex">\(O(n)\)</span>”的表述，请将其直接理解为 <span class="arithmatex">\(\Theta(n)\)</span> 。</p>
|
<p>可能由于 <span class="arithmatex">\(O\)</span> 符号过于朗朗上口，我们常常使用它来表示平均时间复杂度。但从严格意义上看，这种做法并不规范。在本书和其他资料中，若遇到类似“平均时间复杂度 <span class="arithmatex">\(O(n)\)</span>”的表述，请将其直接理解为 <span class="arithmatex">\(\Theta(n)\)</span> 。</p>
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<h1 id="32">3.2 基本数据类型<a class="headerlink" href="#32" title="Permanent link">¶</a></h1>
|
<h1 id="32">3.2 基本数据类型<a class="headerlink" href="#32" title="Permanent link">¶</a></h1>
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||||||
<p>谈及计算机中的数据，我们会想到文本、图片、视频、语音、3D 模型等各种形式。尽管这些数据的组织形式各异，但它们都由各种基本数据类型构成。</p>
|
<p>谈及计算机中的数据，我们会想到文本、图片、视频、语音、3D 模型等各种形式。尽管这些数据的组织形式各异，但它们都由各种基本数据类型构成。</p>
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||||||
<p><strong>基本数据类型是 CPU 可以直接进行运算的类型</strong>，在算法中直接被使用，主要包括以下几种类型。</p>
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<p><strong>基本数据类型是 CPU 可以直接进行运算的类型</strong>，在算法中直接被使用，主要包括以下几种类型。</p>
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<h1 id="34">3.4 字符编码 *<a class="headerlink" href="#34" title="Permanent link">¶</a></h1>
|
<h1 id="34">3.4 字符编码 *<a class="headerlink" href="#34" title="Permanent link">¶</a></h1>
|
||||||
<p>在计算机中，所有数据都是以二进制数的形式存储的，字符 <code>char</code> 也不例外。为了表示字符，我们需要建立一套“字符集”，规定每个字符和二进制数之间的一一对应关系。有了字符集之后，计算机就可以通过查表完成二进制数到字符的转换。</p>
|
<p>在计算机中，所有数据都是以二进制数的形式存储的，字符 <code>char</code> 也不例外。为了表示字符，我们需要建立一套“字符集”，规定每个字符和二进制数之间的一一对应关系。有了字符集之后，计算机就可以通过查表完成二进制数到字符的转换。</p>
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||||||
<h2 id="341-ascii">3.4.1 ASCII 字符集<a class="headerlink" href="#341-ascii" title="Permanent link">¶</a></h2>
|
<h2 id="341-ascii">3.4.1 ASCII 字符集<a class="headerlink" href="#341-ascii" title="Permanent link">¶</a></h2>
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||||||
<p>需要注意的是，以上讨论的都是字符串在编程语言中的存储方式，<strong>这和字符串如何在文件中存储或在网络中传输是两个不同的问题</strong>。在文件存储或网络传输中，我们通常会将字符串编码为 UTF-8 格式，以达到最优的兼容性和空间效率。</p>
|
<p>需要注意的是，以上讨论的都是字符串在编程语言中的存储方式，<strong>这和字符串如何在文件中存储或在网络中传输是两个不同的问题</strong>。在文件存储或网络传输中，我们通常会将字符串编码为 UTF-8 格式，以达到最优的兼容性和空间效率。</p>
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<h1 id="31">3.1 数据结构分类<a class="headerlink" href="#31" title="Permanent link">¶</a></h1>
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<h1 id="31">3.1 数据结构分类<a class="headerlink" href="#31" title="Permanent link">¶</a></h1>
|
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<p>常见的数据结构包括数组、链表、栈、队列、哈希表、树、堆、图，它们可以从“逻辑结构”和“物理结构”两个维度进行分类。</p>
|
<p>常见的数据结构包括数组、链表、栈、队列、哈希表、树、堆、图，它们可以从“逻辑结构”和“物理结构”两个维度进行分类。</p>
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<p>如果你感觉物理结构理解起来有困难，建议先阅读下一章“数组与链表”，然后再回顾本节内容。</p>
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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|
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|
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|
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<!-- Page content -->
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<h1 id="3">第 3 章 数据结构<a class="headerlink" href="#3" title="Permanent link">¶</a></h1>
|
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|
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<div class="center-table">
|
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|
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<p><img alt="数据结构" src="../assets/covers/chapter_data_structure.jpg" width="600" /></p>
|
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|
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<li><a href="https://www.hello-algo.com/chapter_data_structure/summary/">3.5 小结</a></li>
|
<li><a href="https://www.hello-algo.com/chapter_data_structure/summary/">3.5 小结</a></li>
|
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<h1 id="33">3.3 数字编码 *<a class="headerlink" href="#33" title="Permanent link">¶</a></h1>
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|||||||
<p>值得说明的是，次正规数显著提升了浮点数的精度。最小正正规数为 <span class="arithmatex">\(2^{-126}\)</span> ，最小正次正规数为 <span class="arithmatex">\(2^{-126} \times 2^{-23}\)</span> 。</p>
|
<p>值得说明的是，次正规数显著提升了浮点数的精度。最小正正规数为 <span class="arithmatex">\(2^{-126}\)</span> ，最小正次正规数为 <span class="arithmatex">\(2^{-126} \times 2^{-23}\)</span> 。</p>
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<h1 id="35">3.5 小结<a class="headerlink" href="#35" title="Permanent link">¶</a></h1>
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<h1 id="35">3.5 小结<a class="headerlink" href="#35" title="Permanent link">¶</a></h1>
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<h3 id="1">1. 重点回顾<a class="headerlink" href="#1" title="Permanent link">¶</a></h3>
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<p><code>char</code> 类型的长度由编程语言采用的编码方法决定。例如，Java、JS、TS、C# 都采用 UTF-16 编码（保存 Unicode 码点），因此 char 类型的长度为 2 bytes 。</p>
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<p><code>char</code> 类型的长度由编程语言采用的编码方法决定。例如，Java、JS、TS、C# 都采用 UTF-16 编码（保存 Unicode 码点），因此 char 类型的长度为 2 bytes 。</p>
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|
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<h1 id="122">12.2 分治搜索策略<a class="headerlink" href="#122" title="Permanent link">¶</a></h1>
|
<h1 id="122">12.2 分治搜索策略<a class="headerlink" href="#122" title="Permanent link">¶</a></h1>
|
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<p>我们已经学过，搜索算法分为两大类。</p>
|
<p>我们已经学过，搜索算法分为两大类。</p>
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||||||
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deal in the Software without restriction, including without limitation the
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rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
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furnished to do so, subject to the following conditions:
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|
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The above copyright notice and this permission notice shall be included in
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all copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
||||||
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FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_divide_and_conquer/build_binary_tree_problem.md" title="编辑此页" class="md-content__button md-icon">
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<h1 id="123">12.3 构建二叉树问题<a class="headerlink" href="#123" title="Permanent link">¶</a></h1>
|
<h1 id="123">12.3 构建二叉树问题<a class="headerlink" href="#123" title="Permanent link">¶</a></h1>
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|||||||
<p>设树的节点数量为 <span class="arithmatex">\(n\)</span> ，初始化每一个节点（执行一个递归函数 <code>dfs()</code> ）使用 <span class="arithmatex">\(O(1)\)</span> 时间。<strong>因此总体时间复杂度为 <span class="arithmatex">\(O(n)\)</span></strong> 。</p>
|
<p>设树的节点数量为 <span class="arithmatex">\(n\)</span> ，初始化每一个节点（执行一个递归函数 <code>dfs()</code> ）使用 <span class="arithmatex">\(O(1)\)</span> 时间。<strong>因此总体时间复杂度为 <span class="arithmatex">\(O(n)\)</span></strong> 。</p>
|
||||||
<p>哈希表存储 <code>inorder</code> 元素到索引的映射，空间复杂度为 <span class="arithmatex">\(O(n)\)</span> 。最差情况下，即二叉树退化为链表时，递归深度达到 <span class="arithmatex">\(n\)</span> ，使用 <span class="arithmatex">\(O(n)\)</span> 的栈帧空间。<strong>因此总体空间复杂度为 <span class="arithmatex">\(O(n)\)</span></strong> 。</p>
|
<p>哈希表存储 <code>inorder</code> 元素到索引的映射，空间复杂度为 <span class="arithmatex">\(O(n)\)</span> 。最差情况下，即二叉树退化为链表时，递归深度达到 <span class="arithmatex">\(n\)</span> ，使用 <span class="arithmatex">\(O(n)\)</span> 的栈帧空间。<strong>因此总体空间复杂度为 <span class="arithmatex">\(O(n)\)</span></strong> 。</p>
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|
deal in the Software without restriction, including without limitation the
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|
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|
furnished to do so, subject to the following conditions:
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|
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_divide_and_conquer/divide_and_conquer.md" title="编辑此页" class="md-content__button md-icon">
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|||||||
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|
||||||
<h1 id="121">12.1 分治算法<a class="headerlink" href="#121" title="Permanent link">¶</a></h1>
|
<h1 id="121">12.1 分治算法<a class="headerlink" href="#121" title="Permanent link">¶</a></h1>
|
||||||
<p>「分治 divide and conquer」，全称分而治之，是一种非常重要且常见的算法策略。分治通常基于递归实现，包括“分”和“治”两个步骤。</p>
|
<p>「分治 divide and conquer」，全称分而治之，是一种非常重要且常见的算法策略。分治通常基于递归实现，包括“分”和“治”两个步骤。</p>
|
||||||
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||||||
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|
|||||||
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|
||||||
<p>可以看出，<strong>分治是一种“润物细无声”的算法思想</strong>，隐含在各种算法与数据结构之中。</p>
|
<p>可以看出，<strong>分治是一种“润物细无声”的算法思想</strong>，隐含在各种算法与数据结构之中。</p>
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<h1 id="124">12.4 汉诺塔问题<a class="headerlink" href="#124" title="Permanent link">¶</a></h1>
|
<h1 id="124">12.4 汉诺塔问题<a class="headerlink" href="#124" title="Permanent link">¶</a></h1>
|
||||||
<p>在归并排序和构建二叉树中，我们都是将原问题分解为两个规模为原问题一半的子问题。然而对于汉诺塔问题，我们采用不同的分解策略。</p>
|
<p>在归并排序和构建二叉树中，我们都是将原问题分解为两个规模为原问题一半的子问题。然而对于汉诺塔问题，我们采用不同的分解策略。</p>
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<p>然而，即使僧侣们每秒钟移动一次，总共需要大约 <span class="arithmatex">\(2^{64} \approx 1.84×10^{19}\)</span> 秒，合约 <span class="arithmatex">\(5850\)</span> 亿年，远远超过了现在对宇宙年龄的估计。所以，倘若这个传说是真的，我们应该不需要担心世界末日的到来。</p>
|
<p>然而，即使僧侣们每秒钟移动一次，总共需要大约 <span class="arithmatex">\(2^{64} \approx 1.84×10^{19}\)</span> 秒，合约 <span class="arithmatex">\(5850\)</span> 亿年，远远超过了现在对宇宙年龄的估计。所以，倘若这个传说是真的，我们应该不需要担心世界末日的到来。</p>
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<h1 id="12">第 12 章 分治<a class="headerlink" href="#12" title="Permanent link">¶</a></h1>
|
<h1 id="12">第 12 章 分治<a class="headerlink" href="#12" title="Permanent link">¶</a></h1>
|
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<div class="center-table">
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<p><img alt="分治" src="../assets/covers/chapter_divide_and_conquer.jpg" width="600" /></p>
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|||||||
<li><a href="https://www.hello-algo.com/chapter_divide_and_conquer/summary/">12.5 小结</a></li>
|
<li><a href="https://www.hello-algo.com/chapter_divide_and_conquer/summary/">12.5 小结</a></li>
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<h1 id="125">12.5 小结<a class="headerlink" href="#125" title="Permanent link">¶</a></h1>
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<h1 id="125">12.5 小结<a class="headerlink" href="#125" title="Permanent link">¶</a></h1>
|
||||||
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||||||
<li>分治算法是一种常见的算法设计策略，包括分（划分）和治（合并）两个阶段，通常基于递归实现。</li>
|
<li>分治算法是一种常见的算法设计策略，包括分（划分）和治（合并）两个阶段，通常基于递归实现。</li>
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<li>在汉诺塔问题中，一个规模为 <span class="arithmatex">\(n\)</span> 的问题可以被划分为两个规模为 <span class="arithmatex">\(n-1\)</span> 的子问题和一个规模为 <span class="arithmatex">\(1\)</span> 的子问题。按顺序解决这三个子问题后，原问题随之得到解决。</li>
|
<li>在汉诺塔问题中，一个规模为 <span class="arithmatex">\(n\)</span> 的问题可以被划分为两个规模为 <span class="arithmatex">\(n-1\)</span> 的子问题和一个规模为 <span class="arithmatex">\(1\)</span> 的子问题。按顺序解决这三个子问题后，原问题随之得到解决。</li>
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<h1 id="142">14.2 动态规划问题特性<a class="headerlink" href="#142" title="Permanent link">¶</a></h1>
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<h1 id="142">14.2 动态规划问题特性<a class="headerlink" href="#142" title="Permanent link">¶</a></h1>
|
||||||
<p>在上节中，我们学习了动态规划是如何通过子问题分解来求解问题的。实际上，子问题分解是一种通用的算法思路，在分治、动态规划、回溯中的侧重点不同。</p>
|
<p>在上节中，我们学习了动态规划是如何通过子问题分解来求解问题的。实际上，子问题分解是一种通用的算法思路，在分治、动态规划、回溯中的侧重点不同。</p>
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@@ -4165,11 +4197,73 @@ dp[i, 2] = dp[i-2, 1] + dp[i-2, 2]
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<p>在这个问题中，下次跳跃依赖于过去所有的状态，因为每一次跳跃都会在更高的阶梯上设置障碍，并影响未来的跳跃。对于这类问题，动态规划往往难以解决。</p>
|
<p>在这个问题中，下次跳跃依赖于过去所有的状态，因为每一次跳跃都会在更高的阶梯上设置障碍，并影响未来的跳跃。对于这类问题，动态规划往往难以解决。</p>
|
||||||
<p>实际上，许多复杂的组合优化问题（例如旅行商问题）都不满足无后效性。对于这类问题，我们通常会选择使用其他方法，例如启发式搜索、遗传算法、强化学习等，从而在有限时间内得到可用的局部最优解。</p>
|
<p>实际上，许多复杂的组合优化问题（例如旅行商问题）都不满足无后效性。对于这类问题，我们通常会选择使用其他方法，例如启发式搜索、遗传算法、强化学习等，从而在有限时间内得到可用的局部最优解。</p>
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<h1 id="143">14.3 动态规划解题思路<a class="headerlink" href="#143" title="Permanent link">¶</a></h1>
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<h1 id="143">14.3 动态规划解题思路<a class="headerlink" href="#143" title="Permanent link">¶</a></h1>
|
||||||
<p>上两节介绍了动态规划问题的主要特征，接下来我们一起探究两个更加实用的问题。</p>
|
<p>上两节介绍了动态规划问题的主要特征，接下来我们一起探究两个更加实用的问题。</p>
|
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Permission is hereby granted, free of charge, to any person obtaining a copy
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deal in the Software without restriction, including without limitation the
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The above copyright notice and this permission notice shall be included in
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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<h1 id="146">14.6 编辑距离问题<a class="headerlink" href="#146" title="Permanent link">¶</a></h1>
|
<h1 id="146">14.6 编辑距离问题<a class="headerlink" href="#146" title="Permanent link">¶</a></h1>
|
||||||
<p>编辑距离，也被称为 Levenshtein 距离，指两个字符串之间互相转换的最小修改次数，通常用于在信息检索和自然语言处理中度量两个序列的相似度。</p>
|
<p>编辑距离，也被称为 Levenshtein 距离，指两个字符串之间互相转换的最小修改次数，通常用于在信息检索和自然语言处理中度量两个序列的相似度。</p>
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|
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|
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<!-- Page content -->
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<h1 id="14">第 14 章 动态规划<a class="headerlink" href="#14" title="Permanent link">¶</a></h1>
|
<h1 id="14">第 14 章 动态规划<a class="headerlink" href="#14" title="Permanent link">¶</a></h1>
|
||||||
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<p><img alt="动态规划" src="../assets/covers/chapter_dynamic_programming.jpg" width="600" /></p>
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||||||
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|||||||
<li><a href="https://www.hello-algo.com/chapter_dynamic_programming/summary/">14.7 小结</a></li>
|
<li><a href="https://www.hello-algo.com/chapter_dynamic_programming/summary/">14.7 小结</a></li>
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<h1 id="141">14.1 初探动态规划<a class="headerlink" href="#141" title="Permanent link">¶</a></h1>
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<h1 id="141">14.1 初探动态规划<a class="headerlink" href="#141" title="Permanent link">¶</a></h1>
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||||||
<p>「动态规划 dynamic programming」是一个重要的算法范式，它将一个问题分解为一系列更小的子问题，并通过存储子问题的解来避免重复计算，从而大幅提升时间效率。</p>
|
<p>「动态规划 dynamic programming」是一个重要的算法范式，它将一个问题分解为一系列更小的子问题，并通过存储子问题的解来避免重复计算，从而大幅提升时间效率。</p>
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||||||
<p>在本节中，我们从一个经典例题入手，先给出它的暴力回溯解法，观察其中包含的重叠子问题，再逐步导出更高效的动态规划解法。</p>
|
<p>在本节中，我们从一个经典例题入手，先给出它的暴力回溯解法，观察其中包含的重叠子问题，再逐步导出更高效的动态规划解法。</p>
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<p>观察以上代码，由于省去了数组 <code>dp</code> 占用的空间，因此空间复杂度从 <span class="arithmatex">\(O(n)\)</span> 降低至 <span class="arithmatex">\(O(1)\)</span> 。</p>
|
<p>观察以上代码，由于省去了数组 <code>dp</code> 占用的空间，因此空间复杂度从 <span class="arithmatex">\(O(n)\)</span> 降低至 <span class="arithmatex">\(O(1)\)</span> 。</p>
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<p>在动态规划问题中，当前状态往往仅与前面有限个状态有关，这时我们可以只保留必要的状态，通过“降维”来节省内存空间。<strong>这种空间优化技巧被称为“滚动变量”或“滚动数组”</strong>。</p>
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<p>在动态规划问题中，当前状态往往仅与前面有限个状态有关，这时我们可以只保留必要的状态，通过“降维”来节省内存空间。<strong>这种空间优化技巧被称为“滚动变量”或“滚动数组”</strong>。</p>
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<h1 id="144-0-1">14.4 0-1 背包问题<a class="headerlink" href="#144-0-1" title="Permanent link">¶</a></h1>
|
<h1 id="144-0-1">14.4 0-1 背包问题<a class="headerlink" href="#144-0-1" title="Permanent link">¶</a></h1>
|
||||||
<p>背包问题是一个非常好的动态规划入门题目，是动态规划中最常见的问题形式。其具有很多变种，例如 0-1 背包问题、完全背包问题、多重背包问题等。</p>
|
<p>背包问题是一个非常好的动态规划入门题目，是动态规划中最常见的问题形式。其具有很多变种，例如 0-1 背包问题、完全背包问题、多重背包问题等。</p>
|
||||||
<p>在本节中，我们先来求解最常见的 0-1 背包问题。</p>
|
<p>在本节中，我们先来求解最常见的 0-1 背包问题。</p>
|
||||||
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<h1 id="147">14.7 小结<a class="headerlink" href="#147" title="Permanent link">¶</a></h1>
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<h1 id="147">14.7 小结<a class="headerlink" href="#147" title="Permanent link">¶</a></h1>
|
||||||
<ul>
|
<ul>
|
||||||
<li>动态规划对问题进行分解，并通过存储子问题的解来规避重复计算，实现高效的计算效率。</li>
|
<li>动态规划对问题进行分解，并通过存储子问题的解来规避重复计算，实现高效的计算效率。</li>
|
||||||
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|||||||
<li>在编辑距离中，状态依赖于其正上方、正左方、左上方的状态，因此空间优化后正序或倒序遍历都无法正确地进行状态转移。为此，我们利用一个变量暂存左上方状态，从而转化到与完全背包等价的情况，可以在空间优化后进行正序遍历。</li>
|
<li>在编辑距离中，状态依赖于其正上方、正左方、左上方的状态，因此空间优化后正序或倒序遍历都无法正确地进行状态转移。为此，我们利用一个变量暂存左上方状态，从而转化到与完全背包等价的情况，可以在空间优化后进行正序遍历。</li>
|
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<h1 id="145">14.5 完全背包问题<a class="headerlink" href="#145" title="Permanent link">¶</a></h1>
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<h1 id="145">14.5 完全背包问题<a class="headerlink" href="#145" title="Permanent link">¶</a></h1>
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<p>在本节中，我们先求解另一个常见的背包问题：完全背包，再了解它的一种特例：零钱兑换。</p>
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<p>在本节中，我们先求解另一个常见的背包问题：完全背包，再了解它的一种特例：零钱兑换。</p>
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<h2 id="1451">14.5.1 完全背包<a class="headerlink" href="#1451" title="Permanent link">¶</a></h2>
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<h2 id="1451">14.5.1 完全背包<a class="headerlink" href="#1451" title="Permanent link">¶</a></h2>
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<h1 id="91">9.1 图<a class="headerlink" href="#91" title="Permanent link">¶</a></h1>
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<h1 id="91">9.1 图<a class="headerlink" href="#91" title="Permanent link">¶</a></h1>
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||||||
<p>「图 graph」是一种非线性数据结构，由「顶点 vertex」和「边 edge」组成。我们可以将图 <span class="arithmatex">\(G\)</span> 抽象地表示为一组顶点 <span class="arithmatex">\(V\)</span> 和一组边 <span class="arithmatex">\(E\)</span> 的集合。以下示例展示了一个包含 5 个顶点和 7 条边的图。</p>
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<p>「图 graph」是一种非线性数据结构，由「顶点 vertex」和「边 edge」组成。我们可以将图 <span class="arithmatex">\(G\)</span> 抽象地表示为一组顶点 <span class="arithmatex">\(V\)</span> 和一组边 <span class="arithmatex">\(E\)</span> 的集合。以下示例展示了一个包含 5 个顶点和 7 条边的图。</p>
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_graph/graph_operations.md" title="编辑此页" class="md-content__button md-icon">
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<h1 id="92">9.2 图基础操作<a class="headerlink" href="#92" title="Permanent link">¶</a></h1>
|
<h1 id="92">9.2 图基础操作<a class="headerlink" href="#92" title="Permanent link">¶</a></h1>
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||||||
<p>图的基础操作可分为对“边”的操作和对“顶点”的操作。在“邻接矩阵”和“邻接表”两种表示方法下，实现方式有所不同。</p>
|
<p>图的基础操作可分为对“边”的操作和对“顶点”的操作。在“邻接矩阵”和“邻接表”两种表示方法下，实现方式有所不同。</p>
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<h2 id="921">9.2.1 基于邻接矩阵的实现<a class="headerlink" href="#921" title="Permanent link">¶</a></h2>
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<h2 id="921">9.2.1 基于邻接矩阵的实现<a class="headerlink" href="#921" title="Permanent link">¶</a></h2>
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<p>观察表 9-2 ，似乎邻接表（哈希表）的时间与空间效率最优。但实际上，在邻接矩阵中操作边的效率更高，只需要一次数组访问或赋值操作即可。综合来看，邻接矩阵体现了“以空间换时间”的原则，而邻接表体现了“以时间换空间”的原则。</p>
|
<p>观察表 9-2 ，似乎邻接表（哈希表）的时间与空间效率最优。但实际上，在邻接矩阵中操作边的效率更高，只需要一次数组访问或赋值操作即可。综合来看，邻接矩阵体现了“以空间换时间”的原则，而邻接表体现了“以时间换空间”的原则。</p>
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_graph/graph_traversal.md" title="编辑此页" class="md-content__button md-icon">
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<h1 id="93">9.3 图的遍历<a class="headerlink" href="#93" title="Permanent link">¶</a></h1>
|
<h1 id="93">9.3 图的遍历<a class="headerlink" href="#93" title="Permanent link">¶</a></h1>
|
||||||
<p>树代表的是“一对多”的关系，而图则具有更高的自由度，可以表示任意的“多对多”关系。因此，我们可以把树看作是图的一种特例。显然，<strong>树的遍历操作也是图的遍历操作的一种特例</strong>。</p>
|
<p>树代表的是“一对多”的关系，而图则具有更高的自由度，可以表示任意的“多对多”关系。因此，我们可以把树看作是图的一种特例。显然，<strong>树的遍历操作也是图的遍历操作的一种特例</strong>。</p>
|
||||||
<p>图和树都都需要应用搜索算法来实现遍历操作。图的遍历方式可分为两种：「广度优先遍历 breadth-first traversal」和「深度优先遍历 depth-first traversal」。它们也常被称为「广度优先搜索 breadth-first search」和「深度优先搜索 depth-first search」，简称 BFS 和 DFS 。</p>
|
<p>图和树都都需要应用搜索算法来实现遍历操作。图的遍历方式可分为两种：「广度优先遍历 breadth-first traversal」和「深度优先遍历 depth-first traversal」。它们也常被称为「广度优先搜索 breadth-first search」和「深度优先搜索 depth-first search」，简称 BFS 和 DFS 。</p>
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||||||
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|||||||
<p><strong>时间复杂度：</strong> 所有顶点都会被访问 <span class="arithmatex">\(1\)</span> 次，使用 <span class="arithmatex">\(O(|V|)\)</span> 时间；所有边都会被访问 <span class="arithmatex">\(2\)</span> 次，使用 <span class="arithmatex">\(O(2|E|)\)</span> 时间；总体使用 <span class="arithmatex">\(O(|V| + |E|)\)</span> 时间。</p>
|
<p><strong>时间复杂度：</strong> 所有顶点都会被访问 <span class="arithmatex">\(1\)</span> 次，使用 <span class="arithmatex">\(O(|V|)\)</span> 时间；所有边都会被访问 <span class="arithmatex">\(2\)</span> 次，使用 <span class="arithmatex">\(O(2|E|)\)</span> 时间；总体使用 <span class="arithmatex">\(O(|V| + |E|)\)</span> 时间。</p>
|
||||||
<p><strong>空间复杂度：</strong> 列表 <code>res</code> ，哈希表 <code>visited</code> 顶点数量最多为 <span class="arithmatex">\(|V|\)</span> ，递归深度最大为 <span class="arithmatex">\(|V|\)</span> ，因此使用 <span class="arithmatex">\(O(|V|)\)</span> 空间。</p>
|
<p><strong>空间复杂度：</strong> 列表 <code>res</code> ，哈希表 <code>visited</code> 顶点数量最多为 <span class="arithmatex">\(|V|\)</span> ，递归深度最大为 <span class="arithmatex">\(|V|\)</span> ，因此使用 <span class="arithmatex">\(O(|V|)\)</span> 空间。</p>
|
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9.2 图基础操作
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FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in
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all copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
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FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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||||||
<h1 id="9">第 9 章 图<a class="headerlink" href="#9" title="Permanent link">¶</a></h1>
|
<h1 id="9">第 9 章 图<a class="headerlink" href="#9" title="Permanent link">¶</a></h1>
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||||||
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||||||
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<li><a href="https://www.hello-algo.com/chapter_graph/summary/">9.4 小结</a></li>
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|
||||||
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<h5 align="center" id="__comments">欢迎你提出疑问或建议</h5>
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<!-- Insert generated snippet here -->
|
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|
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<script
|
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||||||
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Copyright (c) 2016-2023 Martin Donath <martin.donath@squidfunk.com>
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|
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|
Permission is hereby granted, free of charge, to any person obtaining a copy
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<nav class="md-footer__inner md-grid" aria-label="页脚" >
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of this software and associated documentation files (the "Software"), to
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deal in the Software without restriction, including without limitation the
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|
rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
|
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<a href="../chapter_heap/summary/" class="md-footer__link md-footer__link--prev" aria-label="上一页: 8.4 &nbsp; 小结" rel="prev">
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sell copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
|
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The above copyright notice and this permission notice shall be included in
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all copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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</span>
|
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
|
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<div class="md-ellipsis">
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
||||||
8.4 小结
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
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</div>
|
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
|
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</div>
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IN THE SOFTWARE.
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|
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Permission is hereby granted, free of charge, to any person obtaining a copy
|
||||||
|
of this software and associated documentation files (the "Software"), to
|
||||||
|
deal in the Software without restriction, including without limitation the
|
||||||
|
rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
|
||||||
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sell copies of the Software, and to permit persons to whom the Software is
|
||||||
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furnished to do so, subject to the following conditions:
|
||||||
|
|
||||||
|
The above copyright notice and this permission notice shall be included in
|
||||||
|
all copies or substantial portions of the Software.
|
||||||
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|
||||||
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
||||||
|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
||||||
|
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
|
||||||
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
||||||
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||||
|
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
|
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|
IN THE SOFTWARE.
|
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|
-->
|
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|
|
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|
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|
||||||
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|
||||||
|
|
||||||
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|
||||||
<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_graph/summary.md" title="编辑此页" class="md-content__button md-icon">
|
<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_graph/summary.md" title="编辑此页" class="md-content__button md-icon">
|
||||||
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|
|||||||
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|
||||||
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|
||||||
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|
||||||
|
<!--
|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
|
||||||
|
|
||||||
|
<!-- Page content -->
|
||||||
<h1 id="94">9.4 小结<a class="headerlink" href="#94" title="Permanent link">¶</a></h1>
|
<h1 id="94">9.4 小结<a class="headerlink" href="#94" title="Permanent link">¶</a></h1>
|
||||||
<h3 id="1">1. 重点回顾<a class="headerlink" href="#1" title="Permanent link">¶</a></h3>
|
<h3 id="1">1. 重点回顾<a class="headerlink" href="#1" title="Permanent link">¶</a></h3>
|
||||||
<ul>
|
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|
||||||
@@ -3471,11 +3503,73 @@
|
|||||||
<p>可以是任意顺序。但在实际应用中，可能会需要按照指定规则来排序，比如按照顶点添加的次序、或者按照顶点值大小的顺序等等，这样可以有助于快速查找“带有某种极值”的顶点。</p>
|
<p>可以是任意顺序。但在实际应用中，可能会需要按照指定规则来排序，比如按照顶点添加的次序、或者按照顶点值大小的顺序等等，这样可以有助于快速查找“带有某种极值”的顶点。</p>
|
||||||
</div>
|
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|
||||||
|
|
||||||
|
<!-- Source file information -->
|
||||||
|
|
||||||
|
|
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|
<!-- Was this page helpful? -->
|
||||||
|
|
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|
|
||||||
|
|
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|
|
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<h2 id="__comments">评论</h2>
|
<!-- Previous and next pages link -->
|
||||||
|
<nav
|
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<h1 id="152">15.2 分数背包问题<a class="headerlink" href="#152" title="Permanent link">¶</a></h1>
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<h1 id="151">15.1 贪心算法<a class="headerlink" href="#151" title="Permanent link">¶</a></h1>
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<h1 id="151">15.1 贪心算法<a class="headerlink" href="#151" title="Permanent link">¶</a></h1>
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||||||
<p>「贪心算法 greedy algorithm」是一种常见的解决优化问题的算法，其基本思想是在问题的每个决策阶段，都选择当前看起来最优的选择，即贪心地做出局部最优的决策，以期望获得全局最优解。贪心算法简洁且高效，在许多实际问题中都有着广泛的应用。</p>
|
<p>「贪心算法 greedy algorithm」是一种常见的解决优化问题的算法，其基本思想是在问题的每个决策阶段，都选择当前看起来最优的选择，即贪心地做出局部最优的决策，以期望获得全局最优解。贪心算法简洁且高效，在许多实际问题中都有着广泛的应用。</p>
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<p>贪心算法和动态规划都常用于解决优化问题。它们之间存在一些相似之处，比如都依赖最优子结构性质，但工作原理是不同的。</p>
|
<p>贪心算法和动态规划都常用于解决优化问题。它们之间存在一些相似之处，比如都依赖最优子结构性质，但工作原理是不同的。</p>
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<li><strong>Dijkstra 算法</strong>：它是一种解决给定源顶点到其余各顶点的最短路径问题的贪心算法。</li>
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<li><strong>Dijkstra 算法</strong>：它是一种解决给定源顶点到其余各顶点的最短路径问题的贪心算法。</li>
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<h1 id="15">第 15 章 贪心<a class="headerlink" href="#15" title="Permanent link">¶</a></h1>
|
<h1 id="15">第 15 章 贪心<a class="headerlink" href="#15" title="Permanent link">¶</a></h1>
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<p><img alt="贪心" src="../assets/covers/chapter_greedy.jpg" width="600" /></p>
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<li><a href="https://www.hello-algo.com/chapter_greedy/summary/">15.5 小结</a></li>
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<h1 id="153">15.3 最大容量问题<a class="headerlink" href="#153" title="Permanent link">¶</a></h1>
|
<h1 id="153">15.3 最大容量问题<a class="headerlink" href="#153" title="Permanent link">¶</a></h1>
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||||||
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<p>观察发现，<strong>这些被跳过的状态实际上就是将长板 <span class="arithmatex">\(j\)</span> 向内移动的所有状态</strong>。而在第二步中，我们已经证明内移长板一定会导致容量变小。也就是说，被跳过的状态都不可能是最优解，<strong>跳过它们不会导致错过最优解</strong>。</p>
|
<p>观察发现，<strong>这些被跳过的状态实际上就是将长板 <span class="arithmatex">\(j\)</span> 向内移动的所有状态</strong>。而在第二步中，我们已经证明内移长板一定会导致容量变小。也就是说，被跳过的状态都不可能是最优解，<strong>跳过它们不会导致错过最优解</strong>。</p>
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||||||
<p>以上的分析说明，<strong>移动短板的操作是“安全”的</strong>，贪心策略是有效的。</p>
|
<p>以上的分析说明，<strong>移动短板的操作是“安全”的</strong>，贪心策略是有效的。</p>
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|
|||||||
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||||||
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|
||||||
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||||||
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||||||
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|
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|
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<h1 id="154">15.4 最大切分乘积问题<a class="headerlink" href="#154" title="Permanent link">¶</a></h1>
|
<h1 id="154">15.4 最大切分乘积问题<a class="headerlink" href="#154" title="Permanent link">¶</a></h1>
|
||||||
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|
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|
||||||
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|
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|
||||||
@@ -3767,11 +3799,73 @@ n = 3 a + b
|
|||||||
<li><strong>切分方案最多包含两个 <span class="arithmatex">\(2\)</span></strong> ：假设最优切分方案中包含三个 <span class="arithmatex">\(2\)</span> ，那么一定可以替换为两个 <span class="arithmatex">\(3\)</span> ，乘积更大。这与假设矛盾。</li>
|
<li><strong>切分方案最多包含两个 <span class="arithmatex">\(2\)</span></strong> ：假设最优切分方案中包含三个 <span class="arithmatex">\(2\)</span> ，那么一定可以替换为两个 <span class="arithmatex">\(3\)</span> ，乘积更大。这与假设矛盾。</li>
|
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<h1 id="155">15.5 小结<a class="headerlink" href="#155" title="Permanent link">¶</a></h1>
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<h1 id="155">15.5 小结<a class="headerlink" href="#155" title="Permanent link">¶</a></h1>
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<li>贪心算法通常用于解决最优化问题，其原理是在每个决策阶段都做出局部最优的决策，以期望获得全局最优解。</li>
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<li>贪心算法通常用于解决最优化问题，其原理是在每个决策阶段都做出局部最优的决策，以期望获得全局最优解。</li>
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<li>在最大切分乘积问题中，我们先后推理出两个贪心策略：<span class="arithmatex">\(\geq 4\)</span> 的整数都应该继续切分、最优切分因子为 <span class="arithmatex">\(3\)</span> 。代码中包含幂运算，时间复杂度取决于幂运算实现方法，通常为 <span class="arithmatex">\(O(1)\)</span> 或 <span class="arithmatex">\(O(\log n)\)</span> 。</li>
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<li>在最大切分乘积问题中，我们先后推理出两个贪心策略：<span class="arithmatex">\(\geq 4\)</span> 的整数都应该继续切分、最优切分因子为 <span class="arithmatex">\(3\)</span> 。代码中包含幂运算，时间复杂度取决于幂运算实现方法，通常为 <span class="arithmatex">\(O(1)\)</span> 或 <span class="arithmatex">\(O(\log n)\)</span> 。</li>
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<h1 id="63">6.3 哈希算法<a class="headerlink" href="#63" title="Permanent link">¶</a></h1>
|
<h1 id="63">6.3 哈希算法<a class="headerlink" href="#63" title="Permanent link">¶</a></h1>
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||||||
<p>在上两节中，我们了解了哈希表的工作原理和哈希冲突的处理方法。然而无论是开放寻址还是链地址法，<strong>它们只能保证哈希表可以在发生冲突时正常工作，但无法减少哈希冲突的发生</strong>。</p>
|
<p>在上两节中，我们了解了哈希表的工作原理和哈希冲突的处理方法。然而无论是开放寻址还是链地址法，<strong>它们只能保证哈希表可以在发生冲突时正常工作，但无法减少哈希冲突的发生</strong>。</p>
|
||||||
<p>如果哈希冲突过于频繁，哈希表的性能则会急剧劣化。如图 6-7 所示，对于链地址哈希表，理想情况下键值对平均分布在各个桶中，达到最佳查询效率；最差情况下所有键值对都被存储到同一个桶中，时间复杂度退化至 <span class="arithmatex">\(O(n)\)</span> 。</p>
|
<p>如果哈希冲突过于频繁，哈希表的性能则会急剧劣化。如图 6-8 所示，对于链地址哈希表，理想情况下键值对平均分布在各个桶中，达到最佳查询效率；最差情况下所有键值对都被存储到同一个桶中，时间复杂度退化至 <span class="arithmatex">\(O(n)\)</span> 。</p>
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||||||
<p><img alt="哈希冲突的最佳与最差情况" src="../hash_algorithm.assets/hash_collision_best_worst_condition.png" /></p>
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||||||
<p align="center"> 图 6-7 哈希冲突的最佳与最差情况 </p>
|
<p align="center"> 图 6-8 哈希冲突的最佳与最差情况 </p>
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||||||
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||||||
<p><strong>键值对的分布情况由哈希函数决定</strong>。回忆哈希函数的计算步骤，先计算哈希值，再对数组长度取模：</p>
|
<p><strong>键值对的分布情况由哈希函数决定</strong>。回忆哈希函数的计算步骤，先计算哈希值，再对数组长度取模：</p>
|
||||||
<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nv">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span>hash<span class="o">(</span>key<span class="o">)</span><span class="w"> </span>%<span class="w"> </span>capacity
|
<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nv">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span>hash<span class="o">(</span>key<span class="o">)</span><span class="w"> </span>%<span class="w"> </span>capacity
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||||||
@@ -4276,11 +4308,73 @@
|
|||||||
<p>虽然自定义对象（比如链表节点）的成员变量是可变的，但它是可哈希的。<strong>这是因为对象的哈希值通常是基于内存地址生成的</strong>，即使对象的内容发生了变化，但它的内存地址不变，哈希值仍然是不变的。</p>
|
<p>虽然自定义对象（比如链表节点）的成员变量是可变的，但它是可哈希的。<strong>这是因为对象的哈希值通常是基于内存地址生成的</strong>，即使对象的内容发生了变化，但它的内存地址不变，哈希值仍然是不变的。</p>
|
||||||
<p>细心的你可能发现在不同控制台中运行程序时，输出的哈希值是不同的。<strong>这是因为 Python 解释器在每次启动时，都会为字符串哈希函数加入一个随机的盐（Salt）值</strong>。这种做法可以有效防止 HashDoS 攻击，提升哈希算法的安全性。</p>
|
<p>细心的你可能发现在不同控制台中运行程序时，输出的哈希值是不同的。<strong>这是因为 Python 解释器在每次启动时，都会为字符串哈希函数加入一个随机的盐（Salt）值</strong>。这种做法可以有效防止 HashDoS 攻击，提升哈希算法的安全性。</p>
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<h1 id="62">6.2 哈希冲突<a class="headerlink" href="#62" title="Permanent link">¶</a></h1>
|
<h1 id="62">6.2 哈希冲突<a class="headerlink" href="#62" title="Permanent link">¶</a></h1>
|
||||||
<p>上节提到，<strong>通常情况下哈希函数的输入空间远大于输出空间</strong>，因此理论上哈希冲突是不可避免的。比如，输入空间为全体整数，输出空间为数组容量大小，则必然有多个整数映射至同一数组索引。</p>
|
<p>上节提到，<strong>通常情况下哈希函数的输入空间远大于输出空间</strong>，因此理论上哈希冲突是不可避免的。比如，输入空间为全体整数，输出空间为数组容量大小，则必然有多个整数映射至同一桶索引。</p>
|
||||||
<p>哈希冲突会导致查询结果错误，严重影响哈希表的可用性。为解决该问题，我们可以每当遇到哈希冲突时就进行哈希表扩容，直至冲突消失为止。此方法简单粗暴且有效，但效率太低，因为哈希表扩容需要进行大量的数据搬运与哈希值计算。为了提升效率，我们可以采用以下策略。</p>
|
<p>哈希冲突会导致查询结果错误，严重影响哈希表的可用性。为解决该问题，我们可以每当遇到哈希冲突时就进行哈希表扩容，直至冲突消失为止。此方法简单粗暴且有效，但效率太低，因为哈希表扩容需要进行大量的数据搬运与哈希值计算。为了提升效率，我们可以采用以下策略。</p>
|
||||||
<ol>
|
<ol>
|
||||||
<li>改良哈希表数据结构，<strong>使得哈希表可以在存在哈希冲突时正常工作</strong>。</li>
|
<li>改良哈希表数据结构，<strong>使得哈希表可以在存在哈希冲突时正常工作</strong>。</li>
|
||||||
@@ -3508,9 +3554,9 @@
|
|||||||
<p><img alt="链式地址哈希表" src="../hash_collision.assets/hash_table_chaining.png" /></p>
|
<p><img alt="链式地址哈希表" src="../hash_collision.assets/hash_table_chaining.png" /></p>
|
||||||
<p align="center"> 图 6-5 链式地址哈希表 </p>
|
<p align="center"> 图 6-5 链式地址哈希表 </p>
|
||||||
|
|
||||||
<p>哈希表在链式地址下的操作方法发生了一些变化。</p>
|
<p>基于链式地址实现的哈希表的操作方法发生了以下变化。</p>
|
||||||
<ul>
|
<ul>
|
||||||
<li><strong>查询元素</strong>：输入 <code>key</code> ，经过哈希函数得到数组索引，即可访问链表头节点，然后遍历链表并对比 <code>key</code> 以查找目标键值对。</li>
|
<li><strong>查询元素</strong>：输入 <code>key</code> ，经过哈希函数得到桶索引，即可访问链表头节点，然后遍历链表并对比 <code>key</code> 以查找目标键值对。</li>
|
||||||
<li><strong>添加元素</strong>：先通过哈希函数访问链表头节点，然后将节点（即键值对）添加到链表中。</li>
|
<li><strong>添加元素</strong>：先通过哈希函数访问链表头节点，然后将节点（即键值对）添加到链表中。</li>
|
||||||
<li><strong>删除元素</strong>：根据哈希函数的结果访问链表头部，接着遍历链表以查找目标节点，并将其删除。</li>
|
<li><strong>删除元素</strong>：根据哈希函数的结果访问链表头部，接着遍历链表以查找目标节点，并将其删除。</li>
|
||||||
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|
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||||||
@@ -4800,26 +4846,26 @@
|
|||||||
<p>值得注意的是，当链表很长时，查询效率 <span class="arithmatex">\(O(n)\)</span> 很差。<strong>此时可以将链表转换为“AVL 树”或“红黑树”</strong>，从而将查询操作的时间复杂度优化至 <span class="arithmatex">\(O(\log n)\)</span> 。</p>
|
<p>值得注意的是，当链表很长时，查询效率 <span class="arithmatex">\(O(n)\)</span> 很差。<strong>此时可以将链表转换为“AVL 树”或“红黑树”</strong>，从而将查询操作的时间复杂度优化至 <span class="arithmatex">\(O(\log n)\)</span> 。</p>
|
||||||
<h2 id="622">6.2.2 开放寻址<a class="headerlink" href="#622" title="Permanent link">¶</a></h2>
|
<h2 id="622">6.2.2 开放寻址<a class="headerlink" href="#622" title="Permanent link">¶</a></h2>
|
||||||
<p>「开放寻址 open addressing」不引入额外的数据结构，而是通过“多次探测”来处理哈希冲突，探测方式主要包括线性探测、平方探测、多次哈希等。</p>
|
<p>「开放寻址 open addressing」不引入额外的数据结构，而是通过“多次探测”来处理哈希冲突，探测方式主要包括线性探测、平方探测、多次哈希等。</p>
|
||||||
|
<p>下面将主要以线性探测为例，介绍开放寻址哈希表的工作机制与代码实现。</p>
|
||||||
<h3 id="1">1. 线性探测<a class="headerlink" href="#1" title="Permanent link">¶</a></h3>
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<h3 id="1">1. 线性探测<a class="headerlink" href="#1" title="Permanent link">¶</a></h3>
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<p>线性探测采用固定步长的线性搜索来进行探测，其操作方法与普通哈希表有所不同。</p>
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<p>线性探测采用固定步长的线性搜索来进行探测，其操作方法与普通哈希表有所不同。</p>
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<ul>
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<ul>
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<li><strong>插入元素</strong>：通过哈希函数计算数组索引，若发现桶内已有元素，则从冲突位置向后线性遍历（步长通常为 <span class="arithmatex">\(1\)</span> ），直至找到空位，将元素插入其中。</li>
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<li><strong>插入元素</strong>：通过哈希函数计算桶索引，若发现桶内已有元素，则从冲突位置向后线性遍历（步长通常为 <span class="arithmatex">\(1\)</span> ），直至找到空桶，将元素插入其中。</li>
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<li><strong>查找元素</strong>：若发现哈希冲突，则使用相同步长向后线性遍历，直到找到对应元素，返回 <code>value</code> 即可；如果遇到空位，说明目标键值对不在哈希表中，返回 <span class="arithmatex">\(\text{None}\)</span> 。</li>
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<li><strong>查找元素</strong>：若发现哈希冲突，则使用相同步长向后线性遍历，直到找到对应元素，返回 <code>value</code> 即可；如果遇到空桶，说明目标元素不在哈希表中，返回 <span class="arithmatex">\(\text{None}\)</span> 。</li>
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</ul>
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</ul>
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<p>图 6-6 展示了一个在开放寻址（线性探测）下工作的哈希表。</p>
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<p>图 6-6 展示了开放寻址（线性探测）哈希表的键值对分布。根据此哈希函数，最后两位相同的 <code>key</code> 都会被映射到相同的桶。而通过线性探测，它们被依次存储在该桶以及之下的桶中。</p>
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<p><img alt="开放寻址和线性探测" src="../hash_collision.assets/hash_table_linear_probing.png" /></p>
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<p><img alt="开放寻址和线性探测" src="../hash_collision.assets/hash_table_linear_probing.png" /></p>
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<p align="center"> 图 6-6 开放寻址和线性探测 </p>
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<p align="center"> 图 6-6 开放寻址和线性探测 </p>
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<p>然而，线性探测存在以下缺陷。</p>
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<p>然而，<strong>线性探测容易产生“聚集现象”</strong>。具体来说，数组中连续被占用的位置越长，这些连续位置发生哈希冲突的可能性越大，从而进一步促使该位置的聚堆生长，形成恶性循环，最终导致增删查改操作效率劣化。</p>
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<ul>
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<p>值得注意的是，<strong>我们不能在开放寻址哈希表中直接删除元素</strong>。这是因为删除元素会在数组内产生一个空桶 <span class="arithmatex">\(\text{None}\)</span> ，而当查询元素时，线性探测到该空桶就会返回，因此在该空桶之下的元素都无法再被访问到，程序可能误判这些元素不存在。</p>
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<li><strong>不能直接删除元素</strong>。删除元素会在数组内产生一个空位，当查找该空位之后的元素时，该空位可能导致程序误判元素不存在。为此，通常需要借助一个标志位来标记已删除元素。</li>
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<p><img alt="在开放寻址中删除元素导致的查询问题" src="../hash_collision.assets/hash_table_open_addressing_deletion.png" /></p>
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<li><strong>容易产生聚集</strong>。数组内连续被占用位置越长，这些连续位置发生哈希冲突的可能性越大，进一步促使这一位置的聚堆生长，形成恶性循环，最终导致增删查改操作效率劣化。</li>
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<p align="center"> 图 6-7 在开放寻址中删除元素导致的查询问题 </p>
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</ul>
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<p>以下代码实现了一个简单的开放寻址（线性探测）哈希表。</p>
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<p>为了解决该问题，我们可以采用「懒删除 lazy deletion」机制：它不直接从哈希表中移除元素，<strong>而是利用一个常量 <code>TOMBSTONE</code> 来标记这个桶</strong>。在该机制下，<span class="arithmatex">\(\text{None}\)</span> 和 <code>TOMBSTONE</code> 都代表空桶，都可以放置键值对。但不同的是，线性探测到 <code>TOMBSTONE</code> 时应该继续遍历，因为其之下可能还存在键值对。</p>
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<ul>
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<p>然而，<strong>懒删除可能会加速哈希表的性能退化</strong>。这是因为每次删除操作都会产生一个删除标记，随着 <code>TOMBSTONE</code> 的增加，搜索时间也会增加，因为线性探测可能需要跳过多个 <code>TOMBSTONE</code> 才能找到目标元素。</p>
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<li>我们使用一个固定的键值对实例 <code>removed</code> 来标记已删除元素。也就是说，当一个桶内的元素为 <span class="arithmatex">\(\text{None}\)</span> 或 <code>removed</code> 时，说明这个桶是空的，可用于放置键值对。</li>
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<p>为此，考虑在线性探测中记录遇到的首个 <code>TOMBSTONE</code> 的索引，并将搜索到的目标元素与该 <code>TOMBSTONE</code> 交换位置。这样做的好处是当每次查询或添加元素时，元素会被移动至距离理想位置（探测起始点）更近的桶，从而优化查询效率。</p>
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<li>在线性探测时，我们从当前索引 <code>index</code> 向后遍历；而当越过数组尾部时，需要回到头部继续遍历。</li>
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<p>以下代码实现了一个包含懒删除的开放寻址（线性探测）哈希表。为了更加充分地使用哈希表的空间，我们将哈希表表看作是一个“环形数组”，当越过数组尾部时，回到头部继续遍历。</p>
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<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a> <span class="bp">self</span><span class="o">.</span><span class="n">load_thres</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">/</span> <span class="mi">3</span> <span class="c1"># 触发扩容的负载因子阈值</span>
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<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a> <span class="bp">self</span><span class="o">.</span><span class="n">load_thres</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">/</span> <span class="mi">3</span> <span class="c1"># 触发扩容的负载因子阈值</span>
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<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a> <span class="bp">self</span><span class="o">.</span><span class="n">extend_ratio</span> <span class="o">=</span> <span class="mi">2</span> <span class="c1"># 扩容倍数</span>
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<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a> <span class="bp">self</span><span class="o">.</span><span class="n">extend_ratio</span> <span class="o">=</span> <span class="mi">2</span> <span class="c1"># 扩容倍数</span>
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<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">Pair</span> <span class="o">|</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="kc">None</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span> <span class="c1"># 桶数组</span>
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<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">Pair</span> <span class="o">|</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="kc">None</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span> <span class="c1"># 桶数组</span>
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<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a> <span class="bp">self</span><span class="o">.</span><span class="n">removed</span> <span class="o">=</span> <span class="n">Pair</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="s2">"-1"</span><span class="p">)</span> <span class="c1"># 删除标记</span>
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<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a> <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span> <span class="o">=</span> <span class="n">Pair</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="s2">"-1"</span><span class="p">)</span> <span class="c1"># 删除标记</span>
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<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a> <span class="k">def</span> <span class="nf">hash_func</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
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<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a> <span class="k">def</span> <span class="nf">hash_func</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
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<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w"> </span><span class="sd">"""哈希函数"""</span>
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<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w"> </span><span class="sd">"""哈希函数"""</span>
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@@ -4843,320 +4889,353 @@
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<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w"> </span><span class="sd">"""负载因子"""</span>
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<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w"> </span><span class="sd">"""负载因子"""</span>
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<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span>
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<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span>
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<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a>
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<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a>
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<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a> <span class="k">def</span> <span class="nf">get</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-></span> <span class="nb">str</span><span class="p">:</span>
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<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a> <span class="k">def</span> <span class="nf">find_bucket</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
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<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w"> </span><span class="sd">"""查询操作"""</span>
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<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w"> </span><span class="sd">"""搜索 key 对应的桶索引"""</span>
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<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a> <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
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<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a> <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
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<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a> <span class="c1"># 线性探测，从 index 开始向后遍历</span>
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<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a> <span class="n">first_tombstone</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span>
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<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">):</span>
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<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a> <span class="c1"># 线性探测，当遇到空桶时跳出</span>
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<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a> <span class="c1"># 计算桶索引，越过尾部返回头部</span>
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<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a> <span class="k">while</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
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<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></a> <span class="n">j</span> <span class="o">=</span> <span class="p">(</span><span class="n">index</span> <span class="o">+</span> <span class="n">i</span><span class="p">)</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span>
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<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></a> <span class="c1"># 若遇到 key ，返回对应桶索引</span>
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<a id="__codelineno-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></a> <span class="c1"># 若遇到空桶，说明无此 key ，则返回 None</span>
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<a id="__codelineno-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></a> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="n">key</span><span class="p">:</span>
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<a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></a> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
<a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></a> <span class="c1"># 若之前遇到了删除标记，则将键值对移动至该索引</span>
|
||||||
<a id="__codelineno-12-30" name="__codelineno-12-30" href="#__codelineno-12-30"></a> <span class="k">return</span> <span class="kc">None</span>
|
<a id="__codelineno-12-30" name="__codelineno-12-30" href="#__codelineno-12-30"></a> <span class="k">if</span> <span class="n">first_tombstone</span> <span class="o">!=</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span>
|
||||||
<a id="__codelineno-12-31" name="__codelineno-12-31" href="#__codelineno-12-31"></a> <span class="c1"># 若遇到指定 key ，则返回对应 val</span>
|
<a id="__codelineno-12-31" name="__codelineno-12-31" href="#__codelineno-12-31"></a> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">first_tombstone</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
|
||||||
<a id="__codelineno-12-32" name="__codelineno-12-32" href="#__codelineno-12-32"></a> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="n">key</span> <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">removed</span><span class="p">:</span>
|
<a id="__codelineno-12-32" name="__codelineno-12-32" href="#__codelineno-12-32"></a> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span>
|
||||||
<a id="__codelineno-12-33" name="__codelineno-12-33" href="#__codelineno-12-33"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="o">.</span><span class="n">val</span>
|
<a id="__codelineno-12-33" name="__codelineno-12-33" href="#__codelineno-12-33"></a> <span class="k">return</span> <span class="n">first_tombstone</span> <span class="c1"># 返回移动后的桶索引</span>
|
||||||
<a id="__codelineno-12-34" name="__codelineno-12-34" href="#__codelineno-12-34"></a>
|
<a id="__codelineno-12-34" name="__codelineno-12-34" href="#__codelineno-12-34"></a> <span class="k">return</span> <span class="n">index</span> <span class="c1"># 返回桶索引</span>
|
||||||
<a id="__codelineno-12-35" name="__codelineno-12-35" href="#__codelineno-12-35"></a> <span class="k">def</span> <span class="nf">put</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">str</span><span class="p">):</span>
|
<a id="__codelineno-12-35" name="__codelineno-12-35" href="#__codelineno-12-35"></a> <span class="c1"># 记录遇到的首个删除标记</span>
|
||||||
<a id="__codelineno-12-36" name="__codelineno-12-36" href="#__codelineno-12-36"></a><span class="w"> </span><span class="sd">"""添加操作"""</span>
|
<a id="__codelineno-12-36" name="__codelineno-12-36" href="#__codelineno-12-36"></a> <span class="k">if</span> <span class="n">first_tombstone</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span> <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="ow">is</span> <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span><span class="p">:</span>
|
||||||
<a id="__codelineno-12-37" name="__codelineno-12-37" href="#__codelineno-12-37"></a> <span class="c1"># 当负载因子超过阈值时，执行扩容</span>
|
<a id="__codelineno-12-37" name="__codelineno-12-37" href="#__codelineno-12-37"></a> <span class="n">first_tombstone</span> <span class="o">=</span> <span class="n">index</span>
|
||||||
<a id="__codelineno-12-38" name="__codelineno-12-38" href="#__codelineno-12-38"></a> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">load_factor</span><span class="p">()</span> <span class="o">></span> <span class="bp">self</span><span class="o">.</span><span class="n">load_thres</span><span class="p">:</span>
|
<a id="__codelineno-12-38" name="__codelineno-12-38" href="#__codelineno-12-38"></a> <span class="c1"># 计算桶索引，越过尾部返回头部</span>
|
||||||
<a id="__codelineno-12-39" name="__codelineno-12-39" href="#__codelineno-12-39"></a> <span class="bp">self</span><span class="o">.</span><span class="n">extend</span><span class="p">()</span>
|
<a id="__codelineno-12-39" name="__codelineno-12-39" href="#__codelineno-12-39"></a> <span class="n">index</span> <span class="o">=</span> <span class="p">(</span><span class="n">index</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span>
|
||||||
<a id="__codelineno-12-40" name="__codelineno-12-40" href="#__codelineno-12-40"></a> <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
|
<a id="__codelineno-12-40" name="__codelineno-12-40" href="#__codelineno-12-40"></a> <span class="c1"># 若 key 不存在，则返回添加点的索引</span>
|
||||||
<a id="__codelineno-12-41" name="__codelineno-12-41" href="#__codelineno-12-41"></a> <span class="c1"># 线性探测，从 index 开始向后遍历</span>
|
<a id="__codelineno-12-41" name="__codelineno-12-41" href="#__codelineno-12-41"></a> <span class="k">return</span> <span class="n">index</span> <span class="k">if</span> <span class="n">first_tombstone</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span> <span class="k">else</span> <span class="n">first_tombstone</span>
|
||||||
<a id="__codelineno-12-42" name="__codelineno-12-42" href="#__codelineno-12-42"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">):</span>
|
<a id="__codelineno-12-42" name="__codelineno-12-42" href="#__codelineno-12-42"></a>
|
||||||
<a id="__codelineno-12-43" name="__codelineno-12-43" href="#__codelineno-12-43"></a> <span class="c1"># 计算桶索引，越过尾部返回头部</span>
|
<a id="__codelineno-12-43" name="__codelineno-12-43" href="#__codelineno-12-43"></a> <span class="k">def</span> <span class="nf">get</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-></span> <span class="nb">str</span><span class="p">:</span>
|
||||||
<a id="__codelineno-12-44" name="__codelineno-12-44" href="#__codelineno-12-44"></a> <span class="n">j</span> <span class="o">=</span> <span class="p">(</span><span class="n">index</span> <span class="o">+</span> <span class="n">i</span><span class="p">)</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span>
|
<a id="__codelineno-12-44" name="__codelineno-12-44" href="#__codelineno-12-44"></a><span class="w"> </span><span class="sd">"""查询操作"""</span>
|
||||||
<a id="__codelineno-12-45" name="__codelineno-12-45" href="#__codelineno-12-45"></a> <span class="c1"># 若遇到空桶、或带有删除标记的桶，则将键值对放入该桶</span>
|
<a id="__codelineno-12-45" name="__codelineno-12-45" href="#__codelineno-12-45"></a> <span class="c1"># 搜索 key 对应的桶索引</span>
|
||||||
<a id="__codelineno-12-46" name="__codelineno-12-46" href="#__codelineno-12-46"></a> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="ow">in</span> <span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">removed</span><span class="p">]:</span>
|
<a id="__codelineno-12-46" name="__codelineno-12-46" href="#__codelineno-12-46"></a> <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">find_bucket</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
|
||||||
<a id="__codelineno-12-47" name="__codelineno-12-47" href="#__codelineno-12-47"></a> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
|
<a id="__codelineno-12-47" name="__codelineno-12-47" href="#__codelineno-12-47"></a> <span class="c1"># 若找到键值对，则返回对应 val</span>
|
||||||
<a id="__codelineno-12-48" name="__codelineno-12-48" href="#__codelineno-12-48"></a> <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">+=</span> <span class="mi">1</span>
|
<a id="__codelineno-12-48" name="__codelineno-12-48" href="#__codelineno-12-48"></a> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span><span class="p">]:</span>
|
||||||
<a id="__codelineno-12-49" name="__codelineno-12-49" href="#__codelineno-12-49"></a> <span class="k">return</span>
|
<a id="__codelineno-12-49" name="__codelineno-12-49" href="#__codelineno-12-49"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">.</span><span class="n">val</span>
|
||||||
<a id="__codelineno-12-50" name="__codelineno-12-50" href="#__codelineno-12-50"></a> <span class="c1"># 若遇到指定 key ，则更新对应 val</span>
|
<a id="__codelineno-12-50" name="__codelineno-12-50" href="#__codelineno-12-50"></a> <span class="c1"># 若键值对不存在，则返回 None</span>
|
||||||
<a id="__codelineno-12-51" name="__codelineno-12-51" href="#__codelineno-12-51"></a> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="n">key</span><span class="p">:</span>
|
<a id="__codelineno-12-51" name="__codelineno-12-51" href="#__codelineno-12-51"></a> <span class="k">return</span> <span class="kc">None</span>
|
||||||
<a id="__codelineno-12-52" name="__codelineno-12-52" href="#__codelineno-12-52"></a> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="o">.</span><span class="n">val</span> <span class="o">=</span> <span class="n">val</span>
|
<a id="__codelineno-12-52" name="__codelineno-12-52" href="#__codelineno-12-52"></a>
|
||||||
<a id="__codelineno-12-53" name="__codelineno-12-53" href="#__codelineno-12-53"></a> <span class="k">return</span>
|
<a id="__codelineno-12-53" name="__codelineno-12-53" href="#__codelineno-12-53"></a> <span class="k">def</span> <span class="nf">put</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">str</span><span class="p">):</span>
|
||||||
<a id="__codelineno-12-54" name="__codelineno-12-54" href="#__codelineno-12-54"></a>
|
<a id="__codelineno-12-54" name="__codelineno-12-54" href="#__codelineno-12-54"></a><span class="w"> </span><span class="sd">"""添加操作"""</span>
|
||||||
<a id="__codelineno-12-55" name="__codelineno-12-55" href="#__codelineno-12-55"></a> <span class="k">def</span> <span class="nf">remove</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
<a id="__codelineno-12-55" name="__codelineno-12-55" href="#__codelineno-12-55"></a> <span class="c1"># 当负载因子超过阈值时，执行扩容</span>
|
||||||
<a id="__codelineno-12-56" name="__codelineno-12-56" href="#__codelineno-12-56"></a><span class="w"> </span><span class="sd">"""删除操作"""</span>
|
<a id="__codelineno-12-56" name="__codelineno-12-56" href="#__codelineno-12-56"></a> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">load_factor</span><span class="p">()</span> <span class="o">></span> <span class="bp">self</span><span class="o">.</span><span class="n">load_thres</span><span class="p">:</span>
|
||||||
<a id="__codelineno-12-57" name="__codelineno-12-57" href="#__codelineno-12-57"></a> <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
|
<a id="__codelineno-12-57" name="__codelineno-12-57" href="#__codelineno-12-57"></a> <span class="bp">self</span><span class="o">.</span><span class="n">extend</span><span class="p">()</span>
|
||||||
<a id="__codelineno-12-58" name="__codelineno-12-58" href="#__codelineno-12-58"></a> <span class="c1"># 线性探测，从 index 开始向后遍历</span>
|
<a id="__codelineno-12-58" name="__codelineno-12-58" href="#__codelineno-12-58"></a> <span class="c1"># 搜索 key 对应的桶索引</span>
|
||||||
<a id="__codelineno-12-59" name="__codelineno-12-59" href="#__codelineno-12-59"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">):</span>
|
<a id="__codelineno-12-59" name="__codelineno-12-59" href="#__codelineno-12-59"></a> <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">find_bucket</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
|
||||||
<a id="__codelineno-12-60" name="__codelineno-12-60" href="#__codelineno-12-60"></a> <span class="c1"># 计算桶索引，越过尾部返回头部</span>
|
<a id="__codelineno-12-60" name="__codelineno-12-60" href="#__codelineno-12-60"></a> <span class="c1"># 若找到键值对，则覆盖 val 并返回</span>
|
||||||
<a id="__codelineno-12-61" name="__codelineno-12-61" href="#__codelineno-12-61"></a> <span class="n">j</span> <span class="o">=</span> <span class="p">(</span><span class="n">index</span> <span class="o">+</span> <span class="n">i</span><span class="p">)</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span>
|
<a id="__codelineno-12-61" name="__codelineno-12-61" href="#__codelineno-12-61"></a> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span><span class="p">]:</span>
|
||||||
<a id="__codelineno-12-62" name="__codelineno-12-62" href="#__codelineno-12-62"></a> <span class="c1"># 若遇到空桶，说明无此 key ，则直接返回</span>
|
<a id="__codelineno-12-62" name="__codelineno-12-62" href="#__codelineno-12-62"></a> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">.</span><span class="n">val</span> <span class="o">=</span> <span class="n">val</span>
|
||||||
<a id="__codelineno-12-63" name="__codelineno-12-63" href="#__codelineno-12-63"></a> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
<a id="__codelineno-12-63" name="__codelineno-12-63" href="#__codelineno-12-63"></a> <span class="k">return</span>
|
||||||
<a id="__codelineno-12-64" name="__codelineno-12-64" href="#__codelineno-12-64"></a> <span class="k">return</span>
|
<a id="__codelineno-12-64" name="__codelineno-12-64" href="#__codelineno-12-64"></a> <span class="c1"># 若键值对不存在，则添加该键值对</span>
|
||||||
<a id="__codelineno-12-65" name="__codelineno-12-65" href="#__codelineno-12-65"></a> <span class="c1"># 若遇到指定 key ，则标记删除并返回</span>
|
<a id="__codelineno-12-65" name="__codelineno-12-65" href="#__codelineno-12-65"></a> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
|
||||||
<a id="__codelineno-12-66" name="__codelineno-12-66" href="#__codelineno-12-66"></a> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="n">key</span><span class="p">:</span>
|
<a id="__codelineno-12-66" name="__codelineno-12-66" href="#__codelineno-12-66"></a> <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">+=</span> <span class="mi">1</span>
|
||||||
<a id="__codelineno-12-67" name="__codelineno-12-67" href="#__codelineno-12-67"></a> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">removed</span>
|
<a id="__codelineno-12-67" name="__codelineno-12-67" href="#__codelineno-12-67"></a>
|
||||||
<a id="__codelineno-12-68" name="__codelineno-12-68" href="#__codelineno-12-68"></a> <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">-=</span> <span class="mi">1</span>
|
<a id="__codelineno-12-68" name="__codelineno-12-68" href="#__codelineno-12-68"></a> <span class="k">def</span> <span class="nf">remove</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||||||
<a id="__codelineno-12-69" name="__codelineno-12-69" href="#__codelineno-12-69"></a> <span class="k">return</span>
|
<a id="__codelineno-12-69" name="__codelineno-12-69" href="#__codelineno-12-69"></a><span class="w"> </span><span class="sd">"""删除操作"""</span>
|
||||||
<a id="__codelineno-12-70" name="__codelineno-12-70" href="#__codelineno-12-70"></a>
|
<a id="__codelineno-12-70" name="__codelineno-12-70" href="#__codelineno-12-70"></a> <span class="c1"># 搜索 key 对应的桶索引</span>
|
||||||
<a id="__codelineno-12-71" name="__codelineno-12-71" href="#__codelineno-12-71"></a> <span class="k">def</span> <span class="nf">extend</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
<a id="__codelineno-12-71" name="__codelineno-12-71" href="#__codelineno-12-71"></a> <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">find_bucket</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
|
||||||
<a id="__codelineno-12-72" name="__codelineno-12-72" href="#__codelineno-12-72"></a><span class="w"> </span><span class="sd">"""扩容哈希表"""</span>
|
<a id="__codelineno-12-72" name="__codelineno-12-72" href="#__codelineno-12-72"></a> <span class="c1"># 若找到键值对，则用删除标记覆盖它</span>
|
||||||
<a id="__codelineno-12-73" name="__codelineno-12-73" href="#__codelineno-12-73"></a> <span class="c1"># 暂存原哈希表</span>
|
<a id="__codelineno-12-73" name="__codelineno-12-73" href="#__codelineno-12-73"></a> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span><span class="p">]:</span>
|
||||||
<a id="__codelineno-12-74" name="__codelineno-12-74" href="#__codelineno-12-74"></a> <span class="n">buckets_tmp</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span>
|
<a id="__codelineno-12-74" name="__codelineno-12-74" href="#__codelineno-12-74"></a> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span>
|
||||||
<a id="__codelineno-12-75" name="__codelineno-12-75" href="#__codelineno-12-75"></a> <span class="c1"># 初始化扩容后的新哈希表</span>
|
<a id="__codelineno-12-75" name="__codelineno-12-75" href="#__codelineno-12-75"></a> <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">-=</span> <span class="mi">1</span>
|
||||||
<a id="__codelineno-12-76" name="__codelineno-12-76" href="#__codelineno-12-76"></a> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span> <span class="o">*=</span> <span class="bp">self</span><span class="o">.</span><span class="n">extend_ratio</span>
|
<a id="__codelineno-12-76" name="__codelineno-12-76" href="#__codelineno-12-76"></a>
|
||||||
<a id="__codelineno-12-77" name="__codelineno-12-77" href="#__codelineno-12-77"></a> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span> <span class="o">=</span> <span class="p">[</span><span class="kc">None</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span>
|
<a id="__codelineno-12-77" name="__codelineno-12-77" href="#__codelineno-12-77"></a> <span class="k">def</span> <span class="nf">extend</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||||||
<a id="__codelineno-12-78" name="__codelineno-12-78" href="#__codelineno-12-78"></a> <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">=</span> <span class="mi">0</span>
|
<a id="__codelineno-12-78" name="__codelineno-12-78" href="#__codelineno-12-78"></a><span class="w"> </span><span class="sd">"""扩容哈希表"""</span>
|
||||||
<a id="__codelineno-12-79" name="__codelineno-12-79" href="#__codelineno-12-79"></a> <span class="c1"># 将键值对从原哈希表搬运至新哈希表</span>
|
<a id="__codelineno-12-79" name="__codelineno-12-79" href="#__codelineno-12-79"></a> <span class="c1"># 暂存原哈希表</span>
|
||||||
<a id="__codelineno-12-80" name="__codelineno-12-80" href="#__codelineno-12-80"></a> <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="n">buckets_tmp</span><span class="p">:</span>
|
<a id="__codelineno-12-80" name="__codelineno-12-80" href="#__codelineno-12-80"></a> <span class="n">buckets_tmp</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span>
|
||||||
<a id="__codelineno-12-81" name="__codelineno-12-81" href="#__codelineno-12-81"></a> <span class="k">if</span> <span class="n">pair</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">removed</span><span class="p">]:</span>
|
<a id="__codelineno-12-81" name="__codelineno-12-81" href="#__codelineno-12-81"></a> <span class="c1"># 初始化扩容后的新哈希表</span>
|
||||||
<a id="__codelineno-12-82" name="__codelineno-12-82" href="#__codelineno-12-82"></a> <span class="bp">self</span><span class="o">.</span><span class="n">put</span><span class="p">(</span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="p">,</span> <span class="n">pair</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
|
<a id="__codelineno-12-82" name="__codelineno-12-82" href="#__codelineno-12-82"></a> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span> <span class="o">*=</span> <span class="bp">self</span><span class="o">.</span><span class="n">extend_ratio</span>
|
||||||
<a id="__codelineno-12-83" name="__codelineno-12-83" href="#__codelineno-12-83"></a>
|
<a id="__codelineno-12-83" name="__codelineno-12-83" href="#__codelineno-12-83"></a> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span> <span class="o">=</span> <span class="p">[</span><span class="kc">None</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span>
|
||||||
<a id="__codelineno-12-84" name="__codelineno-12-84" href="#__codelineno-12-84"></a> <span class="k">def</span> <span class="nf">print</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
<a id="__codelineno-12-84" name="__codelineno-12-84" href="#__codelineno-12-84"></a> <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">=</span> <span class="mi">0</span>
|
||||||
<a id="__codelineno-12-85" name="__codelineno-12-85" href="#__codelineno-12-85"></a><span class="w"> </span><span class="sd">"""打印哈希表"""</span>
|
<a id="__codelineno-12-85" name="__codelineno-12-85" href="#__codelineno-12-85"></a> <span class="c1"># 将键值对从原哈希表搬运至新哈希表</span>
|
||||||
<a id="__codelineno-12-86" name="__codelineno-12-86" href="#__codelineno-12-86"></a> <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span>
|
<a id="__codelineno-12-86" name="__codelineno-12-86" href="#__codelineno-12-86"></a> <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="n">buckets_tmp</span><span class="p">:</span>
|
||||||
<a id="__codelineno-12-87" name="__codelineno-12-87" href="#__codelineno-12-87"></a> <span class="k">if</span> <span class="n">pair</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
|
<a id="__codelineno-12-87" name="__codelineno-12-87" href="#__codelineno-12-87"></a> <span class="k">if</span> <span class="n">pair</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span><span class="p">]:</span>
|
||||||
<a id="__codelineno-12-88" name="__codelineno-12-88" href="#__codelineno-12-88"></a> <span class="nb">print</span><span class="p">(</span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="p">,</span> <span class="s2">"->"</span><span class="p">,</span> <span class="n">pair</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
|
<a id="__codelineno-12-88" name="__codelineno-12-88" href="#__codelineno-12-88"></a> <span class="bp">self</span><span class="o">.</span><span class="n">put</span><span class="p">(</span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="p">,</span> <span class="n">pair</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
|
||||||
<a id="__codelineno-12-89" name="__codelineno-12-89" href="#__codelineno-12-89"></a> <span class="k">else</span><span class="p">:</span>
|
<a id="__codelineno-12-89" name="__codelineno-12-89" href="#__codelineno-12-89"></a>
|
||||||
<a id="__codelineno-12-90" name="__codelineno-12-90" href="#__codelineno-12-90"></a> <span class="nb">print</span><span class="p">(</span><span class="s2">"None"</span><span class="p">)</span>
|
<a id="__codelineno-12-90" name="__codelineno-12-90" href="#__codelineno-12-90"></a> <span class="k">def</span> <span class="nf">print</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||||||
|
<a id="__codelineno-12-91" name="__codelineno-12-91" href="#__codelineno-12-91"></a><span class="w"> </span><span class="sd">"""打印哈希表"""</span>
|
||||||
|
<a id="__codelineno-12-92" name="__codelineno-12-92" href="#__codelineno-12-92"></a> <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span>
|
||||||
|
<a id="__codelineno-12-93" name="__codelineno-12-93" href="#__codelineno-12-93"></a> <span class="k">if</span> <span class="n">pair</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
||||||
|
<a id="__codelineno-12-94" name="__codelineno-12-94" href="#__codelineno-12-94"></a> <span class="nb">print</span><span class="p">(</span><span class="s2">"None"</span><span class="p">)</span>
|
||||||
|
<a id="__codelineno-12-95" name="__codelineno-12-95" href="#__codelineno-12-95"></a> <span class="k">elif</span> <span class="n">pair</span> <span class="ow">is</span> <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span><span class="p">:</span>
|
||||||
|
<a id="__codelineno-12-96" name="__codelineno-12-96" href="#__codelineno-12-96"></a> <span class="nb">print</span><span class="p">(</span><span class="s2">"TOMBSTONE"</span><span class="p">)</span>
|
||||||
|
<a id="__codelineno-12-97" name="__codelineno-12-97" href="#__codelineno-12-97"></a> <span class="k">else</span><span class="p">:</span>
|
||||||
|
<a id="__codelineno-12-98" name="__codelineno-12-98" href="#__codelineno-12-98"></a> <span class="nb">print</span><span class="p">(</span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="p">,</span> <span class="s2">"->"</span><span class="p">,</span> <span class="n">pair</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
|
||||||
</code></pre></div>
|
</code></pre></div>
|
||||||
</div>
|
</div>
|
||||||
<div class="tabbed-block">
|
<div class="tabbed-block">
|
||||||
<div class="highlight"><span class="filename">hash_map_open_addressing.cpp</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="cm">/* 开放寻址哈希表 */</span>
|
<div class="highlight"><span class="filename">hash_map_open_addressing.cpp</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="cm">/**</span>
|
||||||
<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">HashMapOpenAddressing</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="cm"> * File: hash_map_open_addressing.cpp</span>
|
||||||
<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="w"> </span><span class="k">private</span><span class="o">:</span>
|
<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="cm"> * Created Time: 2023-06-13</span>
|
||||||
<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="c1">// 键值对数量</span>
|
<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="cm"> * Author: Krahets (krahets@163.com)</span>
|
||||||
<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span><span class="w"> </span><span class="c1">// 哈希表容量</span>
|
<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="cm"> */</span>
|
||||||
<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">loadThres</span><span class="p">;</span><span class="w"> </span><span class="c1">// 触发扩容的负载因子阈值</span>
|
<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>
|
||||||
<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span><span class="w"> </span><span class="c1">// 扩容倍数</span>
|
<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a><span class="cp">#include</span><span class="w"> </span><span class="cpf">"./array_hash_map.cpp"</span>
|
||||||
<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">Pair</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span><span class="w"> </span><span class="c1">// 桶数组</span>
|
<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>
|
||||||
<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="w"> </span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">removed</span><span class="p">;</span><span class="w"> </span><span class="c1">// 删除标记</span>
|
<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="k">class</span><span class="w"> </span><span class="nc">HashMapOpenAddressing</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>
|
<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a><span class="w"> </span><span class="k">private</span><span class="o">:</span>
|
||||||
<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="w"> </span><span class="k">public</span><span class="o">:</span>
|
<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="c1">// 键值对数量</span>
|
||||||
<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a><span class="w"> </span><span class="cm">/* 构造方法 */</span>
|
<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">4</span><span class="p">;</span><span class="w"> </span><span class="c1">// 哈希表容量</span>
|
||||||
<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a><span class="w"> </span><span class="n">HashMapOpenAddressing</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">loadThres</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// 触发扩容的负载因子阈值</span>
|
||||||
<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a><span class="w"> </span><span class="c1">// 构造方法</span>
|
<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 扩容倍数</span>
|
||||||
<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">Pair</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span><span class="w"> </span><span class="c1">// 桶数组</span>
|
||||||
<a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a><span class="w"> </span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">4</span><span class="p">;</span>
|
<a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a><span class="w"> </span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">TOMBSTONE</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="mi">-1</span><span class="p">,</span><span class="w"> </span><span class="s">"-1"</span><span class="p">);</span><span class="w"> </span><span class="c1">// 删除标记</span>
|
||||||
<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a><span class="w"> </span><span class="n">loadThres</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">3.0</span><span class="p">;</span>
|
<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a>
|
||||||
<a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a><span class="w"> </span><span class="n">extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
|
<a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a><span class="w"> </span><span class="k">public</span><span class="o">:</span>
|
||||||
<a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a><span class="w"> </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">Pair</span><span class="w"> </span><span class="o">*></span><span class="p">(</span><span class="n">capacity</span><span class="p">,</span><span class="w"> </span><span class="k">nullptr</span><span class="p">);</span>
|
<a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a><span class="w"> </span><span class="cm">/* 构造方法 */</span>
|
||||||
<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a><span class="w"> </span><span class="n">removed</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="mi">-1</span><span class="p">,</span><span class="w"> </span><span class="s">"-1"</span><span class="p">);</span>
|
<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a><span class="w"> </span><span class="n">HashMapOpenAddressing</span><span class="p">()</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="mi">0</span><span class="p">),</span><span class="w"> </span><span class="n">buckets</span><span class="p">(</span><span class="n">capacity</span><span class="p">,</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-13-21" name="__codelineno-13-21" href="#__codelineno-13-21"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-13-21" name="__codelineno-13-21" href="#__codelineno-13-21"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a>
|
<a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a>
|
||||||
<a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a><span class="w"> </span><span class="cm">/* 哈希函数 */</span>
|
<a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a><span class="w"> </span><span class="cm">/* 析构方法 */</span>
|
||||||
<a id="__codelineno-13-24" name="__codelineno-13-24" href="#__codelineno-13-24"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-13-24" name="__codelineno-13-24" href="#__codelineno-13-24"></a><span class="w"> </span><span class="o">~</span><span class="n">HashMapOpenAddressing</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
|
<a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-13-26" name="__codelineno-13-26" href="#__codelineno-13-26"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-13-26" name="__codelineno-13-26" href="#__codelineno-13-26"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-13-27" name="__codelineno-13-27" href="#__codelineno-13-27"></a>
|
<a id="__codelineno-13-27" name="__codelineno-13-27" href="#__codelineno-13-27"></a><span class="w"> </span><span class="k">delete</span><span class="w"> </span><span class="n">pair</span><span class="p">;</span>
|
||||||
<a id="__codelineno-13-28" name="__codelineno-13-28" href="#__codelineno-13-28"></a><span class="w"> </span><span class="cm">/* 负载因子 */</span>
|
<a id="__codelineno-13-28" name="__codelineno-13-28" href="#__codelineno-13-28"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-13-29" name="__codelineno-13-29" href="#__codelineno-13-29"></a><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-13-29" name="__codelineno-13-29" href="#__codelineno-13-29"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-13-30" name="__codelineno-13-30" href="#__codelineno-13-30"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">static_cast</span><span class="o"><</span><span class="kt">double</span><span class="o">></span><span class="p">(</span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
|
<a id="__codelineno-13-30" name="__codelineno-13-30" href="#__codelineno-13-30"></a><span class="w"> </span><span class="k">delete</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">;</span>
|
||||||
<a id="__codelineno-13-31" name="__codelineno-13-31" href="#__codelineno-13-31"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-13-31" name="__codelineno-13-31" href="#__codelineno-13-31"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-13-32" name="__codelineno-13-32" href="#__codelineno-13-32"></a>
|
<a id="__codelineno-13-32" name="__codelineno-13-32" href="#__codelineno-13-32"></a>
|
||||||
<a id="__codelineno-13-33" name="__codelineno-13-33" href="#__codelineno-13-33"></a><span class="w"> </span><span class="cm">/* 查询操作 */</span>
|
<a id="__codelineno-13-33" name="__codelineno-13-33" href="#__codelineno-13-33"></a><span class="w"> </span><span class="cm">/* 哈希函数 */</span>
|
||||||
<a id="__codelineno-13-34" name="__codelineno-13-34" href="#__codelineno-13-34"></a><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="n">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-13-34" name="__codelineno-13-34" href="#__codelineno-13-34"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-13-35" name="__codelineno-13-35" href="#__codelineno-13-35"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
|
<a id="__codelineno-13-35" name="__codelineno-13-35" href="#__codelineno-13-35"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
|
||||||
<a id="__codelineno-13-36" name="__codelineno-13-36" href="#__codelineno-13-36"></a><span class="w"> </span><span class="c1">// 线性探测，从 index 开始向后遍历</span>
|
<a id="__codelineno-13-36" name="__codelineno-13-36" href="#__codelineno-13-36"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-13-37" name="__codelineno-13-37" href="#__codelineno-13-37"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-13-37" name="__codelineno-13-37" href="#__codelineno-13-37"></a>
|
||||||
<a id="__codelineno-13-38" name="__codelineno-13-38" href="#__codelineno-13-38"></a><span class="w"> </span><span class="c1">// 计算桶索引，越过尾部返回头部</span>
|
<a id="__codelineno-13-38" name="__codelineno-13-38" href="#__codelineno-13-38"></a><span class="w"> </span><span class="cm">/* 负载因子 */</span>
|
||||||
<a id="__codelineno-13-39" name="__codelineno-13-39" href="#__codelineno-13-39"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
|
<a id="__codelineno-13-39" name="__codelineno-13-39" href="#__codelineno-13-39"></a><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-13-40" name="__codelineno-13-40" href="#__codelineno-13-40"></a><span class="w"> </span><span class="c1">// 若遇到空桶，说明无此 key ，则返回 nullptr</span>
|
<a id="__codelineno-13-40" name="__codelineno-13-40" href="#__codelineno-13-40"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="n">size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
|
||||||
<a id="__codelineno-13-41" name="__codelineno-13-41" href="#__codelineno-13-41"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
|
<a id="__codelineno-13-41" name="__codelineno-13-41" href="#__codelineno-13-41"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-13-42" name="__codelineno-13-42" href="#__codelineno-13-42"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
|
<a id="__codelineno-13-42" name="__codelineno-13-42" href="#__codelineno-13-42"></a>
|
||||||
<a id="__codelineno-13-43" name="__codelineno-13-43" href="#__codelineno-13-43"></a><span class="w"> </span><span class="c1">// 若遇到指定 key ，则返回对应 val</span>
|
<a id="__codelineno-13-43" name="__codelineno-13-43" href="#__codelineno-13-43"></a><span class="w"> </span><span class="cm">/* 搜索 key 对应的桶索引 */</span>
|
||||||
<a id="__codelineno-13-44" name="__codelineno-13-44" href="#__codelineno-13-44"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="o">-></span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">removed</span><span class="p">)</span>
|
<a id="__codelineno-13-44" name="__codelineno-13-44" href="#__codelineno-13-44"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-13-45" name="__codelineno-13-45" href="#__codelineno-13-45"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="o">-></span><span class="n">val</span><span class="p">;</span>
|
<a id="__codelineno-13-45" name="__codelineno-13-45" href="#__codelineno-13-45"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
|
||||||
<a id="__codelineno-13-46" name="__codelineno-13-46" href="#__codelineno-13-46"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-13-46" name="__codelineno-13-46" href="#__codelineno-13-46"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
|
||||||
<a id="__codelineno-13-47" name="__codelineno-13-47" href="#__codelineno-13-47"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
|
<a id="__codelineno-13-47" name="__codelineno-13-47" href="#__codelineno-13-47"></a><span class="w"> </span><span class="c1">// 线性探测，当遇到空桶时跳出</span>
|
||||||
<a id="__codelineno-13-48" name="__codelineno-13-48" href="#__codelineno-13-48"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-13-48" name="__codelineno-13-48" href="#__codelineno-13-48"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-13-49" name="__codelineno-13-49" href="#__codelineno-13-49"></a>
|
<a id="__codelineno-13-49" name="__codelineno-13-49" href="#__codelineno-13-49"></a><span class="w"> </span><span class="c1">// 若遇到 key ，返回对应桶索引</span>
|
||||||
<a id="__codelineno-13-50" name="__codelineno-13-50" href="#__codelineno-13-50"></a><span class="w"> </span><span class="cm">/* 添加操作 */</span>
|
<a id="__codelineno-13-50" name="__codelineno-13-50" href="#__codelineno-13-50"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">-></span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-13-51" name="__codelineno-13-51" href="#__codelineno-13-51"></a><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="n">put</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-13-51" name="__codelineno-13-51" href="#__codelineno-13-51"></a><span class="w"> </span><span class="c1">// 若之前遇到了删除标记，则将键值对移动至该索引</span>
|
||||||
<a id="__codelineno-13-52" name="__codelineno-13-52" href="#__codelineno-13-52"></a><span class="w"> </span><span class="c1">// 当负载因子超过阈值时，执行扩容</span>
|
<a id="__codelineno-13-52" name="__codelineno-13-52" href="#__codelineno-13-52"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">-1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-13-53" name="__codelineno-13-53" href="#__codelineno-13-53"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">loadThres</span><span class="p">)</span>
|
<a id="__codelineno-13-53" name="__codelineno-13-53" href="#__codelineno-13-53"></a><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">firstTombstone</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
|
||||||
<a id="__codelineno-13-54" name="__codelineno-13-54" href="#__codelineno-13-54"></a><span class="w"> </span><span class="n">extend</span><span class="p">();</span>
|
<a id="__codelineno-13-54" name="__codelineno-13-54" href="#__codelineno-13-54"></a><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">;</span>
|
||||||
<a id="__codelineno-13-55" name="__codelineno-13-55" href="#__codelineno-13-55"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
|
<a id="__codelineno-13-55" name="__codelineno-13-55" href="#__codelineno-13-55"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">firstTombstone</span><span class="p">;</span><span class="w"> </span><span class="c1">// 返回移动后的桶索引</span>
|
||||||
<a id="__codelineno-13-56" name="__codelineno-13-56" href="#__codelineno-13-56"></a><span class="w"> </span><span class="c1">// 线性探测，从 index 开始向后遍历</span>
|
<a id="__codelineno-13-56" name="__codelineno-13-56" href="#__codelineno-13-56"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-13-57" name="__codelineno-13-57" href="#__codelineno-13-57"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-13-57" name="__codelineno-13-57" href="#__codelineno-13-57"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="c1">// 返回桶索引</span>
|
||||||
<a id="__codelineno-13-58" name="__codelineno-13-58" href="#__codelineno-13-58"></a><span class="w"> </span><span class="c1">// 计算桶索引，越过尾部返回头部</span>
|
<a id="__codelineno-13-58" name="__codelineno-13-58" href="#__codelineno-13-58"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-13-59" name="__codelineno-13-59" href="#__codelineno-13-59"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
|
<a id="__codelineno-13-59" name="__codelineno-13-59" href="#__codelineno-13-59"></a><span class="w"> </span><span class="c1">// 记录遇到的首个删除标记</span>
|
||||||
<a id="__codelineno-13-60" name="__codelineno-13-60" href="#__codelineno-13-60"></a><span class="w"> </span><span class="c1">// 若遇到空桶、或带有删除标记的桶，则将键值对放入该桶</span>
|
<a id="__codelineno-13-60" name="__codelineno-13-60" href="#__codelineno-13-60"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">-1</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-13-61" name="__codelineno-13-61" href="#__codelineno-13-61"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">removed</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-13-61" name="__codelineno-13-61" href="#__codelineno-13-61"></a><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
|
||||||
<a id="__codelineno-13-62" name="__codelineno-13-62" href="#__codelineno-13-62"></a><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
<a id="__codelineno-13-62" name="__codelineno-13-62" href="#__codelineno-13-62"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-13-63" name="__codelineno-13-63" href="#__codelineno-13-63"></a><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
<a id="__codelineno-13-63" name="__codelineno-13-63" href="#__codelineno-13-63"></a><span class="w"> </span><span class="c1">// 计算桶索引，越过尾部返回头部</span>
|
||||||
<a id="__codelineno-13-64" name="__codelineno-13-64" href="#__codelineno-13-64"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
<a id="__codelineno-13-64" name="__codelineno-13-64" href="#__codelineno-13-64"></a><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
|
||||||
<a id="__codelineno-13-65" name="__codelineno-13-65" href="#__codelineno-13-65"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-13-65" name="__codelineno-13-65" href="#__codelineno-13-65"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-13-66" name="__codelineno-13-66" href="#__codelineno-13-66"></a><span class="w"> </span><span class="c1">// 若遇到指定 key ，则更新对应 val</span>
|
<a id="__codelineno-13-66" name="__codelineno-13-66" href="#__codelineno-13-66"></a><span class="w"> </span><span class="c1">// 若 key 不存在，则返回添加点的索引</span>
|
||||||
<a id="__codelineno-13-67" name="__codelineno-13-67" href="#__codelineno-13-67"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="o">-></span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-13-67" name="__codelineno-13-67" href="#__codelineno-13-67"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">-1</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">firstTombstone</span><span class="p">;</span>
|
||||||
<a id="__codelineno-13-68" name="__codelineno-13-68" href="#__codelineno-13-68"></a><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="o">-></span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
|
<a id="__codelineno-13-68" name="__codelineno-13-68" href="#__codelineno-13-68"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-13-69" name="__codelineno-13-69" href="#__codelineno-13-69"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
<a id="__codelineno-13-69" name="__codelineno-13-69" href="#__codelineno-13-69"></a>
|
||||||
<a id="__codelineno-13-70" name="__codelineno-13-70" href="#__codelineno-13-70"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-13-70" name="__codelineno-13-70" href="#__codelineno-13-70"></a><span class="w"> </span><span class="cm">/* 查询操作 */</span>
|
||||||
<a id="__codelineno-13-71" name="__codelineno-13-71" href="#__codelineno-13-71"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-13-71" name="__codelineno-13-71" href="#__codelineno-13-71"></a><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="n">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-13-72" name="__codelineno-13-72" href="#__codelineno-13-72"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-13-72" name="__codelineno-13-72" href="#__codelineno-13-72"></a><span class="w"> </span><span class="c1">// 搜索 key 对应的桶索引</span>
|
||||||
<a id="__codelineno-13-73" name="__codelineno-13-73" href="#__codelineno-13-73"></a>
|
<a id="__codelineno-13-73" name="__codelineno-13-73" href="#__codelineno-13-73"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
|
||||||
<a id="__codelineno-13-74" name="__codelineno-13-74" href="#__codelineno-13-74"></a><span class="w"> </span><span class="cm">/* 删除操作 */</span>
|
<a id="__codelineno-13-74" name="__codelineno-13-74" href="#__codelineno-13-74"></a><span class="w"> </span><span class="c1">// 若找到键值对，则返回对应 val</span>
|
||||||
<a id="__codelineno-13-75" name="__codelineno-13-75" href="#__codelineno-13-75"></a><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-13-75" name="__codelineno-13-75" href="#__codelineno-13-75"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-13-76" name="__codelineno-13-76" href="#__codelineno-13-76"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
|
<a id="__codelineno-13-76" name="__codelineno-13-76" href="#__codelineno-13-76"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">-></span><span class="n">val</span><span class="p">;</span>
|
||||||
<a id="__codelineno-13-77" name="__codelineno-13-77" href="#__codelineno-13-77"></a><span class="w"> </span><span class="c1">// 线性探测，从 index 开始向后遍历</span>
|
<a id="__codelineno-13-77" name="__codelineno-13-77" href="#__codelineno-13-77"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-13-78" name="__codelineno-13-78" href="#__codelineno-13-78"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-13-78" name="__codelineno-13-78" href="#__codelineno-13-78"></a><span class="w"> </span><span class="c1">// 若键值对不存在，则返回空字符串</span>
|
||||||
<a id="__codelineno-13-79" name="__codelineno-13-79" href="#__codelineno-13-79"></a><span class="w"> </span><span class="c1">// 计算桶索引，越过尾部返回头部</span>
|
<a id="__codelineno-13-79" name="__codelineno-13-79" href="#__codelineno-13-79"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="s">""</span><span class="p">;</span>
|
||||||
<a id="__codelineno-13-80" name="__codelineno-13-80" href="#__codelineno-13-80"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
|
<a id="__codelineno-13-80" name="__codelineno-13-80" href="#__codelineno-13-80"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-13-81" name="__codelineno-13-81" href="#__codelineno-13-81"></a><span class="w"> </span><span class="c1">// 若遇到空桶，说明无此 key ，则直接返回</span>
|
<a id="__codelineno-13-81" name="__codelineno-13-81" href="#__codelineno-13-81"></a>
|
||||||
<a id="__codelineno-13-82" name="__codelineno-13-82" href="#__codelineno-13-82"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
|
<a id="__codelineno-13-82" name="__codelineno-13-82" href="#__codelineno-13-82"></a><span class="w"> </span><span class="cm">/* 添加操作 */</span>
|
||||||
<a id="__codelineno-13-83" name="__codelineno-13-83" href="#__codelineno-13-83"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
<a id="__codelineno-13-83" name="__codelineno-13-83" href="#__codelineno-13-83"></a><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="n">put</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-13-84" name="__codelineno-13-84" href="#__codelineno-13-84"></a><span class="w"> </span><span class="c1">// 若遇到指定 key ，则标记删除并返回</span>
|
<a id="__codelineno-13-84" name="__codelineno-13-84" href="#__codelineno-13-84"></a><span class="w"> </span><span class="c1">// 当负载因子超过阈值时，执行扩容</span>
|
||||||
<a id="__codelineno-13-85" name="__codelineno-13-85" href="#__codelineno-13-85"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="o">-></span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-13-85" name="__codelineno-13-85" href="#__codelineno-13-85"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">loadThres</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-13-86" name="__codelineno-13-86" href="#__codelineno-13-86"></a><span class="w"> </span><span class="k">delete</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">j</span><span class="p">];</span><span class="w"> </span><span class="c1">// 释放内存</span>
|
<a id="__codelineno-13-86" name="__codelineno-13-86" href="#__codelineno-13-86"></a><span class="w"> </span><span class="n">extend</span><span class="p">();</span>
|
||||||
<a id="__codelineno-13-87" name="__codelineno-13-87" href="#__codelineno-13-87"></a><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removed</span><span class="p">;</span>
|
<a id="__codelineno-13-87" name="__codelineno-13-87" href="#__codelineno-13-87"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-13-88" name="__codelineno-13-88" href="#__codelineno-13-88"></a><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
<a id="__codelineno-13-88" name="__codelineno-13-88" href="#__codelineno-13-88"></a><span class="w"> </span><span class="c1">// 搜索 key 对应的桶索引</span>
|
||||||
<a id="__codelineno-13-89" name="__codelineno-13-89" href="#__codelineno-13-89"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
<a id="__codelineno-13-89" name="__codelineno-13-89" href="#__codelineno-13-89"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
|
||||||
<a id="__codelineno-13-90" name="__codelineno-13-90" href="#__codelineno-13-90"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-13-90" name="__codelineno-13-90" href="#__codelineno-13-90"></a><span class="w"> </span><span class="c1">// 若找到键值对，则覆盖 val 并返回</span>
|
||||||
<a id="__codelineno-13-91" name="__codelineno-13-91" href="#__codelineno-13-91"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-13-91" name="__codelineno-13-91" href="#__codelineno-13-91"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-13-92" name="__codelineno-13-92" href="#__codelineno-13-92"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-13-92" name="__codelineno-13-92" href="#__codelineno-13-92"></a><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">-></span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
|
||||||
<a id="__codelineno-13-93" name="__codelineno-13-93" href="#__codelineno-13-93"></a>
|
<a id="__codelineno-13-93" name="__codelineno-13-93" href="#__codelineno-13-93"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
||||||
<a id="__codelineno-13-94" name="__codelineno-13-94" href="#__codelineno-13-94"></a><span class="w"> </span><span class="cm">/* 扩容哈希表 */</span>
|
<a id="__codelineno-13-94" name="__codelineno-13-94" href="#__codelineno-13-94"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-13-95" name="__codelineno-13-95" href="#__codelineno-13-95"></a><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="n">extend</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-13-95" name="__codelineno-13-95" href="#__codelineno-13-95"></a><span class="w"> </span><span class="c1">// 若键值对不存在，则添加该键值对</span>
|
||||||
<a id="__codelineno-13-96" name="__codelineno-13-96" href="#__codelineno-13-96"></a><span class="w"> </span><span class="c1">// 暂存原哈希表</span>
|
<a id="__codelineno-13-96" name="__codelineno-13-96" href="#__codelineno-13-96"></a><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||||||
<a id="__codelineno-13-97" name="__codelineno-13-97" href="#__codelineno-13-97"></a><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">Pair</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="n">bucketsTmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span>
|
<a id="__codelineno-13-97" name="__codelineno-13-97" href="#__codelineno-13-97"></a><span class="w"> </span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
|
||||||
<a id="__codelineno-13-98" name="__codelineno-13-98" href="#__codelineno-13-98"></a><span class="w"> </span><span class="c1">// 初始化扩容后的新哈希表</span>
|
<a id="__codelineno-13-98" name="__codelineno-13-98" href="#__codelineno-13-98"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-13-99" name="__codelineno-13-99" href="#__codelineno-13-99"></a><span class="w"> </span><span class="n">capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span>
|
<a id="__codelineno-13-99" name="__codelineno-13-99" href="#__codelineno-13-99"></a>
|
||||||
<a id="__codelineno-13-100" name="__codelineno-13-100" href="#__codelineno-13-100"></a><span class="w"> </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">Pair</span><span class="w"> </span><span class="o">*></span><span class="p">(</span><span class="n">capacity</span><span class="p">,</span><span class="w"> </span><span class="k">nullptr</span><span class="p">);</span>
|
<a id="__codelineno-13-100" name="__codelineno-13-100" href="#__codelineno-13-100"></a><span class="w"> </span><span class="cm">/* 删除操作 */</span>
|
||||||
<a id="__codelineno-13-101" name="__codelineno-13-101" href="#__codelineno-13-101"></a><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
<a id="__codelineno-13-101" name="__codelineno-13-101" href="#__codelineno-13-101"></a><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-13-102" name="__codelineno-13-102" href="#__codelineno-13-102"></a><span class="w"> </span><span class="c1">// 将键值对从原哈希表搬运至新哈希表</span>
|
<a id="__codelineno-13-102" name="__codelineno-13-102" href="#__codelineno-13-102"></a><span class="w"> </span><span class="c1">// 搜索 key 对应的桶索引</span>
|
||||||
<a id="__codelineno-13-103" name="__codelineno-13-103" href="#__codelineno-13-103"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-13-103" name="__codelineno-13-103" href="#__codelineno-13-103"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
|
||||||
<a id="__codelineno-13-104" name="__codelineno-13-104" href="#__codelineno-13-104"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">removed</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-13-104" name="__codelineno-13-104" href="#__codelineno-13-104"></a><span class="w"> </span><span class="c1">// 若找到键值对，则用删除标记覆盖它</span>
|
||||||
<a id="__codelineno-13-105" name="__codelineno-13-105" href="#__codelineno-13-105"></a><span class="w"> </span><span class="n">put</span><span class="p">(</span><span class="n">pair</span><span class="o">-></span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="o">-></span><span class="n">val</span><span class="p">);</span>
|
<a id="__codelineno-13-105" name="__codelineno-13-105" href="#__codelineno-13-105"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-13-106" name="__codelineno-13-106" href="#__codelineno-13-106"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-13-106" name="__codelineno-13-106" href="#__codelineno-13-106"></a><span class="w"> </span><span class="k">delete</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
|
||||||
<a id="__codelineno-13-107" name="__codelineno-13-107" href="#__codelineno-13-107"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-13-107" name="__codelineno-13-107" href="#__codelineno-13-107"></a><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">;</span>
|
||||||
<a id="__codelineno-13-108" name="__codelineno-13-108" href="#__codelineno-13-108"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-13-108" name="__codelineno-13-108" href="#__codelineno-13-108"></a><span class="w"> </span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
|
||||||
<a id="__codelineno-13-109" name="__codelineno-13-109" href="#__codelineno-13-109"></a>
|
<a id="__codelineno-13-109" name="__codelineno-13-109" href="#__codelineno-13-109"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-13-110" name="__codelineno-13-110" href="#__codelineno-13-110"></a><span class="w"> </span><span class="cm">/* 打印哈希表 */</span>
|
<a id="__codelineno-13-110" name="__codelineno-13-110" href="#__codelineno-13-110"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-13-111" name="__codelineno-13-111" href="#__codelineno-13-111"></a><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="n">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-13-111" name="__codelineno-13-111" href="#__codelineno-13-111"></a>
|
||||||
<a id="__codelineno-13-112" name="__codelineno-13-112" href="#__codelineno-13-112"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="o">&</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-13-112" name="__codelineno-13-112" href="#__codelineno-13-112"></a><span class="w"> </span><span class="cm">/* 扩容哈希表 */</span>
|
||||||
<a id="__codelineno-13-113" name="__codelineno-13-113" href="#__codelineno-13-113"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-13-113" name="__codelineno-13-113" href="#__codelineno-13-113"></a><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="n">extend</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-13-114" name="__codelineno-13-114" href="#__codelineno-13-114"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">pair</span><span class="o">-></span><span class="n">key</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">" -> "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">pair</span><span class="o">-></span><span class="n">val</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
|
<a id="__codelineno-13-114" name="__codelineno-13-114" href="#__codelineno-13-114"></a><span class="w"> </span><span class="c1">// 暂存原哈希表</span>
|
||||||
<a id="__codelineno-13-115" name="__codelineno-13-115" href="#__codelineno-13-115"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-13-115" name="__codelineno-13-115" href="#__codelineno-13-115"></a><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">Pair</span><span class="w"> </span><span class="o">*></span><span class="w"> </span><span class="n">bucketsTmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span>
|
||||||
<a id="__codelineno-13-116" name="__codelineno-13-116" href="#__codelineno-13-116"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"nullptr"</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
|
<a id="__codelineno-13-116" name="__codelineno-13-116" href="#__codelineno-13-116"></a><span class="w"> </span><span class="c1">// 初始化扩容后的新哈希表</span>
|
||||||
<a id="__codelineno-13-117" name="__codelineno-13-117" href="#__codelineno-13-117"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-13-117" name="__codelineno-13-117" href="#__codelineno-13-117"></a><span class="w"> </span><span class="n">capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span>
|
||||||
<a id="__codelineno-13-118" name="__codelineno-13-118" href="#__codelineno-13-118"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-13-118" name="__codelineno-13-118" href="#__codelineno-13-118"></a><span class="w"> </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="n">Pair</span><span class="w"> </span><span class="o">*></span><span class="p">(</span><span class="n">capacity</span><span class="p">,</span><span class="w"> </span><span class="k">nullptr</span><span class="p">);</span>
|
||||||
<a id="__codelineno-13-119" name="__codelineno-13-119" href="#__codelineno-13-119"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-13-119" name="__codelineno-13-119" href="#__codelineno-13-119"></a><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||||||
<a id="__codelineno-13-120" name="__codelineno-13-120" href="#__codelineno-13-120"></a><span class="p">};</span>
|
<a id="__codelineno-13-120" name="__codelineno-13-120" href="#__codelineno-13-120"></a><span class="w"> </span><span class="c1">// 将键值对从原哈希表搬运至新哈希表</span>
|
||||||
|
<a id="__codelineno-13-121" name="__codelineno-13-121" href="#__codelineno-13-121"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
|
<a id="__codelineno-13-122" name="__codelineno-13-122" href="#__codelineno-13-122"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
|
<a id="__codelineno-13-123" name="__codelineno-13-123" href="#__codelineno-13-123"></a><span class="w"> </span><span class="n">put</span><span class="p">(</span><span class="n">pair</span><span class="o">-></span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="o">-></span><span class="n">val</span><span class="p">);</span>
|
||||||
|
<a id="__codelineno-13-124" name="__codelineno-13-124" href="#__codelineno-13-124"></a><span class="w"> </span><span class="k">delete</span><span class="w"> </span><span class="n">pair</span><span class="p">;</span>
|
||||||
|
<a id="__codelineno-13-125" name="__codelineno-13-125" href="#__codelineno-13-125"></a><span class="w"> </span><span class="p">}</span>
|
||||||
|
<a id="__codelineno-13-126" name="__codelineno-13-126" href="#__codelineno-13-126"></a><span class="w"> </span><span class="p">}</span>
|
||||||
|
<a id="__codelineno-13-127" name="__codelineno-13-127" href="#__codelineno-13-127"></a><span class="w"> </span><span class="p">}</span>
|
||||||
|
<a id="__codelineno-13-128" name="__codelineno-13-128" href="#__codelineno-13-128"></a>
|
||||||
|
<a id="__codelineno-13-129" name="__codelineno-13-129" href="#__codelineno-13-129"></a><span class="w"> </span><span class="cm">/* 打印哈希表 */</span>
|
||||||
|
<a id="__codelineno-13-130" name="__codelineno-13-130" href="#__codelineno-13-130"></a><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="n">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||||||
|
<a id="__codelineno-13-131" name="__codelineno-13-131" href="#__codelineno-13-131"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
|
<a id="__codelineno-13-132" name="__codelineno-13-132" href="#__codelineno-13-132"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
|
<a id="__codelineno-13-133" name="__codelineno-13-133" href="#__codelineno-13-133"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"nullptr"</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
|
||||||
|
<a id="__codelineno-13-134" name="__codelineno-13-134" href="#__codelineno-13-134"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
|
<a id="__codelineno-13-135" name="__codelineno-13-135" href="#__codelineno-13-135"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">"TOMBSTONE"</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
|
||||||
|
<a id="__codelineno-13-136" name="__codelineno-13-136" href="#__codelineno-13-136"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||||
|
<a id="__codelineno-13-137" name="__codelineno-13-137" href="#__codelineno-13-137"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">pair</span><span class="o">-></span><span class="n">key</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="s">" -> "</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">pair</span><span class="o">-></span><span class="n">val</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
|
||||||
|
<a id="__codelineno-13-138" name="__codelineno-13-138" href="#__codelineno-13-138"></a><span class="w"> </span><span class="p">}</span>
|
||||||
|
<a id="__codelineno-13-139" name="__codelineno-13-139" href="#__codelineno-13-139"></a><span class="w"> </span><span class="p">}</span>
|
||||||
|
<a id="__codelineno-13-140" name="__codelineno-13-140" href="#__codelineno-13-140"></a><span class="w"> </span><span class="p">}</span>
|
||||||
|
<a id="__codelineno-13-141" name="__codelineno-13-141" href="#__codelineno-13-141"></a><span class="p">};</span>
|
||||||
</code></pre></div>
|
</code></pre></div>
|
||||||
</div>
|
</div>
|
||||||
<div class="tabbed-block">
|
<div class="tabbed-block">
|
||||||
<div class="highlight"><span class="filename">hash_map_open_addressing.java</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 开放寻址哈希表 */</span>
|
<div class="highlight"><span class="filename">hash_map_open_addressing.java</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 开放寻址哈希表 */</span>
|
||||||
<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kd">class</span> <span class="nc">HashMapOpenAddressing</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kd">class</span> <span class="nc">HashMapOpenAddressing</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w"> </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="c1">// 键值对数量</span>
|
<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w"> </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="c1">// 键值对数量</span>
|
||||||
<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w"> </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span><span class="w"> </span><span class="c1">// 哈希表容量</span>
|
<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w"> </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">4</span><span class="p">;</span><span class="w"> </span><span class="c1">// 哈希表容量</span>
|
||||||
<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w"> </span><span class="kd">private</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">loadThres</span><span class="p">;</span><span class="w"> </span><span class="c1">// 触发扩容的负载因子阈值</span>
|
<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w"> </span><span class="kd">private</span><span class="w"> </span><span class="kd">final</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">loadThres</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// 触发扩容的负载因子阈值</span>
|
||||||
<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w"> </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span><span class="w"> </span><span class="c1">// 扩容倍数</span>
|
<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w"> </span><span class="kd">private</span><span class="w"> </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 扩容倍数</span>
|
||||||
<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w"> </span><span class="kd">private</span><span class="w"> </span><span class="n">Pair</span><span class="o">[]</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span><span class="w"> </span><span class="c1">// 桶数组</span>
|
<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w"> </span><span class="kd">private</span><span class="w"> </span><span class="n">Pair</span><span class="o">[]</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span><span class="w"> </span><span class="c1">// 桶数组</span>
|
||||||
<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w"> </span><span class="kd">private</span><span class="w"> </span><span class="n">Pair</span><span class="w"> </span><span class="n">removed</span><span class="p">;</span><span class="w"> </span><span class="c1">// 删除标记</span>
|
<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w"> </span><span class="kd">private</span><span class="w"> </span><span class="kd">final</span><span class="w"> </span><span class="n">Pair</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="s">"-1"</span><span class="p">);</span><span class="w"> </span><span class="c1">// 删除标记</span>
|
||||||
<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>
|
<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>
|
||||||
<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w"> </span><span class="cm">/* 构造方法 */</span>
|
<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w"> </span><span class="cm">/* 构造方法 */</span>
|
||||||
<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="nf">HashMapOpenAddressing</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="nf">HashMapOpenAddressing</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||||||
<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w"> </span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">4</span><span class="p">;</span>
|
<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w"> </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="o">[</span><span class="n">capacity</span><span class="o">]</span><span class="p">;</span>
|
||||||
<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w"> </span><span class="n">loadThres</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">3.0</span><span class="p">;</span>
|
<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w"> </span><span class="n">extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
|
<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a>
|
||||||
<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w"> </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="o">[</span><span class="n">capacity</span><span class="o">]</span><span class="p">;</span>
|
<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w"> </span><span class="cm">/* 哈希函数 */</span>
|
||||||
<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w"> </span><span class="n">removed</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="s">"-1"</span><span class="p">);</span>
|
<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w"> </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">hashFunc</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
|
||||||
<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a>
|
<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w"> </span><span class="cm">/* 哈希函数 */</span>
|
<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a>
|
||||||
<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">hashFunc</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a><span class="w"> </span><span class="cm">/* 负载因子 */</span>
|
||||||
<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
|
<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a><span class="w"> </span><span class="kd">private</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="nf">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
|
||||||
<a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a>
|
<a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a><span class="w"> </span><span class="cm">/* 负载因子 */</span>
|
<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a>
|
||||||
<a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="nf">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a><span class="w"> </span><span class="cm">/* 搜索 key 对应的桶索引 */</span>
|
||||||
<a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
|
<a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a><span class="w"> </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">findBucket</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-14-28" name="__codelineno-14-28" href="#__codelineno-14-28"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-14-28" name="__codelineno-14-28" href="#__codelineno-14-28"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
|
||||||
<a id="__codelineno-14-29" name="__codelineno-14-29" href="#__codelineno-14-29"></a>
|
<a id="__codelineno-14-29" name="__codelineno-14-29" href="#__codelineno-14-29"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
|
||||||
<a id="__codelineno-14-30" name="__codelineno-14-30" href="#__codelineno-14-30"></a><span class="w"> </span><span class="cm">/* 查询操作 */</span>
|
<a id="__codelineno-14-30" name="__codelineno-14-30" href="#__codelineno-14-30"></a><span class="w"> </span><span class="c1">// 线性探测，当遇到空桶时跳出</span>
|
||||||
<a id="__codelineno-14-31" name="__codelineno-14-31" href="#__codelineno-14-31"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-14-31" name="__codelineno-14-31" href="#__codelineno-14-31"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-14-32" name="__codelineno-14-32" href="#__codelineno-14-32"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
|
<a id="__codelineno-14-32" name="__codelineno-14-32" href="#__codelineno-14-32"></a><span class="w"> </span><span class="c1">// 若遇到 key ，返回对应桶索引</span>
|
||||||
<a id="__codelineno-14-33" name="__codelineno-14-33" href="#__codelineno-14-33"></a><span class="w"> </span><span class="c1">// 线性探测，从 index 开始向后遍历</span>
|
<a id="__codelineno-14-33" name="__codelineno-14-33" href="#__codelineno-14-33"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-14-34" name="__codelineno-14-34" href="#__codelineno-14-34"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-14-34" name="__codelineno-14-34" href="#__codelineno-14-34"></a><span class="w"> </span><span class="c1">// 若之前遇到了删除标记，则将键值对移动至该索引</span>
|
||||||
<a id="__codelineno-14-35" name="__codelineno-14-35" href="#__codelineno-14-35"></a><span class="w"> </span><span class="c1">// 计算桶索引，越过尾部返回头部</span>
|
<a id="__codelineno-14-35" name="__codelineno-14-35" href="#__codelineno-14-35"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-14-36" name="__codelineno-14-36" href="#__codelineno-14-36"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
|
<a id="__codelineno-14-36" name="__codelineno-14-36" href="#__codelineno-14-36"></a><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">firstTombstone</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="p">;</span>
|
||||||
<a id="__codelineno-14-37" name="__codelineno-14-37" href="#__codelineno-14-37"></a><span class="w"> </span><span class="c1">// 若遇到空桶，说明无此 key ，则返回 null</span>
|
<a id="__codelineno-14-37" name="__codelineno-14-37" href="#__codelineno-14-37"></a><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">;</span>
|
||||||
<a id="__codelineno-14-38" name="__codelineno-14-38" href="#__codelineno-14-38"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
|
<a id="__codelineno-14-38" name="__codelineno-14-38" href="#__codelineno-14-38"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">firstTombstone</span><span class="p">;</span><span class="w"> </span><span class="c1">// 返回移动后的桶索引</span>
|
||||||
<a id="__codelineno-14-39" name="__codelineno-14-39" href="#__codelineno-14-39"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
|
<a id="__codelineno-14-39" name="__codelineno-14-39" href="#__codelineno-14-39"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-14-40" name="__codelineno-14-40" href="#__codelineno-14-40"></a><span class="w"> </span><span class="c1">// 若遇到指定 key ，则返回对应 val</span>
|
<a id="__codelineno-14-40" name="__codelineno-14-40" href="#__codelineno-14-40"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="c1">// 返回桶索引</span>
|
||||||
<a id="__codelineno-14-41" name="__codelineno-14-41" href="#__codelineno-14-41"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">removed</span><span class="p">)</span>
|
<a id="__codelineno-14-41" name="__codelineno-14-41" href="#__codelineno-14-41"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-14-42" name="__codelineno-14-42" href="#__codelineno-14-42"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
|
<a id="__codelineno-14-42" name="__codelineno-14-42" href="#__codelineno-14-42"></a><span class="w"> </span><span class="c1">// 记录遇到的首个删除标记</span>
|
||||||
<a id="__codelineno-14-43" name="__codelineno-14-43" href="#__codelineno-14-43"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-14-43" name="__codelineno-14-43" href="#__codelineno-14-43"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-14-44" name="__codelineno-14-44" href="#__codelineno-14-44"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
|
<a id="__codelineno-14-44" name="__codelineno-14-44" href="#__codelineno-14-44"></a><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
|
||||||
<a id="__codelineno-14-45" name="__codelineno-14-45" href="#__codelineno-14-45"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-14-45" name="__codelineno-14-45" href="#__codelineno-14-45"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-14-46" name="__codelineno-14-46" href="#__codelineno-14-46"></a>
|
<a id="__codelineno-14-46" name="__codelineno-14-46" href="#__codelineno-14-46"></a><span class="w"> </span><span class="c1">// 计算桶索引，越过尾部返回头部</span>
|
||||||
<a id="__codelineno-14-47" name="__codelineno-14-47" href="#__codelineno-14-47"></a><span class="w"> </span><span class="cm">/* 添加操作 */</span>
|
<a id="__codelineno-14-47" name="__codelineno-14-47" href="#__codelineno-14-47"></a><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
|
||||||
<a id="__codelineno-14-48" name="__codelineno-14-48" href="#__codelineno-14-48"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-14-48" name="__codelineno-14-48" href="#__codelineno-14-48"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-14-49" name="__codelineno-14-49" href="#__codelineno-14-49"></a><span class="w"> </span><span class="c1">// 当负载因子超过阈值时，执行扩容</span>
|
<a id="__codelineno-14-49" name="__codelineno-14-49" href="#__codelineno-14-49"></a><span class="w"> </span><span class="c1">// 若 key 不存在，则返回添加点的索引</span>
|
||||||
<a id="__codelineno-14-50" name="__codelineno-14-50" href="#__codelineno-14-50"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">loadThres</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-14-50" name="__codelineno-14-50" href="#__codelineno-14-50"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">firstTombstone</span><span class="p">;</span>
|
||||||
<a id="__codelineno-14-51" name="__codelineno-14-51" href="#__codelineno-14-51"></a><span class="w"> </span><span class="n">extend</span><span class="p">();</span>
|
<a id="__codelineno-14-51" name="__codelineno-14-51" href="#__codelineno-14-51"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-14-52" name="__codelineno-14-52" href="#__codelineno-14-52"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-14-52" name="__codelineno-14-52" href="#__codelineno-14-52"></a>
|
||||||
<a id="__codelineno-14-53" name="__codelineno-14-53" href="#__codelineno-14-53"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
|
<a id="__codelineno-14-53" name="__codelineno-14-53" href="#__codelineno-14-53"></a><span class="w"> </span><span class="cm">/* 查询操作 */</span>
|
||||||
<a id="__codelineno-14-54" name="__codelineno-14-54" href="#__codelineno-14-54"></a><span class="w"> </span><span class="c1">// 线性探测，从 index 开始向后遍历</span>
|
<a id="__codelineno-14-54" name="__codelineno-14-54" href="#__codelineno-14-54"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-14-55" name="__codelineno-14-55" href="#__codelineno-14-55"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-14-55" name="__codelineno-14-55" href="#__codelineno-14-55"></a><span class="w"> </span><span class="c1">// 搜索 key 对应的桶索引</span>
|
||||||
<a id="__codelineno-14-56" name="__codelineno-14-56" href="#__codelineno-14-56"></a><span class="w"> </span><span class="c1">// 计算桶索引，越过尾部返回头部</span>
|
<a id="__codelineno-14-56" name="__codelineno-14-56" href="#__codelineno-14-56"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
|
||||||
<a id="__codelineno-14-57" name="__codelineno-14-57" href="#__codelineno-14-57"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
|
<a id="__codelineno-14-57" name="__codelineno-14-57" href="#__codelineno-14-57"></a><span class="w"> </span><span class="c1">// 若找到键值对，则返回对应 val</span>
|
||||||
<a id="__codelineno-14-58" name="__codelineno-14-58" href="#__codelineno-14-58"></a><span class="w"> </span><span class="c1">// 若遇到空桶、或带有删除标记的桶，则将键值对放入该桶</span>
|
<a id="__codelineno-14-58" name="__codelineno-14-58" href="#__codelineno-14-58"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-14-59" name="__codelineno-14-59" href="#__codelineno-14-59"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">removed</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-14-59" name="__codelineno-14-59" href="#__codelineno-14-59"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
|
||||||
<a id="__codelineno-14-60" name="__codelineno-14-60" href="#__codelineno-14-60"></a><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
<a id="__codelineno-14-60" name="__codelineno-14-60" href="#__codelineno-14-60"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-14-61" name="__codelineno-14-61" href="#__codelineno-14-61"></a><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
<a id="__codelineno-14-61" name="__codelineno-14-61" href="#__codelineno-14-61"></a><span class="w"> </span><span class="c1">// 若键值对不存在，则返回 null</span>
|
||||||
<a id="__codelineno-14-62" name="__codelineno-14-62" href="#__codelineno-14-62"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
<a id="__codelineno-14-62" name="__codelineno-14-62" href="#__codelineno-14-62"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
|
||||||
<a id="__codelineno-14-63" name="__codelineno-14-63" href="#__codelineno-14-63"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-14-63" name="__codelineno-14-63" href="#__codelineno-14-63"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-14-64" name="__codelineno-14-64" href="#__codelineno-14-64"></a><span class="w"> </span><span class="c1">// 若遇到指定 key ，则更新对应 val</span>
|
<a id="__codelineno-14-64" name="__codelineno-14-64" href="#__codelineno-14-64"></a>
|
||||||
<a id="__codelineno-14-65" name="__codelineno-14-65" href="#__codelineno-14-65"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-14-65" name="__codelineno-14-65" href="#__codelineno-14-65"></a><span class="w"> </span><span class="cm">/* 添加操作 */</span>
|
||||||
<a id="__codelineno-14-66" name="__codelineno-14-66" href="#__codelineno-14-66"></a><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
|
<a id="__codelineno-14-66" name="__codelineno-14-66" href="#__codelineno-14-66"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-14-67" name="__codelineno-14-67" href="#__codelineno-14-67"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
<a id="__codelineno-14-67" name="__codelineno-14-67" href="#__codelineno-14-67"></a><span class="w"> </span><span class="c1">// 当负载因子超过阈值时，执行扩容</span>
|
||||||
<a id="__codelineno-14-68" name="__codelineno-14-68" href="#__codelineno-14-68"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-14-68" name="__codelineno-14-68" href="#__codelineno-14-68"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">loadThres</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-14-69" name="__codelineno-14-69" href="#__codelineno-14-69"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-14-69" name="__codelineno-14-69" href="#__codelineno-14-69"></a><span class="w"> </span><span class="n">extend</span><span class="p">();</span>
|
||||||
<a id="__codelineno-14-70" name="__codelineno-14-70" href="#__codelineno-14-70"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-14-70" name="__codelineno-14-70" href="#__codelineno-14-70"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-14-71" name="__codelineno-14-71" href="#__codelineno-14-71"></a>
|
<a id="__codelineno-14-71" name="__codelineno-14-71" href="#__codelineno-14-71"></a><span class="w"> </span><span class="c1">// 搜索 key 对应的桶索引</span>
|
||||||
<a id="__codelineno-14-72" name="__codelineno-14-72" href="#__codelineno-14-72"></a><span class="w"> </span><span class="cm">/* 删除操作 */</span>
|
<a id="__codelineno-14-72" name="__codelineno-14-72" href="#__codelineno-14-72"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
|
||||||
<a id="__codelineno-14-73" name="__codelineno-14-73" href="#__codelineno-14-73"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-14-73" name="__codelineno-14-73" href="#__codelineno-14-73"></a><span class="w"> </span><span class="c1">// 若找到键值对，则覆盖 val 并返回</span>
|
||||||
<a id="__codelineno-14-74" name="__codelineno-14-74" href="#__codelineno-14-74"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
|
<a id="__codelineno-14-74" name="__codelineno-14-74" href="#__codelineno-14-74"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-14-75" name="__codelineno-14-75" href="#__codelineno-14-75"></a><span class="w"> </span><span class="c1">// 线性探测，从 index 开始向后遍历</span>
|
<a id="__codelineno-14-75" name="__codelineno-14-75" href="#__codelineno-14-75"></a><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
|
||||||
<a id="__codelineno-14-76" name="__codelineno-14-76" href="#__codelineno-14-76"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-14-76" name="__codelineno-14-76" href="#__codelineno-14-76"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
||||||
<a id="__codelineno-14-77" name="__codelineno-14-77" href="#__codelineno-14-77"></a><span class="w"> </span><span class="c1">// 计算桶索引，越过尾部返回头部</span>
|
<a id="__codelineno-14-77" name="__codelineno-14-77" href="#__codelineno-14-77"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-14-78" name="__codelineno-14-78" href="#__codelineno-14-78"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
|
<a id="__codelineno-14-78" name="__codelineno-14-78" href="#__codelineno-14-78"></a><span class="w"> </span><span class="c1">// 若键值对不存在，则添加该键值对</span>
|
||||||
<a id="__codelineno-14-79" name="__codelineno-14-79" href="#__codelineno-14-79"></a><span class="w"> </span><span class="c1">// 若遇到空桶，说明无此 key ，则直接返回</span>
|
<a id="__codelineno-14-79" name="__codelineno-14-79" href="#__codelineno-14-79"></a><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
|
||||||
<a id="__codelineno-14-80" name="__codelineno-14-80" href="#__codelineno-14-80"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-14-80" name="__codelineno-14-80" href="#__codelineno-14-80"></a><span class="w"> </span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
|
||||||
<a id="__codelineno-14-81" name="__codelineno-14-81" href="#__codelineno-14-81"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
<a id="__codelineno-14-81" name="__codelineno-14-81" href="#__codelineno-14-81"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-14-82" name="__codelineno-14-82" href="#__codelineno-14-82"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-14-82" name="__codelineno-14-82" href="#__codelineno-14-82"></a>
|
||||||
<a id="__codelineno-14-83" name="__codelineno-14-83" href="#__codelineno-14-83"></a><span class="w"> </span><span class="c1">// 若遇到指定 key ，则标记删除并返回</span>
|
<a id="__codelineno-14-83" name="__codelineno-14-83" href="#__codelineno-14-83"></a><span class="w"> </span><span class="cm">/* 删除操作 */</span>
|
||||||
<a id="__codelineno-14-84" name="__codelineno-14-84" href="#__codelineno-14-84"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-14-84" name="__codelineno-14-84" href="#__codelineno-14-84"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-14-85" name="__codelineno-14-85" href="#__codelineno-14-85"></a><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removed</span><span class="p">;</span>
|
<a id="__codelineno-14-85" name="__codelineno-14-85" href="#__codelineno-14-85"></a><span class="w"> </span><span class="c1">// 搜索 key 对应的桶索引</span>
|
||||||
<a id="__codelineno-14-86" name="__codelineno-14-86" href="#__codelineno-14-86"></a><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
<a id="__codelineno-14-86" name="__codelineno-14-86" href="#__codelineno-14-86"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
|
||||||
<a id="__codelineno-14-87" name="__codelineno-14-87" href="#__codelineno-14-87"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
<a id="__codelineno-14-87" name="__codelineno-14-87" href="#__codelineno-14-87"></a><span class="w"> </span><span class="c1">// 若找到键值对，则用删除标记覆盖它</span>
|
||||||
<a id="__codelineno-14-88" name="__codelineno-14-88" href="#__codelineno-14-88"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-14-88" name="__codelineno-14-88" href="#__codelineno-14-88"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-14-89" name="__codelineno-14-89" href="#__codelineno-14-89"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-14-89" name="__codelineno-14-89" href="#__codelineno-14-89"></a><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">;</span>
|
||||||
<a id="__codelineno-14-90" name="__codelineno-14-90" href="#__codelineno-14-90"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-14-90" name="__codelineno-14-90" href="#__codelineno-14-90"></a><span class="w"> </span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
|
||||||
<a id="__codelineno-14-91" name="__codelineno-14-91" href="#__codelineno-14-91"></a>
|
<a id="__codelineno-14-91" name="__codelineno-14-91" href="#__codelineno-14-91"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-14-92" name="__codelineno-14-92" href="#__codelineno-14-92"></a><span class="w"> </span><span class="cm">/* 扩容哈希表 */</span>
|
<a id="__codelineno-14-92" name="__codelineno-14-92" href="#__codelineno-14-92"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-14-93" name="__codelineno-14-93" href="#__codelineno-14-93"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">extend</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-14-93" name="__codelineno-14-93" href="#__codelineno-14-93"></a>
|
||||||
<a id="__codelineno-14-94" name="__codelineno-14-94" href="#__codelineno-14-94"></a><span class="w"> </span><span class="c1">// 暂存原哈希表</span>
|
<a id="__codelineno-14-94" name="__codelineno-14-94" href="#__codelineno-14-94"></a><span class="w"> </span><span class="cm">/* 扩容哈希表 */</span>
|
||||||
<a id="__codelineno-14-95" name="__codelineno-14-95" href="#__codelineno-14-95"></a><span class="w"> </span><span class="n">Pair</span><span class="o">[]</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span>
|
<a id="__codelineno-14-95" name="__codelineno-14-95" href="#__codelineno-14-95"></a><span class="w"> </span><span class="kd">private</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">extend</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-14-96" name="__codelineno-14-96" href="#__codelineno-14-96"></a><span class="w"> </span><span class="c1">// 初始化扩容后的新哈希表</span>
|
<a id="__codelineno-14-96" name="__codelineno-14-96" href="#__codelineno-14-96"></a><span class="w"> </span><span class="c1">// 暂存原哈希表</span>
|
||||||
<a id="__codelineno-14-97" name="__codelineno-14-97" href="#__codelineno-14-97"></a><span class="w"> </span><span class="n">capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span>
|
<a id="__codelineno-14-97" name="__codelineno-14-97" href="#__codelineno-14-97"></a><span class="w"> </span><span class="n">Pair</span><span class="o">[]</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span>
|
||||||
<a id="__codelineno-14-98" name="__codelineno-14-98" href="#__codelineno-14-98"></a><span class="w"> </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="o">[</span><span class="n">capacity</span><span class="o">]</span><span class="p">;</span>
|
<a id="__codelineno-14-98" name="__codelineno-14-98" href="#__codelineno-14-98"></a><span class="w"> </span><span class="c1">// 初始化扩容后的新哈希表</span>
|
||||||
<a id="__codelineno-14-99" name="__codelineno-14-99" href="#__codelineno-14-99"></a><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
<a id="__codelineno-14-99" name="__codelineno-14-99" href="#__codelineno-14-99"></a><span class="w"> </span><span class="n">capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span>
|
||||||
<a id="__codelineno-14-100" name="__codelineno-14-100" href="#__codelineno-14-100"></a><span class="w"> </span><span class="c1">// 将键值对从原哈希表搬运至新哈希表</span>
|
<a id="__codelineno-14-100" name="__codelineno-14-100" href="#__codelineno-14-100"></a><span class="w"> </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="o">[</span><span class="n">capacity</span><span class="o">]</span><span class="p">;</span>
|
||||||
<a id="__codelineno-14-101" name="__codelineno-14-101" href="#__codelineno-14-101"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-14-101" name="__codelineno-14-101" href="#__codelineno-14-101"></a><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||||||
<a id="__codelineno-14-102" name="__codelineno-14-102" href="#__codelineno-14-102"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">removed</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-14-102" name="__codelineno-14-102" href="#__codelineno-14-102"></a><span class="w"> </span><span class="c1">// 将键值对从原哈希表搬运至新哈希表</span>
|
||||||
<a id="__codelineno-14-103" name="__codelineno-14-103" href="#__codelineno-14-103"></a><span class="w"> </span><span class="n">put</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
|
<a id="__codelineno-14-103" name="__codelineno-14-103" href="#__codelineno-14-103"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-14-104" name="__codelineno-14-104" href="#__codelineno-14-104"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-14-104" name="__codelineno-14-104" href="#__codelineno-14-104"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-14-105" name="__codelineno-14-105" href="#__codelineno-14-105"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-14-105" name="__codelineno-14-105" href="#__codelineno-14-105"></a><span class="w"> </span><span class="n">put</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
|
||||||
<a id="__codelineno-14-106" name="__codelineno-14-106" href="#__codelineno-14-106"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-14-106" name="__codelineno-14-106" href="#__codelineno-14-106"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-14-107" name="__codelineno-14-107" href="#__codelineno-14-107"></a>
|
<a id="__codelineno-14-107" name="__codelineno-14-107" href="#__codelineno-14-107"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-14-108" name="__codelineno-14-108" href="#__codelineno-14-108"></a><span class="w"> </span><span class="cm">/* 打印哈希表 */</span>
|
<a id="__codelineno-14-108" name="__codelineno-14-108" href="#__codelineno-14-108"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-14-109" name="__codelineno-14-109" href="#__codelineno-14-109"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-14-109" name="__codelineno-14-109" href="#__codelineno-14-109"></a>
|
||||||
<a id="__codelineno-14-110" name="__codelineno-14-110" href="#__codelineno-14-110"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-14-110" name="__codelineno-14-110" href="#__codelineno-14-110"></a><span class="w"> </span><span class="cm">/* 打印哈希表 */</span>
|
||||||
<a id="__codelineno-14-111" name="__codelineno-14-111" href="#__codelineno-14-111"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-14-111" name="__codelineno-14-111" href="#__codelineno-14-111"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-14-112" name="__codelineno-14-112" href="#__codelineno-14-112"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">" -> "</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
|
<a id="__codelineno-14-112" name="__codelineno-14-112" href="#__codelineno-14-112"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-14-113" name="__codelineno-14-113" href="#__codelineno-14-113"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-14-113" name="__codelineno-14-113" href="#__codelineno-14-113"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-14-114" name="__codelineno-14-114" href="#__codelineno-14-114"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="s">"null"</span><span class="p">);</span>
|
<a id="__codelineno-14-114" name="__codelineno-14-114" href="#__codelineno-14-114"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="s">"null"</span><span class="p">);</span>
|
||||||
<a id="__codelineno-14-115" name="__codelineno-14-115" href="#__codelineno-14-115"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-14-115" name="__codelineno-14-115" href="#__codelineno-14-115"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-14-116" name="__codelineno-14-116" href="#__codelineno-14-116"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-14-116" name="__codelineno-14-116" href="#__codelineno-14-116"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="s">"TOMBSTONE"</span><span class="p">);</span>
|
||||||
<a id="__codelineno-14-117" name="__codelineno-14-117" href="#__codelineno-14-117"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-14-117" name="__codelineno-14-117" href="#__codelineno-14-117"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-14-118" name="__codelineno-14-118" href="#__codelineno-14-118"></a><span class="p">}</span>
|
<a id="__codelineno-14-118" name="__codelineno-14-118" href="#__codelineno-14-118"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">" -> "</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
|
||||||
|
<a id="__codelineno-14-119" name="__codelineno-14-119" href="#__codelineno-14-119"></a><span class="w"> </span><span class="p">}</span>
|
||||||
|
<a id="__codelineno-14-120" name="__codelineno-14-120" href="#__codelineno-14-120"></a><span class="w"> </span><span class="p">}</span>
|
||||||
|
<a id="__codelineno-14-121" name="__codelineno-14-121" href="#__codelineno-14-121"></a><span class="w"> </span><span class="p">}</span>
|
||||||
|
<a id="__codelineno-14-122" name="__codelineno-14-122" href="#__codelineno-14-122"></a><span class="p">}</span>
|
||||||
</code></pre></div>
|
</code></pre></div>
|
||||||
</div>
|
</div>
|
||||||
<div class="tabbed-block">
|
<div class="tabbed-block">
|
||||||
@@ -6062,23 +6141,104 @@
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
<h3 id="2">2. 多次哈希<a class="headerlink" href="#2" title="Permanent link">¶</a></h3>
|
<h3 id="2">2. 平方探测<a class="headerlink" href="#2" title="Permanent link">¶</a></h3>
|
||||||
<p>顾名思义，多次哈希方法是使用多个哈希函数 <span class="arithmatex">\(f_1(x)\)</span>、<span class="arithmatex">\(f_2(x)\)</span>、<span class="arithmatex">\(f_3(x)\)</span>、<span class="arithmatex">\(\dots\)</span> 进行探测。</p>
|
<p>平方探测与线性探测类似，都是开放寻址的常见策略之一。当发生冲突时，平方探测不是简单地跳过一个固定的步数，而是跳过“探测次数的平方”的步数，即 <span class="arithmatex">\(1, 4, 9, \dots\)</span> 步。</p>
|
||||||
|
<p>平方探测通主要具有以下优势。</p>
|
||||||
<ul>
|
<ul>
|
||||||
<li><strong>插入元素</strong>：若哈希函数 <span class="arithmatex">\(f_1(x)\)</span> 出现冲突，则尝试 <span class="arithmatex">\(f_2(x)\)</span> ，以此类推，直到找到空位后插入元素。</li>
|
<li>平方探测通过跳过平方的距离，试图缓解线性探测的聚集效应。</li>
|
||||||
<li><strong>查找元素</strong>：在相同的哈希函数顺序下进行查找，直到找到目标元素时返回；或遇到空位或已尝试所有哈希函数，说明哈希表中不存在该元素，则返回 <span class="arithmatex">\(\text{None}\)</span> 。</li>
|
<li>平方探测会跳过更大的距离来寻找空位置，有助于数据分布得更加均匀。</li>
|
||||||
|
</ul>
|
||||||
|
<p>然而，平方探测也并不是完美的。</p>
|
||||||
|
<ul>
|
||||||
|
<li>仍然存在聚集现象，即某些位置比其他位置更容易被占用。</li>
|
||||||
|
<li>由于平方的增长，平方探测可能不会探测整个哈希表，这意味着即使哈希表中有空桶，平方探测也可能无法访问到它。</li>
|
||||||
|
</ul>
|
||||||
|
<h3 id="3">3. 多次哈希<a class="headerlink" href="#3" title="Permanent link">¶</a></h3>
|
||||||
|
<p>多次哈希使用多个哈希函数 <span class="arithmatex">\(f_1(x)\)</span>、<span class="arithmatex">\(f_2(x)\)</span>、<span class="arithmatex">\(f_3(x)\)</span>、<span class="arithmatex">\(\dots\)</span> 进行探测。</p>
|
||||||
|
<ul>
|
||||||
|
<li><strong>插入元素</strong>：若哈希函数 <span class="arithmatex">\(f_1(x)\)</span> 出现冲突，则尝试 <span class="arithmatex">\(f_2(x)\)</span> ，以此类推，直到找到空桶后插入元素。</li>
|
||||||
|
<li><strong>查找元素</strong>：在相同的哈希函数顺序下进行查找，直到找到目标元素时返回；或当遇到空桶或已尝试所有哈希函数，说明哈希表中不存在该元素，则返回 <span class="arithmatex">\(\text{None}\)</span> 。</li>
|
||||||
</ul>
|
</ul>
|
||||||
<p>与线性探测相比，多次哈希方法不易产生聚集，但多个哈希函数会增加额外的计算量。</p>
|
<p>与线性探测相比，多次哈希方法不易产生聚集，但多个哈希函数会增加额外的计算量。</p>
|
||||||
|
<div class="admonition tip">
|
||||||
|
<p class="admonition-title">Tip</p>
|
||||||
|
<p>请注意，开放寻址（线性探测、平方探测和多次哈希）哈希表都存在“不能直接删除元素”的问题。</p>
|
||||||
|
</div>
|
||||||
<h2 id="623">6.2.3 编程语言的选择<a class="headerlink" href="#623" title="Permanent link">¶</a></h2>
|
<h2 id="623">6.2.3 编程语言的选择<a class="headerlink" href="#623" title="Permanent link">¶</a></h2>
|
||||||
<p>Java 采用链式地址。自 JDK 1.8 以来，当 HashMap 内数组长度达到 64 且链表长度达到 8 时，链表会被转换为红黑树以提升查找性能。</p>
|
<p>各个编程语言采取了不同的哈希表实现策略，以下举几个例子。</p>
|
||||||
<p>Python 采用开放寻址。字典 dict 使用伪随机数进行探测。</p>
|
<ul>
|
||||||
<p>Golang 采用链式地址。Go 规定每个桶最多存储 8 个键值对，超出容量则连接一个溢出桶；当溢出桶过多时，会执行一次特殊的等量扩容操作，以确保性能。</p>
|
<li>Java 采用链式地址。自 JDK 1.8 以来，当 HashMap 内数组长度达到 64 且链表长度达到 8 时，链表会被转换为红黑树以提升查找性能。</li>
|
||||||
|
<li>Python 采用开放寻址。字典 dict 使用伪随机数进行探测。</li>
|
||||||
|
<li>Golang 采用链式地址。Go 规定每个桶最多存储 8 个键值对，超出容量则连接一个溢出桶。当溢出桶过多时，会执行一次特殊的等量扩容操作，以确保性能。</li>
|
||||||
|
</ul>
|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
|
||||||
|
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_hashing/hash_map.md" title="编辑此页" class="md-content__button md-icon">
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<h1 id="61">6.1 哈希表<a class="headerlink" href="#61" title="Permanent link">¶</a></h1>
|
<h1 id="61">6.1 哈希表<a class="headerlink" href="#61" title="Permanent link">¶</a></h1>
|
||||||
<p>「哈希表 hash table」，又称「散列表」，其通过建立键 <code>key</code> 与值 <code>value</code> 之间的映射，实现高效的元素查询。具体而言，我们向哈希表输入一个键 <code>key</code> ，则可以在 <span class="arithmatex">\(O(1)\)</span> 时间内获取对应的值 <code>value</code> 。</p>
|
<p>「哈希表 hash table」，又称「散列表」，其通过建立键 <code>key</code> 与值 <code>value</code> 之间的映射，实现高效的元素查询。具体而言，我们向哈希表输入一个键 <code>key</code> ，则可以在 <span class="arithmatex">\(O(1)\)</span> 时间内获取对应的值 <code>value</code> 。</p>
|
||||||
<p>如图 6-1 所示，给定 <span class="arithmatex">\(n\)</span> 个学生，每个学生都有“姓名”和“学号”两项数据。假如我们希望实现“输入一个学号，返回对应的姓名”的查询功能，则可以采用图 6-1 所示的哈希表来实现。</p>
|
<p>如图 6-1 所示，给定 <span class="arithmatex">\(n\)</span> 个学生，每个学生都有“姓名”和“学号”两项数据。假如我们希望实现“输入一个学号，返回对应的姓名”的查询功能，则可以采用图 6-1 所示的哈希表来实现。</p>
|
||||||
@@ -4543,11 +4575,10 @@
|
|||||||
<a id="__codelineno-31-77" name="__codelineno-31-77" href="#__codelineno-31-77"></a><span class="w"> </span><span class="nx">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-31-77" name="__codelineno-31-77" href="#__codelineno-31-77"></a><span class="w"> </span><span class="nx">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-31-78" name="__codelineno-31-78" href="#__codelineno-31-78"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">pairSet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">entries</span><span class="p">();</span>
|
<a id="__codelineno-31-78" name="__codelineno-31-78" href="#__codelineno-31-78"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">pairSet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">entries</span><span class="p">();</span>
|
||||||
<a id="__codelineno-31-79" name="__codelineno-31-79" href="#__codelineno-31-79"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">pairSet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-31-79" name="__codelineno-31-79" href="#__codelineno-31-79"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">pairSet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-31-80" name="__codelineno-31-80" href="#__codelineno-31-80"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="nx">pair</span><span class="p">)</span><span class="w"> </span><span class="k">continue</span><span class="p">;</span>
|
<a id="__codelineno-31-80" name="__codelineno-31-80" href="#__codelineno-31-80"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="sb">`</span><span class="si">${</span><span class="nx">pair</span><span class="p">.</span><span class="nx">key</span><span class="si">}</span><span class="sb"> -> </span><span class="si">${</span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span><span class="si">}</span><span class="sb">`</span><span class="p">);</span>
|
||||||
<a id="__codelineno-31-81" name="__codelineno-31-81" href="#__codelineno-31-81"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="sb">`</span><span class="si">${</span><span class="nx">pair</span><span class="p">.</span><span class="nx">key</span><span class="si">}</span><span class="sb"> -> </span><span class="si">${</span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span><span class="si">}</span><span class="sb">`</span><span class="p">);</span>
|
<a id="__codelineno-31-81" name="__codelineno-31-81" href="#__codelineno-31-81"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-31-82" name="__codelineno-31-82" href="#__codelineno-31-82"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-31-82" name="__codelineno-31-82" href="#__codelineno-31-82"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-31-83" name="__codelineno-31-83" href="#__codelineno-31-83"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-31-83" name="__codelineno-31-83" href="#__codelineno-31-83"></a><span class="p">}</span>
|
||||||
<a id="__codelineno-31-84" name="__codelineno-31-84" href="#__codelineno-31-84"></a><span class="p">}</span>
|
|
||||||
</code></pre></div>
|
</code></pre></div>
|
||||||
</div>
|
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|
||||||
<div class="tabbed-block">
|
<div class="tabbed-block">
|
||||||
@@ -4634,11 +4665,10 @@
|
|||||||
<a id="__codelineno-32-81" name="__codelineno-32-81" href="#__codelineno-32-81"></a><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="nx">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-32-81" name="__codelineno-32-81" href="#__codelineno-32-81"></a><span class="w"> </span><span class="k">public</span><span class="w"> </span><span class="nx">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-32-82" name="__codelineno-32-82" href="#__codelineno-32-82"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">pairSet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">entries</span><span class="p">();</span>
|
<a id="__codelineno-32-82" name="__codelineno-32-82" href="#__codelineno-32-82"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">pairSet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">entries</span><span class="p">();</span>
|
||||||
<a id="__codelineno-32-83" name="__codelineno-32-83" href="#__codelineno-32-83"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">pairSet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-32-83" name="__codelineno-32-83" href="#__codelineno-32-83"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">pair</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">pairSet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-32-84" name="__codelineno-32-84" href="#__codelineno-32-84"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="nx">pair</span><span class="p">)</span><span class="w"> </span><span class="k">continue</span><span class="p">;</span>
|
<a id="__codelineno-32-84" name="__codelineno-32-84" href="#__codelineno-32-84"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="sb">`</span><span class="si">${</span><span class="nx">pair</span><span class="p">.</span><span class="nx">key</span><span class="si">}</span><span class="sb"> -> </span><span class="si">${</span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span><span class="si">}</span><span class="sb">`</span><span class="p">);</span>
|
||||||
<a id="__codelineno-32-85" name="__codelineno-32-85" href="#__codelineno-32-85"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="sb">`</span><span class="si">${</span><span class="nx">pair</span><span class="p">.</span><span class="nx">key</span><span class="si">}</span><span class="sb"> -> </span><span class="si">${</span><span class="nx">pair</span><span class="p">.</span><span class="nx">val</span><span class="si">}</span><span class="sb">`</span><span class="p">);</span>
|
<a id="__codelineno-32-85" name="__codelineno-32-85" href="#__codelineno-32-85"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-32-86" name="__codelineno-32-86" href="#__codelineno-32-86"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-32-86" name="__codelineno-32-86" href="#__codelineno-32-86"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-32-87" name="__codelineno-32-87" href="#__codelineno-32-87"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-32-87" name="__codelineno-32-87" href="#__codelineno-32-87"></a><span class="p">}</span>
|
||||||
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</code></pre></div>
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<p>类似于数组扩容，哈希表扩容需将所有键值对从原哈希表迁移至新哈希表，非常耗时。并且由于哈希表容量 <code>capacity</code> 改变，我们需要通过哈希函数来重新计算所有键值对的存储位置，这进一步提高了扩容过程的计算开销。为此，编程语言通常会预留足够大的哈希表容量，防止频繁扩容。</p>
|
<p>类似于数组扩容，哈希表扩容需将所有键值对从原哈希表迁移至新哈希表，非常耗时。并且由于哈希表容量 <code>capacity</code> 改变，我们需要通过哈希函数来重新计算所有键值对的存储位置，这进一步提高了扩容过程的计算开销。为此，编程语言通常会预留足够大的哈希表容量，防止频繁扩容。</p>
|
||||||
<p>「负载因子 load factor」是哈希表的一个重要概念，其定义为哈希表的元素数量除以桶数量，用于衡量哈希冲突的严重程度，<strong>也常被作为哈希表扩容的触发条件</strong>。例如在 Java 中，当负载因子超过 <span class="arithmatex">\(0.75\)</span> 时，系统会将哈希表容量扩展为原先的 <span class="arithmatex">\(2\)</span> 倍。</p>
|
<p>「负载因子 load factor」是哈希表的一个重要概念，其定义为哈希表的元素数量除以桶数量，用于衡量哈希冲突的严重程度，<strong>也常被作为哈希表扩容的触发条件</strong>。例如在 Java 中，当负载因子超过 <span class="arithmatex">\(0.75\)</span> 时，系统会将哈希表容量扩展为原先的 <span class="arithmatex">\(2\)</span> 倍。</p>
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|
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<h1 id="6">第 6 章 哈希表<a class="headerlink" href="#6" title="Permanent link">¶</a></h1>
|
<h1 id="6">第 6 章 哈希表<a class="headerlink" href="#6" title="Permanent link">¶</a></h1>
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|
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|
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<li><a href="https://www.hello-algo.com/chapter_hashing/summary/">6.4 小结</a></li>
|
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<h1 id="64">6.4 小结<a class="headerlink" href="#64" title="Permanent link">¶</a></h1>
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<h1 id="64">6.4 小结<a class="headerlink" href="#64" title="Permanent link">¶</a></h1>
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<h3 id="1">1. 重点回顾<a class="headerlink" href="#1" title="Permanent link">¶</a></h3>
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<p>哈希函数的最后一步往往是对数组长度 <span class="arithmatex">\(n\)</span> 取余，让输出值落入在数组索引范围；在扩容后，数组长度 <span class="arithmatex">\(n\)</span> 发生变化，而 <code>key</code> 对应的索引也可能发生变化。原先落在同一个桶的多个 <code>key</code> ，在扩容后可能会被分配到多个桶中，从而实现哈希冲突的缓解。</p>
|
<p>哈希函数的最后一步往往是对数组长度 <span class="arithmatex">\(n\)</span> 取余，让输出值落入在数组索引范围；在扩容后，数组长度 <span class="arithmatex">\(n\)</span> 发生变化，而 <code>key</code> 对应的索引也可能发生变化。原先落在同一个桶的多个 <code>key</code> ，在扩容后可能会被分配到多个桶中，从而实现哈希冲突的缓解。</p>
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deal in the Software without restriction, including without limitation the
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rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
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furnished to do so, subject to the following conditions:
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all copies or substantial portions of the Software.
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|
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|
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|
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|
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||||||
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|
||||||
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||||||
<h1 id="82">8.2 建堆操作<a class="headerlink" href="#82" title="Permanent link">¶</a></h1>
|
<h1 id="82">8.2 建堆操作<a class="headerlink" href="#82" title="Permanent link">¶</a></h1>
|
||||||
<p>在某些情况下，我们希望使用一个列表的所有元素来构建一个堆，这个过程被称为“建堆操作”。</p>
|
<p>在某些情况下，我们希望使用一个列表的所有元素来构建一个堆，这个过程被称为“建堆操作”。</p>
|
||||||
<h2 id="821">8.2.1 借助入堆操作实现<a class="headerlink" href="#821" title="Permanent link">¶</a></h2>
|
<h2 id="821">8.2.1 借助入堆操作实现<a class="headerlink" href="#821" title="Permanent link">¶</a></h2>
|
||||||
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|
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|
||||||
<p>进一步地，高度为 <span class="arithmatex">\(h\)</span> 的完美二叉树的节点数量为 <span class="arithmatex">\(n = 2^{h+1} - 1\)</span> ，易得复杂度为 <span class="arithmatex">\(O(2^h) = O(n)\)</span> 。以上推算表明，<strong>输入列表并建堆的时间复杂度为 <span class="arithmatex">\(O(n)\)</span> ，非常高效</strong>。</p>
|
<p>进一步地，高度为 <span class="arithmatex">\(h\)</span> 的完美二叉树的节点数量为 <span class="arithmatex">\(n = 2^{h+1} - 1\)</span> ，易得复杂度为 <span class="arithmatex">\(O(2^h) = O(n)\)</span> 。以上推算表明，<strong>输入列表并建堆的时间复杂度为 <span class="arithmatex">\(O(n)\)</span> ，非常高效</strong>。</p>
|
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<h1 id="81">8.1 堆<a class="headerlink" href="#81" title="Permanent link">¶</a></h1>
|
<h1 id="81">8.1 堆<a class="headerlink" href="#81" title="Permanent link">¶</a></h1>
|
||||||
<p>「堆 heap」是一种满足特定条件的完全二叉树，主要可分为图 8-1 所示的两种类型。</p>
|
<p>「堆 heap」是一种满足特定条件的完全二叉树，主要可分为图 8-1 所示的两种类型。</p>
|
||||||
<ul>
|
<ul>
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||||||
@@ -4600,19 +4632,18 @@
|
|||||||
<a id="__codelineno-49-17" name="__codelineno-49-17" href="#__codelineno-49-17"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nb">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-49-17" name="__codelineno-49-17" href="#__codelineno-49-17"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nb">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-49-18" name="__codelineno-49-18" href="#__codelineno-49-18"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
|
<a id="__codelineno-49-18" name="__codelineno-49-18" href="#__codelineno-49-18"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
|
||||||
<a id="__codelineno-49-19" name="__codelineno-49-19" href="#__codelineno-49-19"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
|
<a id="__codelineno-49-19" name="__codelineno-49-19" href="#__codelineno-49-19"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
|
||||||
<a id="__codelineno-49-20" name="__codelineno-49-20" href="#__codelineno-49-20"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
|
<a id="__codelineno-49-20" name="__codelineno-49-20" href="#__codelineno-49-20"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
|
||||||
<a id="__codelineno-49-21" name="__codelineno-49-21" href="#__codelineno-49-21"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
|
<a id="__codelineno-49-21" name="__codelineno-49-21" href="#__codelineno-49-21"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
|
||||||
<a id="__codelineno-49-22" name="__codelineno-49-22" href="#__codelineno-49-22"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
|
<a id="__codelineno-49-22" name="__codelineno-49-22" href="#__codelineno-49-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
|
||||||
<a id="__codelineno-49-23" name="__codelineno-49-23" href="#__codelineno-49-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
|
<a id="__codelineno-49-23" name="__codelineno-49-23" href="#__codelineno-49-23"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
|
||||||
<a id="__codelineno-49-24" name="__codelineno-49-24" href="#__codelineno-49-24"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
|
<a id="__codelineno-49-24" name="__codelineno-49-24" href="#__codelineno-49-24"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
|
||||||
<a id="__codelineno-49-25" name="__codelineno-49-25" href="#__codelineno-49-25"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
|
<a id="__codelineno-49-25" name="__codelineno-49-25" href="#__codelineno-49-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
|
||||||
<a id="__codelineno-49-26" name="__codelineno-49-26" href="#__codelineno-49-26"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
|
<a id="__codelineno-49-26" name="__codelineno-49-26" href="#__codelineno-49-26"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||||||
<a id="__codelineno-49-27" name="__codelineno-49-27" href="#__codelineno-49-27"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
<a id="__codelineno-49-27" name="__codelineno-49-27" href="#__codelineno-49-27"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">]);</span>
|
||||||
<a id="__codelineno-49-28" name="__codelineno-49-28" href="#__codelineno-49-28"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">]);</span>
|
<a id="__codelineno-49-28" name="__codelineno-49-28" href="#__codelineno-49-28"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
|
||||||
<a id="__codelineno-49-29" name="__codelineno-49-29" href="#__codelineno-49-29"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
|
<a id="__codelineno-49-29" name="__codelineno-49-29" href="#__codelineno-49-29"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
|
||||||
<a id="__codelineno-49-30" name="__codelineno-49-30" href="#__codelineno-49-30"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
|
<a id="__codelineno-49-30" name="__codelineno-49-30" href="#__codelineno-49-30"></a><span class="w"> </span><span class="p">}</span>
|
||||||
<a id="__codelineno-49-31" name="__codelineno-49-31" href="#__codelineno-49-31"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-49-31" name="__codelineno-49-31" href="#__codelineno-49-31"></a><span class="p">}</span>
|
||||||
<a id="__codelineno-49-32" name="__codelineno-49-32" href="#__codelineno-49-32"></a><span class="p">}</span>
|
|
||||||
</code></pre></div>
|
</code></pre></div>
|
||||||
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|
||||||
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|
||||||
@@ -5004,11 +5035,73 @@
|
|||||||
<li><strong>获取最大的 <span class="arithmatex">\(k\)</span> 个元素</strong>：这是一个经典的算法问题，同时也是一种典型应用，例如选择热度前 10 的新闻作为微博热搜，选取销量前 10 的商品等。</li>
|
<li><strong>获取最大的 <span class="arithmatex">\(k\)</span> 个元素</strong>：这是一个经典的算法问题，同时也是一种典型应用，例如选择热度前 10 的新闻作为微博热搜，选取销量前 10 的商品等。</li>
|
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
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<h1 id="8">第 8 章 堆<a class="headerlink" href="#8" title="Permanent link">¶</a></h1>
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<h1 id="8">第 8 章 堆<a class="headerlink" href="#8" title="Permanent link">¶</a></h1>
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||||||
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<li><a href="https://www.hello-algo.com/chapter_heap/summary/">8.4 小结</a></li>
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Permission is hereby granted, free of charge, to any person obtaining a copy
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7.6 小结
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|
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|
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|
of this software and associated documentation files (the "Software"), to
|
||||||
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deal in the Software without restriction, including without limitation the
|
||||||
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rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
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|
||||||
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furnished to do so, subject to the following conditions:
|
||||||
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|
||||||
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|
||||||
|
all copies or substantial portions of the Software.
|
||||||
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|
||||||
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
||||||
|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
||||||
|
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
|
||||||
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
||||||
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||||
|
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
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IN THE SOFTWARE.
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_heap/summary.md" title="编辑此页" class="md-content__button md-icon">
|
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|
|||||||
|
|
||||||
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|
||||||
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|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
|
||||||
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|
||||||
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|
||||||
<h1 id="84">8.4 小结<a class="headerlink" href="#84" title="Permanent link">¶</a></h1>
|
<h1 id="84">8.4 小结<a class="headerlink" href="#84" title="Permanent link">¶</a></h1>
|
||||||
<h3 id="1">1. 重点回顾<a class="headerlink" href="#1" title="Permanent link">¶</a></h3>
|
<h3 id="1">1. 重点回顾<a class="headerlink" href="#1" title="Permanent link">¶</a></h3>
|
||||||
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|
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|
||||||
@@ -3458,11 +3490,73 @@
|
|||||||
<p>两者不是同一个概念，只是碰巧都叫堆。计算机系统内存中的堆是动态内存分配的一部分，程序在运行时可以使用它来存储数据。程序可以请求一定量的堆内存，用于存储如对象和数组等复杂结构。当这些数据不再需要时，程序需要释放这些内存，以防止内存泄露。相较于栈内存，堆内存的管理和使用需要更谨慎，不恰当的使用可能会导致内存泄露和野指针等问题。</p>
|
<p>两者不是同一个概念，只是碰巧都叫堆。计算机系统内存中的堆是动态内存分配的一部分，程序在运行时可以使用它来存储数据。程序可以请求一定量的堆内存，用于存储如对象和数组等复杂结构。当这些数据不再需要时，程序需要释放这些内存，以防止内存泄露。相较于栈内存，堆内存的管理和使用需要更谨慎，不恰当的使用可能会导致内存泄露和野指针等问题。</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
<!-- Source file information -->
|
||||||
|
|
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|
|
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|
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|
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|
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|
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Permission is hereby granted, free of charge, to any person obtaining a copy
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deal in the Software without restriction, including without limitation the
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rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in
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all copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
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|
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
|
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|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
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|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_heap/top_k.md" title="编辑此页" class="md-content__button md-icon">
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|
|||||||
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|
||||||
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||||||
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||||||
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|
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|
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|
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|
<!-- Page content -->
|
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<h1 id="83-top-k">8.3 Top-K 问题<a class="headerlink" href="#83-top-k" title="Permanent link">¶</a></h1>
|
<h1 id="83-top-k">8.3 Top-K 问题<a class="headerlink" href="#83-top-k" title="Permanent link">¶</a></h1>
|
||||||
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|
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|
<h5 align="center" id="__comments">欢迎你提出疑问或建议</h5>
|
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<!-- Insert generated snippet here -->
|
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|
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<script
|
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src="https://giscus.app/client.js"
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Copyright (c) 2016-2023 Martin Donath <martin.donath@squidfunk.com>
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|
Permission is hereby granted, free of charge, to any person obtaining a copy
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<nav class="md-footer__inner md-grid" aria-label="页脚" >
|
of this software and associated documentation files (the "Software"), to
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deal in the Software without restriction, including without limitation the
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|
rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
|
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<a href="../build_heap/" class="md-footer__link md-footer__link--prev" aria-label="上一页: 8.2 &nbsp; 建堆操作" rel="prev">
|
sell copies of the Software, and to permit persons to whom the Software is
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<div class="md-footer__button md-icon">
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furnished to do so, subject to the following conditions:
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11h12Z"/></svg>
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The above copyright notice and this permission notice shall be included in
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</div>
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all copies or substantial portions of the Software.
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<div class="md-footer__title">
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<span class="md-footer__direction">
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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</span>
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FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
|
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<div class="md-ellipsis">
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
||||||
8.2 建堆操作
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
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</div>
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FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
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</div>
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IN THE SOFTWARE.
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|
||||||
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||||||
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Permission is hereby granted, free of charge, to any person obtaining a copy
|
||||||
|
of this software and associated documentation files (the "Software"), to
|
||||||
|
deal in the Software without restriction, including without limitation the
|
||||||
|
rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
|
||||||
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sell copies of the Software, and to permit persons to whom the Software is
|
||||||
|
furnished to do so, subject to the following conditions:
|
||||||
|
|
||||||
|
The above copyright notice and this permission notice shall be included in
|
||||||
|
all copies or substantial portions of the Software.
|
||||||
|
|
||||||
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
||||||
|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
||||||
|
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
|
||||||
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
||||||
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||||
|
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
|
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IN THE SOFTWARE.
|
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|
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|
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_introduction/algorithms_are_everywhere.md" title="编辑此页" class="md-content__button md-icon">
|
<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_introduction/algorithms_are_everywhere.md" title="编辑此页" class="md-content__button md-icon">
|
||||||
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|
|||||||
|
|
||||||
|
|
||||||
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|
||||||
|
<!--
|
||||||
|
Hack: check whether the content contains a h1 headline. If it doesn't, the
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<h1 id="11">1.1 算法无处不在<a class="headerlink" href="#11" title="Permanent link">¶</a></h1>
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<h1 id="11">1.1 算法无处不在<a class="headerlink" href="#11" title="Permanent link">¶</a></h1>
|
||||||
<p>当我们听到“算法”这个词时，很自然地会想到数学。然而实际上，许多算法并不涉及复杂数学，而是更多地依赖于基本逻辑，这些逻辑在我们的日常生活中处处可见。</p>
|
<p>当我们听到“算法”这个词时，很自然地会想到数学。然而实际上，许多算法并不涉及复杂数学，而是更多地依赖于基本逻辑，这些逻辑在我们的日常生活中处处可见。</p>
|
||||||
<p>在正式探讨算法之前，有一个有趣的事实值得分享：<strong>你已经在不知不觉中学会了许多算法，并习惯将它们应用到日常生活中了</strong>。下面，我将举几个具体例子来证实这一点。</p>
|
<p>在正式探讨算法之前，有一个有趣的事实值得分享：<strong>你已经在不知不觉中学会了许多算法，并习惯将它们应用到日常生活中了</strong>。下面，我将举几个具体例子来证实这一点。</p>
|
||||||
@@ -3434,11 +3466,73 @@
|
|||||||
<p>如果你对数据结构、算法、数组和二分查找等概念仍感到一知半解，请继续往下阅读，这本书将引导你迈入数据结构与算法的知识殿堂。</p>
|
<p>如果你对数据结构、算法、数组和二分查找等概念仍感到一知半解，请继续往下阅读，这本书将引导你迈入数据结构与算法的知识殿堂。</p>
|
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<h1 id="1">第 1 章 初识算法<a class="headerlink" href="#1" title="Permanent link">¶</a></h1>
|
<h1 id="1">第 1 章 初识算法<a class="headerlink" href="#1" title="Permanent link">¶</a></h1>
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<li><a href="https://www.hello-algo.com/chapter_introduction/summary/">1.3 小结</a></li>
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<li><a href="https://www.hello-algo.com/chapter_introduction/summary/">1.3 小结</a></li>
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<h1 id="13">1.3 小结<a class="headerlink" href="#13" title="Permanent link">¶</a></h1>
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<h1 id="13">1.3 小结<a class="headerlink" href="#13" title="Permanent link">¶</a></h1>
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||||||
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<li>算法在日常生活中无处不在，并不是遥不可及的高深知识。实际上，我们已经在不知不觉中学会了许多算法，用以解决生活中的大小问题。</li>
|
<li>算法在日常生活中无处不在，并不是遥不可及的高深知识。实际上，我们已经在不知不觉中学会了许多算法，用以解决生活中的大小问题。</li>
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<li>我们可以将数据结构与算法类比为拼装积木，积木代表数据，积木的形状和连接方式代表数据结构，拼装积木的步骤则对应算法。</li>
|
<li>我们可以将数据结构与算法类比为拼装积木，积木代表数据，积木的形状和连接方式代表数据结构，拼装积木的步骤则对应算法。</li>
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<h1 id="12">1.2 算法是什么<a class="headerlink" href="#12" title="Permanent link">¶</a></h1>
|
<h1 id="12">1.2 算法是什么<a class="headerlink" href="#12" title="Permanent link">¶</a></h1>
|
||||||
<h2 id="121">1.2.1 算法定义<a class="headerlink" href="#121" title="Permanent link">¶</a></h2>
|
<h2 id="121">1.2.1 算法定义<a class="headerlink" href="#121" title="Permanent link">¶</a></h2>
|
||||||
<p>「算法 algorithm」是在有限时间内解决特定问题的一组指令或操作步骤，它具有以下特性。</p>
|
<p>「算法 algorithm」是在有限时间内解决特定问题的一组指令或操作步骤，它具有以下特性。</p>
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||||||
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<p>在实际讨论时，我们通常会将“数据结构与算法”简称为“算法”。比如众所周知的 LeetCode 算法题目，实际上同时考察了数据结构和算法两方面的知识。</p>
|
<p>在实际讨论时，我们通常会将“数据结构与算法”简称为“算法”。比如众所周知的 LeetCode 算法题目，实际上同时考察了数据结构和算法两方面的知识。</p>
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The above copyright notice and this permission notice shall be included in
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<h1 id="01">0.1 关于本书<a class="headerlink" href="#01" title="Permanent link">¶</a></h1>
|
<h1 id="01">0.1 关于本书<a class="headerlink" href="#01" title="Permanent link">¶</a></h1>
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<p>本项目旨在创建一本开源免费、新手友好的数据结构与算法入门教程。</p>
|
<p>本项目旨在创建一本开源免费、新手友好的数据结构与算法入门教程。</p>
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<p>本书倡导手脑并用的学习方式，在这一点上深受<a href="https://github.com/d2l-ai/d2l-zh">《动手学深度学习》</a>的启发。在此向各位读者强烈推荐这本优秀著作。</p>
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<p>本书倡导手脑并用的学习方式，在这一点上深受<a href="https://github.com/d2l-ai/d2l-zh">《动手学深度学习》</a>的启发。在此向各位读者强烈推荐这本优秀著作。</p>
|
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<p>衷心感谢我的父母，正是你们一直以来的支持与鼓励，让我有机会做这件富有趣味的事。</p>
|
<p>衷心感谢我的父母，正是你们一直以来的支持与鼓励，让我有机会做这件富有趣味的事。</p>
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deal in the Software without restriction, including without limitation the
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sell copies of the Software, and to permit persons to whom the Software is
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The above copyright notice and this permission notice shall be included in
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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||||||
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<!-- Page content -->
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<h1 id="0">第 0 章 前言<a class="headerlink" href="#0" title="Permanent link">¶</a></h1>
|
<h1 id="0">第 0 章 前言<a class="headerlink" href="#0" title="Permanent link">¶</a></h1>
|
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|
||||||
<p><img alt="前言" src="../assets/covers/chapter_preface.jpg" width="600" /></p>
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|
||||||
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|
|||||||
<li><a href="https://www.hello-algo.com/chapter_preface/summary/">0.3 小结</a></li>
|
<li><a href="https://www.hello-algo.com/chapter_preface/summary/">0.3 小结</a></li>
|
||||||
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|
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_preface/suggestions.md" title="编辑此页" class="md-content__button md-icon">
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<h1 id="02">0.2 如何使用本书<a class="headerlink" href="#02" title="Permanent link">¶</a></h1>
|
<h1 id="02">0.2 如何使用本书<a class="headerlink" href="#02" title="Permanent link">¶</a></h1>
|
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<div class="admonition tip">
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<div class="admonition tip">
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<p class="admonition-title">Tip</p>
|
<p class="admonition-title">Tip</p>
|
||||||
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|
|||||||
<p><img alt="算法学习路线" src="../suggestions.assets/learning_route.png" /></p>
|
<p><img alt="算法学习路线" src="../suggestions.assets/learning_route.png" /></p>
|
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<p align="center"> 图 0-7 算法学习路线 </p>
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<p align="center"> 图 0-7 算法学习路线 </p>
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<h5 align="center" id="__comments">欢迎你提出疑问或建议</h5>
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<script
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|
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Copyright (c) 2016-2023 Martin Donath <martin.donath@squidfunk.com>
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Permission is hereby granted, free of charge, to any person obtaining a copy
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deal in the Software without restriction, including without limitation the
|
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|
rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
|
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|
sell copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in
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all copies or substantial portions of the Software.
|
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
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|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
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|
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
|
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|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
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FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
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|
<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_preface/summary.md" title="编辑此页" class="md-content__button md-icon">
|
||||||
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|
|||||||
|
|
||||||
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|
||||||
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|
||||||
|
<!--
|
||||||
|
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|
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|
page title (or respectively site name) is used as the main headline.
|
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|
-->
|
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|
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|
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|
<!-- Page content -->
|
||||||
<h1 id="03">0.3 小结<a class="headerlink" href="#03" title="Permanent link">¶</a></h1>
|
<h1 id="03">0.3 小结<a class="headerlink" href="#03" title="Permanent link">¶</a></h1>
|
||||||
<ul>
|
<ul>
|
||||||
<li>本书的主要受众是算法初学者。如果已有一定基础，本书能帮助您系统回顾算法知识，书内源代码也可作为“刷题工具库”使用。</li>
|
<li>本书的主要受众是算法初学者。如果已有一定基础，本书能帮助您系统回顾算法知识，书内源代码也可作为“刷题工具库”使用。</li>
|
||||||
@@ -3385,11 +3417,73 @@
|
|||||||
<li>本书网页版的每个章节都设有讨论区，欢迎随时分享你的疑惑与见解。</li>
|
<li>本书网页版的每个章节都设有讨论区，欢迎随时分享你的疑惑与见解。</li>
|
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0.2 如何使用本书
|
||||||
|
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|
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|
</div>
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第 1 章 初识算法
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|
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</a>
|
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<h1 id="_1">参考文献<a class="headerlink" href="#_1" title="Permanent link">¶</a></h1>
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<h1 id="_1">参考文献<a class="headerlink" href="#_1" title="Permanent link">¶</a></h1>
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||||||
<p>[1] Thomas H. Cormen, et al. Introduction to Algorithms (3<sup>rd</sup> Edition).</p>
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<p>[1] Thomas H. Cormen, et al. Introduction to Algorithms (3<sup>rd</sup> Edition).</p>
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||||||
<p>[2] Aditya Bhargava. Grokking Algorithms: An Illustrated Guide for Programmers and Other Curious People (1<sup>st</sup> Edition).</p>
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<p>[8] Gayle Laakmann McDowell. Cracking the Coding Interview: 189 Programming Questions and Solutions (6<sup>th</sup> Edition). </p>
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<p>[8] Gayle Laakmann McDowell. Cracking the Coding Interview: 189 Programming Questions and Solutions (6<sup>th</sup> Edition). </p>
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<p>[9] Aston Zhang, et al. Dive into Deep Learning.</p>
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<h1 id="101">10.1 二分查找<a class="headerlink" href="#101" title="Permanent link">¶</a></h1>
|
<h1 id="101">10.1 二分查找<a class="headerlink" href="#101" title="Permanent link">¶</a></h1>
|
||||||
<p>「二分查找 binary search」是一种基于分治策略的高效搜索算法。它利用数据的有序性，每轮减少一半搜索范围，直至找到目标元素或搜索区间为空为止。</p>
|
<p>「二分查找 binary search」是一种基于分治策略的高效搜索算法。它利用数据的有序性，每轮减少一半搜索范围，直至找到目标元素或搜索区间为空为止。</p>
|
||||||
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||||||
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|||||||
<li>小数据量下，线性查找性能更佳。在线性查找中，每轮只需要 1 次判断操作；而在二分查找中，需要 1 次加法、1 次除法、1 ~ 3 次判断操作、1 次加法（减法），共 4 ~ 6 个单元操作；因此，当数据量 <span class="arithmatex">\(n\)</span> 较小时，线性查找反而比二分查找更快。</li>
|
<li>小数据量下，线性查找性能更佳。在线性查找中，每轮只需要 1 次判断操作；而在二分查找中，需要 1 次加法、1 次除法、1 ~ 3 次判断操作、1 次加法（减法），共 4 ~ 6 个单元操作；因此，当数据量 <span class="arithmatex">\(n\)</span> 较小时，线性查找反而比二分查找更快。</li>
|
||||||
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第 10 章 搜索
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|
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of this software and associated documentation files (the "Software"), to
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||||||
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deal in the Software without restriction, including without limitation the
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|
||||||
|
furnished to do so, subject to the following conditions:
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|
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|
The above copyright notice and this permission notice shall be included in
|
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|
all copies or substantial portions of the Software.
|
||||||
|
|
||||||
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
||||||
|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
||||||
|
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
|
||||||
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
||||||
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||||
|
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
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IN THE SOFTWARE.
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-->
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|
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_searching/binary_search_edge.md" title="编辑此页" class="md-content__button md-icon">
|
<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_searching/binary_search_edge.md" title="编辑此页" class="md-content__button md-icon">
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|
|||||||
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||||||
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||||||
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|
||||||
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|
||||||
|
-->
|
||||||
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|
||||||
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|
||||||
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|
||||||
<h1 id="103">10.3 二分查找边界<a class="headerlink" href="#103" title="Permanent link">¶</a></h1>
|
<h1 id="103">10.3 二分查找边界<a class="headerlink" href="#103" title="Permanent link">¶</a></h1>
|
||||||
<h2 id="1031">10.3.1 查找左边界<a class="headerlink" href="#1031" title="Permanent link">¶</a></h2>
|
<h2 id="1031">10.3.1 查找左边界<a class="headerlink" href="#1031" title="Permanent link">¶</a></h2>
|
||||||
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|
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|
||||||
@@ -3870,11 +3902,73 @@
|
|||||||
<li>因为该方法引入了小数，所以需要将函数中的变量 <code>target</code> 改为浮点数类型。</li>
|
<li>因为该方法引入了小数，所以需要将函数中的变量 <code>target</code> 改为浮点数类型。</li>
|
||||||
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|
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|
||||||
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href="../binary_search_insertion/"
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|
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|
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|
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|
<h5 align="center" id="__comments">欢迎你提出疑问或建议</h5>
|
||||||
<!-- Insert generated snippet here -->
|
<!-- Insert generated snippet here -->
|
||||||
<script
|
<script
|
||||||
src="https://giscus.app/client.js"
|
src="https://giscus.app/client.js"
|
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|
|
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</main>
|
</main>
|
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|
|
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<footer class="md-footer">
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|
Copyright (c) 2016-2023 Martin Donath <martin.donath@squidfunk.com>
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|
|
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|
Permission is hereby granted, free of charge, to any person obtaining a copy
|
||||||
<nav class="md-footer__inner md-grid" aria-label="页脚" >
|
of this software and associated documentation files (the "Software"), to
|
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|
deal in the Software without restriction, including without limitation the
|
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|
rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
|
||||||
<a href="../binary_search_insertion/" class="md-footer__link md-footer__link--prev" aria-label="上一页: 10.2 &nbsp; 二分查找插入点" rel="prev">
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sell copies of the Software, and to permit persons to whom the Software is
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<div class="md-footer__button md-icon">
|
furnished to do so, subject to the following conditions:
|
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11h12Z"/></svg>
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The above copyright notice and this permission notice shall be included in
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</div>
|
all copies or substantial portions of the Software.
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<div class="md-footer__title">
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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上一页
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
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</span>
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FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
|
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<div class="md-ellipsis">
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
||||||
10.2 二分查找插入点
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
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</div>
|
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
|
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</div>
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|
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<a href="../replace_linear_by_hashing/" class="md-footer__link md-footer__link--next" aria-label="下一页: 10.4 &nbsp; 哈希优化策略" rel="next">
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|
|
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|
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|
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|
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|
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|
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||||||
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|
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|
||||||
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|
||||||
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|
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|
Copyright (c) 2016-2023 Martin Donath <martin.donath@squidfunk.com>
|
||||||
|
|
||||||
|
Permission is hereby granted, free of charge, to any person obtaining a copy
|
||||||
|
of this software and associated documentation files (the "Software"), to
|
||||||
|
deal in the Software without restriction, including without limitation the
|
||||||
|
rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
|
||||||
|
sell copies of the Software, and to permit persons to whom the Software is
|
||||||
|
furnished to do so, subject to the following conditions:
|
||||||
|
|
||||||
|
The above copyright notice and this permission notice shall be included in
|
||||||
|
all copies or substantial portions of the Software.
|
||||||
|
|
||||||
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
||||||
|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
||||||
|
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
|
||||||
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
||||||
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||||
|
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
|
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|
IN THE SOFTWARE.
|
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|
-->
|
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|
|
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|
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|
||||||
|
|
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|
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|
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|
||||||
|
|
||||||
|
|
||||||
<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_searching/binary_search_insertion.md" title="编辑此页" class="md-content__button md-icon">
|
<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_searching/binary_search_insertion.md" title="编辑此页" class="md-content__button md-icon">
|
||||||
@@ -3449,6 +3474,13 @@
|
|||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
<!--
|
||||||
|
Hack: check whether the content contains a h1 headline. If it doesn't, the
|
||||||
|
page title (or respectively site name) is used as the main headline.
|
||||||
|
-->
|
||||||
|
|
||||||
|
|
||||||
|
<!-- Page content -->
|
||||||
<h1 id="102">10.2 二分查找插入点<a class="headerlink" href="#102" title="Permanent link">¶</a></h1>
|
<h1 id="102">10.2 二分查找插入点<a class="headerlink" href="#102" title="Permanent link">¶</a></h1>
|
||||||
<p>二分查找不仅可用于搜索目标元素，还具有许多变种问题，比如搜索目标元素的插入位置。</p>
|
<p>二分查找不仅可用于搜索目标元素，还具有许多变种问题，比如搜索目标元素的插入位置。</p>
|
||||||
<h2 id="1021">10.2.1 无重复元素的情况<a class="headerlink" href="#1021" title="Permanent link">¶</a></h2>
|
<h2 id="1021">10.2.1 无重复元素的情况<a class="headerlink" href="#1021" title="Permanent link">¶</a></h2>
|
||||||
@@ -3970,11 +4002,73 @@
|
|||||||
<p>总的来看，二分查找无非就是给指针 <span class="arithmatex">\(i\)</span> 和 <span class="arithmatex">\(j\)</span> 分别设定搜索目标，目标可能是一个具体的元素（例如 <code>target</code> ），也可能是一个元素范围（例如小于 <code>target</code> 的元素）。</p>
|
<p>总的来看，二分查找无非就是给指针 <span class="arithmatex">\(i\)</span> 和 <span class="arithmatex">\(j\)</span> 分别设定搜索目标，目标可能是一个具体的元素（例如 <code>target</code> ），也可能是一个元素范围（例如小于 <code>target</code> 的元素）。</p>
|
||||||
<p>在不断的循环二分中，指针 <span class="arithmatex">\(i\)</span> 和 <span class="arithmatex">\(j\)</span> 都逐渐逼近预先设定的目标。最终，它们或是成功找到答案，或是越过边界后停止。</p>
|
<p>在不断的循环二分中，指针 <span class="arithmatex">\(i\)</span> 和 <span class="arithmatex">\(j\)</span> 都逐渐逼近预先设定的目标。最终，它们或是成功找到答案，或是越过边界后停止。</p>
|
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|
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|
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|
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<script
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<script
|
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src="https://giscus.app/client.js"
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src="https://giscus.app/client.js"
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@@ -4040,48 +4134,31 @@
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10.1 二分查找
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<div class="md-footer__button md-icon">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M4 11v2h12l-5.5 5.5 1.42 1.42L19.84 12l-7.92-7.92L10.5 5.5 16 11H4Z"/></svg>
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|
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+123
-44
@@ -3369,7 +3369,32 @@
|
|||||||
<div class="md-content" data-md-component="content">
|
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|
||||||
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|
<article class="md-content__inner md-typeset">
|
||||||
|
|
||||||
|
<!--
|
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|
Copyright (c) 2016-2023 Martin Donath <martin.donath@squidfunk.com>
|
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|
|
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|
Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to
|
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|
deal in the Software without restriction, including without limitation the
|
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|
rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
|
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|
sell copies of the Software, and to permit persons to whom the Software is
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||||||
|
furnished to do so, subject to the following conditions:
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|
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|
The above copyright notice and this permission notice shall be included in
|
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|
all copies or substantial portions of the Software.
|
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|
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|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
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|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
||||||
|
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
|
||||||
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
||||||
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||||
|
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
|
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IN THE SOFTWARE.
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-->
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|
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<!-- Actions -->
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|
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|
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_searching/index.md" title="编辑此页" class="md-content__button md-icon">
|
<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_searching/index.md" title="编辑此页" class="md-content__button md-icon">
|
||||||
@@ -3380,6 +3405,13 @@
|
|||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
<!--
|
||||||
|
Hack: check whether the content contains a h1 headline. If it doesn't, the
|
||||||
|
page title (or respectively site name) is used as the main headline.
|
||||||
|
-->
|
||||||
|
|
||||||
|
|
||||||
|
<!-- Page content -->
|
||||||
<h1 id="10">第 10 章 搜索<a class="headerlink" href="#10" title="Permanent link">¶</a></h1>
|
<h1 id="10">第 10 章 搜索<a class="headerlink" href="#10" title="Permanent link">¶</a></h1>
|
||||||
<div class="center-table">
|
<div class="center-table">
|
||||||
<p><img alt="搜索" src="../assets/covers/chapter_searching.jpg" width="600" /></p>
|
<p><img alt="搜索" src="../assets/covers/chapter_searching.jpg" width="600" /></p>
|
||||||
@@ -3399,11 +3431,73 @@
|
|||||||
<li><a href="https://www.hello-algo.com/chapter_searching/summary/">10.6 小结</a></li>
|
<li><a href="https://www.hello-algo.com/chapter_searching/summary/">10.6 小结</a></li>
|
||||||
</ul>
|
</ul>
|
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|
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|
<!-- Source file information -->
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class="md-footer__link md-footer__link--prev"
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9.4 小结
|
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|
</div>
|
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|
</div>
|
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|
</a>
|
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|
|
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|
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class="md-footer__link md-footer__link--next"
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<div class="md-footer__button md-icon">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M4 11v2h12l-5.5 5.5 1.42 1.42L19.84 12l-7.92-7.92L10.5 5.5 16 11H4Z"/></svg>
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|
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|
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</nav>
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|
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|
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|
<h5 align="center" id="__comments">欢迎你提出疑问或建议</h5>
|
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<!-- Insert generated snippet here -->
|
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|
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<script
|
<script
|
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src="https://giscus.app/client.js"
|
src="https://giscus.app/client.js"
|
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@@ -3469,48 +3563,31 @@
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</main>
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<footer class="md-footer">
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Copyright (c) 2016-2023 Martin Donath <martin.donath@squidfunk.com>
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|
Permission is hereby granted, free of charge, to any person obtaining a copy
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<nav class="md-footer__inner md-grid" aria-label="页脚" >
|
of this software and associated documentation files (the "Software"), to
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deal in the Software without restriction, including without limitation the
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rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
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<a href="../chapter_graph/summary/" class="md-footer__link md-footer__link--prev" aria-label="上一页: 9.4 &nbsp; 小结" rel="prev">
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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</span>
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FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
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<div class="md-ellipsis">
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
||||||
9.4 小结
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
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</div>
|
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
|
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</div>
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</a>
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|
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下一页
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10.1 二分查找
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|
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|
|
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|
|
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<div class="md-footer__button md-icon">
|
|
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|
|
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|
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|
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@@ -3521,6 +3598,8 @@
|
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|
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|
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|
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|
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|
|
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|
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|
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|
<div class="md-social">
|
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|
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|
|||||||
@@ -3430,7 +3430,32 @@
|
|||||||
<div class="md-content" data-md-component="content">
|
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|
||||||
<article class="md-content__inner md-typeset">
|
<article class="md-content__inner md-typeset">
|
||||||
|
|
||||||
|
<!--
|
||||||
|
Copyright (c) 2016-2023 Martin Donath <martin.donath@squidfunk.com>
|
||||||
|
|
||||||
|
Permission is hereby granted, free of charge, to any person obtaining a copy
|
||||||
|
of this software and associated documentation files (the "Software"), to
|
||||||
|
deal in the Software without restriction, including without limitation the
|
||||||
|
rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
|
||||||
|
sell copies of the Software, and to permit persons to whom the Software is
|
||||||
|
furnished to do so, subject to the following conditions:
|
||||||
|
|
||||||
|
The above copyright notice and this permission notice shall be included in
|
||||||
|
all copies or substantial portions of the Software.
|
||||||
|
|
||||||
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
||||||
|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
||||||
|
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
|
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|
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<h1 id="104">10.4 哈希优化策略<a class="headerlink" href="#104" title="Permanent link">¶</a></h1>
|
<h1 id="104">10.4 哈希优化策略<a class="headerlink" href="#104" title="Permanent link">¶</a></h1>
|
||||||
<p>在算法题中，<strong>我们常通过将线性查找替换为哈希查找来降低算法的时间复杂度</strong>。我们借助一个算法题来加深理解。</p>
|
<p>在算法题中，<strong>我们常通过将线性查找替换为哈希查找来降低算法的时间复杂度</strong>。我们借助一个算法题来加深理解。</p>
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<p>此方法通过哈希查找将时间复杂度从 <span class="arithmatex">\(O(n^2)\)</span> 降低至 <span class="arithmatex">\(O(n)\)</span> ，大幅提升运行效率。</p>
|
<p>此方法通过哈希查找将时间复杂度从 <span class="arithmatex">\(O(n^2)\)</span> 降低至 <span class="arithmatex">\(O(n)\)</span> ，大幅提升运行效率。</p>
|
||||||
<p>由于需要维护一个额外的哈希表，因此空间复杂度为 <span class="arithmatex">\(O(n)\)</span> 。<strong>尽管如此，该方法的整体时空效率更为均衡，因此它是本题的最优解法</strong>。</p>
|
<p>由于需要维护一个额外的哈希表，因此空间复杂度为 <span class="arithmatex">\(O(n)\)</span> 。<strong>尽管如此，该方法的整体时空效率更为均衡，因此它是本题的最优解法</strong>。</p>
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<h1 id="105">10.5 重识搜索算法<a class="headerlink" href="#105" title="Permanent link">¶</a></h1>
|
<h1 id="105">10.5 重识搜索算法<a class="headerlink" href="#105" title="Permanent link">¶</a></h1>
|
||||||
<p>「搜索算法 searching algorithm」用于在数据结构（例如数组、链表、树或图）中搜索一个或一组满足特定条件的元素。</p>
|
<p>「搜索算法 searching algorithm」用于在数据结构（例如数组、链表、树或图）中搜索一个或一组满足特定条件的元素。</p>
|
||||||
<p>搜索算法可根据实现思路分为以下两类。</p>
|
<p>搜索算法可根据实现思路分为以下两类。</p>
|
||||||
@@ -3577,11 +3609,73 @@
|
|||||||
<li>若使用 AVL 树或红黑树，则各项操作可在 <span class="arithmatex">\(O(\log n)\)</span> 效率下稳定运行，但维护树平衡的操作会增加额外开销。</li>
|
<li>若使用 AVL 树或红黑树，则各项操作可在 <span class="arithmatex">\(O(\log n)\)</span> 效率下稳定运行，但维护树平衡的操作会增加额外开销。</li>
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<h1 id="106">10.6 小结<a class="headerlink" href="#106" title="Permanent link">¶</a></h1>
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||||||
<li>二分查找依赖于数据的有序性，通过循环逐步缩减一半搜索区间来实现查找。它要求输入数据有序，且仅适用于数组或基于数组实现的数据结构。</li>
|
<li>二分查找依赖于数据的有序性，通过循环逐步缩减一半搜索区间来实现查找。它要求输入数据有序，且仅适用于数组或基于数组实现的数据结构。</li>
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<li>用哈希查找替换线性查找是一种常用的优化运行时间的策略，可将时间复杂度从 <span class="arithmatex">\(O(n)\)</span> 降低至 <span class="arithmatex">\(O(1)\)</span> 。</li>
|
<li>用哈希查找替换线性查找是一种常用的优化运行时间的策略，可将时间复杂度从 <span class="arithmatex">\(O(n)\)</span> 降低至 <span class="arithmatex">\(O(1)\)</span> 。</li>
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<h1 id="113">11.3 冒泡排序<a class="headerlink" href="#113" title="Permanent link">¶</a></h1>
|
<h1 id="113">11.3 冒泡排序<a class="headerlink" href="#113" title="Permanent link">¶</a></h1>
|
||||||
<p>「冒泡排序 bubble sort」通过连续地比较与交换相邻元素实现排序。这个过程就像气泡从底部升到顶部一样，因此得名冒泡排序。</p>
|
<p>「冒泡排序 bubble sort」通过连续地比较与交换相邻元素实现排序。这个过程就像气泡从底部升到顶部一样，因此得名冒泡排序。</p>
|
||||||
<p>如图 11-4 所示，冒泡过程可以利用元素交换操作来模拟：从数组最左端开始向右遍历，依次比较相邻元素大小，如果“左元素 > 右元素”就交换它俩。遍历完成后，最大的元素会被移动到数组的最右端。</p>
|
<p>如图 11-4 所示，冒泡过程可以利用元素交换操作来模拟：从数组最左端开始向右遍历，依次比较相邻元素大小，如果“左元素 > 右元素”就交换它俩。遍历完成后，最大的元素会被移动到数组的最右端。</p>
|
||||||
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|||||||
<li><strong>稳定排序</strong>：由于在“冒泡”中遇到相等元素不交换。</li>
|
<li><strong>稳定排序</strong>：由于在“冒泡”中遇到相等元素不交换。</li>
|
||||||
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<h1 id="118">11.8 桶排序<a class="headerlink" href="#118" title="Permanent link">¶</a></h1>
|
<h1 id="118">11.8 桶排序<a class="headerlink" href="#118" title="Permanent link">¶</a></h1>
|
||||||
<p>前述的几种排序算法都属于“基于比较的排序算法”，它们通过比较元素间的大小来实现排序。此类排序算法的时间复杂度无法超越 <span class="arithmatex">\(O(n \log n)\)</span> 。接下来，我们将探讨几种“非比较排序算法”，它们的时间复杂度可以达到线性阶。</p>
|
<p>前述的几种排序算法都属于“基于比较的排序算法”，它们通过比较元素间的大小来实现排序。此类排序算法的时间复杂度无法超越 <span class="arithmatex">\(O(n \log n)\)</span> 。接下来，我们将探讨几种“非比较排序算法”，它们的时间复杂度可以达到线性阶。</p>
|
||||||
<p>「桶排序 bucket sort」是分治策略的一个典型应用。它通过设置一些具有大小顺序的桶，每个桶对应一个数据范围，将数据平均分配到各个桶中；然后，在每个桶内部分别执行排序；最终按照桶的顺序将所有数据合并。</p>
|
<p>「桶排序 bucket sort」是分治策略的一个典型应用。它通过设置一些具有大小顺序的桶，每个桶对应一个数据范围，将数据平均分配到各个桶中；然后，在每个桶内部分别执行排序；最终按照桶的顺序将所有数据合并。</p>
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<p><img alt="根据概率分布划分桶" src="../bucket_sort.assets/scatter_in_buckets_distribution.png" /></p>
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<p><img alt="根据概率分布划分桶" src="../bucket_sort.assets/scatter_in_buckets_distribution.png" /></p>
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||||||
<p align="center"> 图 11-15 根据概率分布划分桶 </p>
|
<p align="center"> 图 11-15 根据概率分布划分桶 </p>
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|
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|
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<h1 id="119">11.9 计数排序<a class="headerlink" href="#119" title="Permanent link">¶</a></h1>
|
<h1 id="119">11.9 计数排序<a class="headerlink" href="#119" title="Permanent link">¶</a></h1>
|
||||||
<p>「计数排序 counting sort」通过统计元素数量来实现排序，通常应用于整数数组。</p>
|
<p>「计数排序 counting sort」通过统计元素数量来实现排序，通常应用于整数数组。</p>
|
||||||
<h2 id="1191">11.9.1 简单实现<a class="headerlink" href="#1191" title="Permanent link">¶</a></h2>
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<h2 id="1191">11.9.1 简单实现<a class="headerlink" href="#1191" title="Permanent link">¶</a></h2>
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<p><strong>计数排序只适用于非负整数</strong>。若想要将其用于其他类型的数据，需要确保这些数据可以被转换为非负整数，并且在转换过程中不能改变各个元素之间的相对大小关系。例如，对于包含负数的整数数组，可以先给所有数字加上一个常数，将全部数字转化为正数，排序完成后再转换回去即可。</p>
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<p><strong>计数排序只适用于非负整数</strong>。若想要将其用于其他类型的数据，需要确保这些数据可以被转换为非负整数，并且在转换过程中不能改变各个元素之间的相对大小关系。例如，对于包含负数的整数数组，可以先给所有数字加上一个常数，将全部数字转化为正数，排序完成后再转换回去即可。</p>
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<p><strong>计数排序适用于数据量大但数据范围较小的情况</strong>。比如，在上述示例中 <span class="arithmatex">\(m\)</span> 不能太大，否则会占用过多空间。而当 <span class="arithmatex">\(n \ll m\)</span> 时，计数排序使用 <span class="arithmatex">\(O(m)\)</span> 时间，可能比 <span class="arithmatex">\(O(n \log n)\)</span> 的排序算法还要慢。</p>
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<p><strong>计数排序适用于数据量大但数据范围较小的情况</strong>。比如，在上述示例中 <span class="arithmatex">\(m\)</span> 不能太大，否则会占用过多空间。而当 <span class="arithmatex">\(n \ll m\)</span> 时，计数排序使用 <span class="arithmatex">\(O(m)\)</span> 时间，可能比 <span class="arithmatex">\(O(n \log n)\)</span> 的排序算法还要慢。</p>
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<h1 id="117">11.7 堆排序<a class="headerlink" href="#117" title="Permanent link">¶</a></h1>
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<h1 id="117">11.7 堆排序<a class="headerlink" href="#117" title="Permanent link">¶</a></h1>
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<li><strong>非稳定排序</strong>：在交换堆顶元素和堆底元素时，相等元素的相对位置可能发生变化。</li>
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<li><strong>非稳定排序</strong>：在交换堆顶元素和堆底元素时，相等元素的相对位置可能发生变化。</li>
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<h1 id="11">第 11 章 排序<a class="headerlink" href="#11" title="Permanent link">¶</a></h1>
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10.6 小结
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11.1 排序算法
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|
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|
all copies or substantial portions of the Software.
|
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|
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
||||||
|
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
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IN THE SOFTWARE.
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|
<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_sorting/insertion_sort.md" title="编辑此页" class="md-content__button md-icon">
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||||||
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|
||||||
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||||||
|
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|
||||||
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||||||
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||||||
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|
||||||
<h1 id="114">11.4 插入排序<a class="headerlink" href="#114" title="Permanent link">¶</a></h1>
|
<h1 id="114">11.4 插入排序<a class="headerlink" href="#114" title="Permanent link">¶</a></h1>
|
||||||
<p>「插入排序 insertion sort」是一种简单的排序算法，它的工作原理与手动整理一副牌的过程非常相似。</p>
|
<p>「插入排序 insertion sort」是一种简单的排序算法，它的工作原理与手动整理一副牌的过程非常相似。</p>
|
||||||
<p>具体来说，我们在未排序区间选择一个基准元素，将该元素与其左侧已排序区间的元素逐一比较大小，并将该元素插入到正确的位置。</p>
|
<p>具体来说，我们在未排序区间选择一个基准元素，将该元素与其左侧已排序区间的元素逐一比较大小，并将该元素插入到正确的位置。</p>
|
||||||
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|
|||||||
<li>选择排序不稳定，无法应用于多级排序。</li>
|
<li>选择排序不稳定，无法应用于多级排序。</li>
|
||||||
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|
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|
||||||
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|
||||||
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|
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|
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|
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|
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11.3 冒泡排序
|
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|
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|
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11.5 快速排序
|
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|
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|
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<!-- Insert generated snippet here -->
|
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|
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<script
|
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|
||||||
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|
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|
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Copyright (c) 2016-2023 Martin Donath <martin.donath@squidfunk.com>
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|
Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to
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deal in the Software without restriction, including without limitation the
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<div class="md-ellipsis">
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
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11.3 冒泡排序
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
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</div>
|
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
|
||||||
</div>
|
IN THE SOFTWARE.
|
||||||
</a>
|
-->
|
||||||
|
|
||||||
|
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|
||||||
|
<footer class="md-footer">
|
||||||
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|
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Copyright (c) 2016-2023 Martin Donath <martin.donath@squidfunk.com>
|
||||||
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||||||
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Permission is hereby granted, free of charge, to any person obtaining a copy
|
||||||
|
of this software and associated documentation files (the "Software"), to
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||||||
|
deal in the Software without restriction, including without limitation the
|
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rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
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||||||
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sell copies of the Software, and to permit persons to whom the Software is
|
||||||
|
furnished to do so, subject to the following conditions:
|
||||||
|
|
||||||
|
The above copyright notice and this permission notice shall be included in
|
||||||
|
all copies or substantial portions of the Software.
|
||||||
|
|
||||||
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
||||||
|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
||||||
|
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
|
||||||
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
||||||
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||||
|
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
|
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|
IN THE SOFTWARE.
|
||||||
|
-->
|
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|
||||||
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|
||||||
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|
||||||
<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_sorting/merge_sort.md" title="编辑此页" class="md-content__button md-icon">
|
<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_sorting/merge_sort.md" title="编辑此页" class="md-content__button md-icon">
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|
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|
||||||
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||||||
<h1 id="116">11.6 归并排序<a class="headerlink" href="#116" title="Permanent link">¶</a></h1>
|
<h1 id="116">11.6 归并排序<a class="headerlink" href="#116" title="Permanent link">¶</a></h1>
|
||||||
<p>「归并排序 merge sort」是一种基于分治策略的排序算法，包含图 11-10 所示的“划分”和“合并”阶段。</p>
|
<p>「归并排序 merge sort」是一种基于分治策略的排序算法，包含图 11-10 所示的“划分”和“合并”阶段。</p>
|
||||||
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||||||
@@ -4072,11 +4104,73 @@
|
|||||||
</ul>
|
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|
||||||
<p>具体实现细节比较复杂，有兴趣的同学可以查阅相关资料进行学习。</p>
|
<p>具体实现细节比较复杂，有兴趣的同学可以查阅相关资料进行学习。</p>
|
||||||
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|
||||||
|
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|
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|
|
||||||
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|
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|
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href="../quick_sort/"
|
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|
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11.5 快速排序
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|
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11.7 堆排序
|
||||||
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|
||||||
|
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|
||||||
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|
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|
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|
||||||
|
|
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|
<!-- Comment system -->
|
||||||
|
|
||||||
|
<h5 align="center" id="__comments">欢迎你提出疑问或建议</h5>
|
||||||
<!-- Insert generated snippet here -->
|
<!-- Insert generated snippet here -->
|
||||||
<script
|
<script
|
||||||
src="https://giscus.app/client.js"
|
src="https://giscus.app/client.js"
|
||||||
@@ -4142,48 +4236,31 @@
|
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|
|
||||||
</main>
|
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|
||||||
|
|
||||||
<footer class="md-footer">
|
<!--
|
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|
Copyright (c) 2016-2023 Martin Donath <martin.donath@squidfunk.com>
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|
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|
Permission is hereby granted, free of charge, to any person obtaining a copy
|
||||||
<nav class="md-footer__inner md-grid" aria-label="页脚" >
|
of this software and associated documentation files (the "Software"), to
|
||||||
|
deal in the Software without restriction, including without limitation the
|
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|
rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
|
||||||
<a href="../quick_sort/" class="md-footer__link md-footer__link--prev" aria-label="上一页: 11.5 &nbsp; 快速排序" rel="prev">
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sell copies of the Software, and to permit persons to whom the Software is
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<div class="md-footer__button md-icon">
|
furnished to do so, subject to the following conditions:
|
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|
|
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11h12Z"/></svg>
|
The above copyright notice and this permission notice shall be included in
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</div>
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all copies or substantial portions of the Software.
|
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<div class="md-footer__title">
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|
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<span class="md-footer__direction">
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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上一页
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
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</span>
|
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
|
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<div class="md-ellipsis">
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
||||||
11.5 快速排序
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||||
</div>
|
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
|
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</div>
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IN THE SOFTWARE.
|
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</a>
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|
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|
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|
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|
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|
<footer class="md-footer">
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<a href="../heap_sort/" class="md-footer__link md-footer__link--next" aria-label="下一页: 11.7 &nbsp; 堆排序" rel="next">
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<div class="md-footer__title">
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|
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下一页
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|
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|
|
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11.7 堆排序
|
|
||||||
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|
|
||||||
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|
|
||||||
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|
|
||||||
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|
||||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M4 11v2h12l-5.5 5.5 1.42 1.42L19.84 12l-7.92-7.92L10.5 5.5 16 11H4Z"/></svg>
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||||||
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|
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||||||
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|
||||||
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||||||
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||||||
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|
||||||
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||||||
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|
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|
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||||||
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|
||||||
|
Copyright (c) 2016-2023 Martin Donath <martin.donath@squidfunk.com>
|
||||||
|
|
||||||
|
Permission is hereby granted, free of charge, to any person obtaining a copy
|
||||||
|
of this software and associated documentation files (the "Software"), to
|
||||||
|
deal in the Software without restriction, including without limitation the
|
||||||
|
rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
|
||||||
|
sell copies of the Software, and to permit persons to whom the Software is
|
||||||
|
furnished to do so, subject to the following conditions:
|
||||||
|
|
||||||
|
The above copyright notice and this permission notice shall be included in
|
||||||
|
all copies or substantial portions of the Software.
|
||||||
|
|
||||||
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
||||||
|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
||||||
|
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
|
||||||
|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
||||||
|
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
||||||
|
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
|
||||||
|
IN THE SOFTWARE.
|
||||||
|
-->
|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
|
||||||
|
<!-- Actions -->
|
||||||
|
|
||||||
|
|
||||||
<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_sorting/quick_sort.md" title="编辑此页" class="md-content__button md-icon">
|
<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_sorting/quick_sort.md" title="编辑此页" class="md-content__button md-icon">
|
||||||
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|
|||||||
|
|
||||||
|
|
||||||
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|
||||||
|
<!--
|
||||||
|
Hack: check whether the content contains a h1 headline. If it doesn't, the
|
||||||
|
page title (or respectively site name) is used as the main headline.
|
||||||
|
-->
|
||||||
|
|
||||||
|
|
||||||
|
<!-- Page content -->
|
||||||
<h1 id="115">11.5 快速排序<a class="headerlink" href="#115" title="Permanent link">¶</a></h1>
|
<h1 id="115">11.5 快速排序<a class="headerlink" href="#115" title="Permanent link">¶</a></h1>
|
||||||
<p>「快速排序 quick sort」是一种基于分治策略的排序算法，运行高效，应用广泛。</p>
|
<p>「快速排序 quick sort」是一种基于分治策略的排序算法，运行高效，应用广泛。</p>
|
||||||
<p>快速排序的核心操作是“哨兵划分”，其目标是：选择数组中的某个元素作为“基准数”，将所有小于基准数的元素移到其左侧，而大于基准数的元素移到其右侧。具体来说，哨兵划分的流程如图 11-8 所示。</p>
|
<p>快速排序的核心操作是“哨兵划分”，其目标是：选择数组中的某个元素作为“基准数”，将所有小于基准数的元素移到其左侧，而大于基准数的元素移到其右侧。具体来说，哨兵划分的流程如图 11-8 所示。</p>
|
||||||
@@ -4707,11 +4739,73 @@
|
|||||||
</div>
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||||||
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|
||||||
|
|
||||||
|
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|
||||||
|
|
||||||
|
|
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|
<!-- Was this page helpful? -->
|
||||||
|
|
||||||
|
|
||||||
|
|
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|
|
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<h2 id="__comments">评论</h2>
|
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|
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|
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|
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|
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|
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|
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|
||||||
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|
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|
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|
||||||
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|
||||||
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||||||
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|
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|
||||||
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|
||||||
|
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|
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rel="prev"
|
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|
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|
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|
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|
||||||
|
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|
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|
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|
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|
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|
||||||
|
11.4 插入排序
|
||||||
|
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|
||||||
|
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|
||||||
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|
||||||
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|
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|
||||||
|
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|
||||||
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|
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|
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|
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|
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|
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|
||||||
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|
||||||
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<h1 id="1110">11.10 基数排序<a class="headerlink" href="#1110" title="Permanent link">¶</a></h1>
|
<h1 id="1110">11.10 基数排序<a class="headerlink" href="#1110" title="Permanent link">¶</a></h1>
|
||||||
<p>上一节我们介绍了计数排序，它适用于数据量 <span class="arithmatex">\(n\)</span> 较大但数据范围 <span class="arithmatex">\(m\)</span> 较小的情况。假设我们需要对 <span class="arithmatex">\(n = 10^6\)</span> 个学号进行排序，而学号是一个 <span class="arithmatex">\(8\)</span> 位数字，这意味着数据范围 <span class="arithmatex">\(m = 10^8\)</span> 非常大，使用计数排序需要分配大量内存空间，而基数排序可以避免这种情况。</p>
|
<p>上一节我们介绍了计数排序，它适用于数据量 <span class="arithmatex">\(n\)</span> 较大但数据范围 <span class="arithmatex">\(m\)</span> 较小的情况。假设我们需要对 <span class="arithmatex">\(n = 10^6\)</span> 个学号进行排序，而学号是一个 <span class="arithmatex">\(8\)</span> 位数字，这意味着数据范围 <span class="arithmatex">\(m = 10^8\)</span> 非常大，使用计数排序需要分配大量内存空间，而基数排序可以避免这种情况。</p>
|
||||||
<p>「基数排序 radix sort」的核心思想与计数排序一致，也通过统计个数来实现排序。在此基础上，基数排序利用数字各位之间的递进关系，依次对每一位进行排序，从而得到最终的排序结果。</p>
|
<p>「基数排序 radix sort」的核心思想与计数排序一致，也通过统计个数来实现排序。在此基础上，基数排序利用数字各位之间的递进关系，依次对每一位进行排序，从而得到最终的排序结果。</p>
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|||||||
<li><strong>稳定排序</strong>：与计数排序相同。</li>
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<li><strong>稳定排序</strong>：与计数排序相同。</li>
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_sorting/selection_sort.md" title="编辑此页" class="md-content__button md-icon">
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<h1 id="112">11.2 选择排序<a class="headerlink" href="#112" title="Permanent link">¶</a></h1>
|
<h1 id="112">11.2 选择排序<a class="headerlink" href="#112" title="Permanent link">¶</a></h1>
|
||||||
<p>「选择排序 selection sort」的工作原理非常直接：开启一个循环，每轮从未排序区间选择最小的元素，将其放到已排序区间的末尾。</p>
|
<p>「选择排序 selection sort」的工作原理非常直接：开启一个循环，每轮从未排序区间选择最小的元素，将其放到已排序区间的末尾。</p>
|
||||||
<p>设数组的长度为 <span class="arithmatex">\(n\)</span> ，选择排序的算法流程如图 11-2 所示。</p>
|
<p>设数组的长度为 <span class="arithmatex">\(n\)</span> ，选择排序的算法流程如图 11-2 所示。</p>
|
||||||
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|||||||
<p><img alt="选择排序非稳定示例" src="../selection_sort.assets/selection_sort_instability.png" /></p>
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<p align="center"> 图 11-3 选择排序非稳定示例 </p>
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<h1 id="111">11.1 排序算法<a class="headerlink" href="#111" title="Permanent link">¶</a></h1>
|
<h1 id="111">11.1 排序算法<a class="headerlink" href="#111" title="Permanent link">¶</a></h1>
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||||||
<p>「排序算法 sorting algorithm」用于对一组数据按照特定顺序进行排列。排序算法有着广泛的应用，因为有序数据通常能够被更有效地查找、分析和处理。</p>
|
<p>「排序算法 sorting algorithm」用于对一组数据按照特定顺序进行排列。排序算法有着广泛的应用，因为有序数据通常能够被更有效地查找、分析和处理。</p>
|
||||||
<p>如图 11-1 所示，排序算法中的数据类型可以是整数、浮点数、字符或字符串等。排序的判断规则可根据需求设定，如数字大小、字符 ASCII 码顺序或自定义规则。</p>
|
<p>如图 11-1 所示，排序算法中的数据类型可以是整数、浮点数、字符或字符串等。排序的判断规则可根据需求设定，如数字大小、字符 ASCII 码顺序或自定义规则。</p>
|
||||||
@@ -3476,11 +3508,73 @@
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|||||||
<p><strong>运行快、原地、稳定、正向自适应、通用性好</strong>。显然，迄今为止尚未发现兼具以上所有特性的排序算法。因此，在选择排序算法时，需要根据具体的数据特点和问题需求来决定。</p>
|
<p><strong>运行快、原地、稳定、正向自适应、通用性好</strong>。显然，迄今为止尚未发现兼具以上所有特性的排序算法。因此，在选择排序算法时，需要根据具体的数据特点和问题需求来决定。</p>
|
||||||
<p>接下来，我们将共同学习各种排序算法，并基于上述评价维度对各个排序算法的优缺点进行分析。</p>
|
<p>接下来，我们将共同学习各种排序算法，并基于上述评价维度对各个排序算法的优缺点进行分析。</p>
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<h1 id="1111">11.11 小结<a class="headerlink" href="#1111" title="Permanent link">¶</a></h1>
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<h1 id="1111">11.11 小结<a class="headerlink" href="#1111" title="Permanent link">¶</a></h1>
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<h3 id="1">1. 重点回顾<a class="headerlink" href="#1" title="Permanent link">¶</a></h3>
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<p>最差情况下，所有元素被分至同一个桶中。如果我们采用一个 <span class="arithmatex">\(O(n^2)\)</span> 算法来排序这些元素，则时间复杂度为 <span class="arithmatex">\(O(n^2)\)</span> 。</p>
|
<p>最差情况下，所有元素被分至同一个桶中。如果我们采用一个 <span class="arithmatex">\(O(n^2)\)</span> 算法来排序这些元素，则时间复杂度为 <span class="arithmatex">\(O(n^2)\)</span> 。</p>
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<h1 id="53">5.3 双向队列<a class="headerlink" href="#53" title="Permanent link">¶</a></h1>
|
<h1 id="53">5.3 双向队列<a class="headerlink" href="#53" title="Permanent link">¶</a></h1>
|
||||||
<p>在队列中，我们仅能在头部删除或在尾部添加元素。如图 5-7 所示，「双向队列 deque」提供了更高的灵活性，允许在头部和尾部执行元素的添加或删除操作。</p>
|
<p>在队列中，我们仅能在头部删除或在尾部添加元素。如图 5-7 所示，「双向队列 deque」提供了更高的灵活性，允许在头部和尾部执行元素的添加或删除操作。</p>
|
||||||
<p><img alt="双向队列的操作" src="../deque.assets/deque_operations.png" /></p>
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||||||
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<p>双向队列兼具栈与队列的逻辑，<strong>因此它可以实现这两者的所有应用场景，同时提供更高的自由度</strong>。</p>
|
<p>双向队列兼具栈与队列的逻辑，<strong>因此它可以实现这两者的所有应用场景，同时提供更高的自由度</strong>。</p>
|
||||||
<p>我们知道，软件的“撤销”功能通常使用栈来实现：系统将每次更改操作 <code>push</code> 到栈中，然后通过 <code>pop</code> 实现撤销。然而，考虑到系统资源的限制，软件通常会限制撤销的步数（例如仅允许保存 <span class="arithmatex">\(50\)</span> 步）。当栈的长度超过 <span class="arithmatex">\(50\)</span> 时，软件需要在栈底（即队首）执行删除操作。<strong>但栈无法实现该功能，此时就需要使用双向队列来替代栈</strong>。请注意，“撤销”的核心逻辑仍然遵循栈的先入后出原则，只是双向队列能够更加灵活地实现一些额外逻辑。</p>
|
<p>我们知道，软件的“撤销”功能通常使用栈来实现：系统将每次更改操作 <code>push</code> 到栈中，然后通过 <code>pop</code> 实现撤销。然而，考虑到系统资源的限制，软件通常会限制撤销的步数（例如仅允许保存 <span class="arithmatex">\(50\)</span> 步）。当栈的长度超过 <span class="arithmatex">\(50\)</span> 时，软件需要在栈底（即队首）执行删除操作。<strong>但栈无法实现该功能，此时就需要使用双向队列来替代栈</strong>。请注意，“撤销”的核心逻辑仍然遵循栈的先入后出原则，只是双向队列能够更加灵活地实现一些额外逻辑。</p>
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<h1 id="5">第 5 章 栈与队列<a class="headerlink" href="#5" title="Permanent link">¶</a></h1>
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|
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|
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<h1 id="52">5.2 队列<a class="headerlink" href="#52" title="Permanent link">¶</a></h1>
|
<h1 id="52">5.2 队列<a class="headerlink" href="#52" title="Permanent link">¶</a></h1>
|
||||||
<p>「队列 queue」是一种遵循先入先出规则的线性数据结构。顾名思义，队列模拟了排队现象，即新来的人不断加入队列的尾部，而位于队列头部的人逐个离开。</p>
|
<p>「队列 queue」是一种遵循先入先出规则的线性数据结构。顾名思义，队列模拟了排队现象，即新来的人不断加入队列的尾部，而位于队列头部的人逐个离开。</p>
|
||||||
<p>如图 5-4 所示，我们将队列的头部称为“队首”，尾部称为“队尾”，将把元素加入队尾的操作称为“入队”，删除队首元素的操作称为“出队”。</p>
|
<p>如图 5-4 所示，我们将队列的头部称为“队首”，尾部称为“队尾”，将把元素加入队尾的操作称为“入队”，删除队首元素的操作称为“出队”。</p>
|
||||||
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|
|||||||
<a id="__codelineno-22-75" name="__codelineno-22-75" href="#__codelineno-22-75"></a><span class="w"> </span><span class="c1">// 拷贝链表中的数据到数组</span>
|
<a id="__codelineno-22-75" name="__codelineno-22-75" href="#__codelineno-22-75"></a><span class="w"> </span><span class="c1">// 拷贝链表中的数据到数组</span>
|
||||||
<a id="__codelineno-22-76" name="__codelineno-22-76" href="#__codelineno-22-76"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
|
<a id="__codelineno-22-76" name="__codelineno-22-76" href="#__codelineno-22-76"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
|
||||||
<a id="__codelineno-22-77" name="__codelineno-22-77" href="#__codelineno-22-77"></a><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">;</span>
|
<a id="__codelineno-22-77" name="__codelineno-22-77" href="#__codelineno-22-77"></a><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">;</span>
|
||||||
<a id="__codelineno-22-78" name="__codelineno-22-78" href="#__codelineno-22-78"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">-></span><span class="n">front</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">queue</span><span class="o">-></span><span class="n">queSize</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">queue</span><span class="o">-></span><span class="n">front</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">queue</span><span class="o">-></span><span class="n">rear</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
<a id="__codelineno-22-78" name="__codelineno-22-78" href="#__codelineno-22-78"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">-></span><span class="n">front</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">queue</span><span class="o">-></span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||||
<a id="__codelineno-22-79" name="__codelineno-22-79" href="#__codelineno-22-79"></a><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">val</span><span class="p">;</span>
|
<a id="__codelineno-22-79" name="__codelineno-22-79" href="#__codelineno-22-79"></a><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">val</span><span class="p">;</span>
|
||||||
<a id="__codelineno-22-80" name="__codelineno-22-80" href="#__codelineno-22-80"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">next</span><span class="p">;</span>
|
<a id="__codelineno-22-80" name="__codelineno-22-80" href="#__codelineno-22-80"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-></span><span class="n">next</span><span class="p">;</span>
|
||||||
<a id="__codelineno-22-81" name="__codelineno-22-81" href="#__codelineno-22-81"></a><span class="w"> </span><span class="p">}</span>
|
<a id="__codelineno-22-81" name="__codelineno-22-81" href="#__codelineno-22-81"></a><span class="w"> </span><span class="p">}</span>
|
||||||
@@ -5574,11 +5606,73 @@
|
|||||||
<li><strong>各类待办事项</strong>。任何需要实现“先来后到”功能的场景，例如打印机的任务队列、餐厅的出餐队列等。队列在这些场景中可以有效地维护处理顺序。</li>
|
<li><strong>各类待办事项</strong>。任何需要实现“先来后到”功能的场景，例如打印机的任务队列、餐厅的出餐队列等。队列在这些场景中可以有效地维护处理顺序。</li>
|
||||||
</ul>
|
</ul>
|
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|
|
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|
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<h1 id="51">5.1 栈<a class="headerlink" href="#51" title="Permanent link">¶</a></h1>
|
<h1 id="51">5.1 栈<a class="headerlink" href="#51" title="Permanent link">¶</a></h1>
|
||||||
<p>「栈 stack」是一种遵循先入后出的逻辑的线性数据结构。</p>
|
<p>「栈 stack」是一种遵循先入后出的逻辑的线性数据结构。</p>
|
||||||
<p>我们可以将栈类比为桌面上的一摞盘子，如果需要拿出底部的盘子，则需要先将上面的盘子依次取出。我们将盘子替换为各种类型的元素（如整数、字符、对象等），就得到了栈数据结构。</p>
|
<p>我们可以将栈类比为桌面上的一摞盘子，如果需要拿出底部的盘子，则需要先将上面的盘子依次取出。我们将盘子替换为各种类型的元素（如整数、字符、对象等），就得到了栈数据结构。</p>
|
||||||
@@ -5170,11 +5202,73 @@
|
|||||||
<li><strong>程序内存管理</strong>。每次调用函数时，系统都会在栈顶添加一个栈帧，用于记录函数的上下文信息。在递归函数中，向下递推阶段会不断执行入栈操作，而向上回溯阶段则会执行出栈操作。</li>
|
<li><strong>程序内存管理</strong>。每次调用函数时，系统都会在栈顶添加一个栈帧，用于记录函数的上下文信息。在递归函数中，向下递推阶段会不断执行入栈操作，而向上回溯阶段则会执行出栈操作。</li>
|
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<h1 id="54">5.4 小结<a class="headerlink" href="#54" title="Permanent link">¶</a></h1>
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<h3 id="1">1. 重点回顾<a class="headerlink" href="#1" title="Permanent link">¶</a></h3>
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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||||||
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|
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|
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<h1 id="73">7.3 二叉树数组表示<a class="headerlink" href="#73" title="Permanent link">¶</a></h1>
|
<h1 id="73">7.3 二叉树数组表示<a class="headerlink" href="#73" title="Permanent link">¶</a></h1>
|
||||||
<p>在链表表示下，二叉树的存储单元为节点 <code>TreeNode</code> ，节点之间通过指针相连接。在上节中，我们学习了在链表表示下的二叉树的各项基本操作。</p>
|
<p>在链表表示下，二叉树的存储单元为节点 <code>TreeNode</code> ，节点之间通过指针相连接。在上节中，我们学习了在链表表示下的二叉树的各项基本操作。</p>
|
||||||
<p>那么，我们能否用数组来表示二叉树呢？答案是肯定的。</p>
|
<p>那么，我们能否用数组来表示二叉树呢？答案是肯定的。</p>
|
||||||
@@ -4567,11 +4599,73 @@
|
|||||||
<li>当二叉树中存在大量 <span class="arithmatex">\(\text{None}\)</span> 时，数组中包含的节点数据比重较低，空间利用率较低。</li>
|
<li>当二叉树中存在大量 <span class="arithmatex">\(\text{None}\)</span> 时，数组中包含的节点数据比重较低，空间利用率较低。</li>
|
||||||
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|
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|
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Permission is hereby granted, free of charge, to any person obtaining a copy
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deal in the Software without restriction, including without limitation the
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|
rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
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|
sell copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in
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all copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
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|
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
||||||
|
FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
|
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|
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_tree/avl_tree.md" title="编辑此页" class="md-content__button md-icon">
|
<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_tree/avl_tree.md" title="编辑此页" class="md-content__button md-icon">
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||||||
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|
|||||||
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|
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|
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|
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|
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<h1 id="75-avl">7.5 AVL 树 *<a class="headerlink" href="#75-avl" title="Permanent link">¶</a></h1>
|
<h1 id="75-avl">7.5 AVL 树 *<a class="headerlink" href="#75-avl" title="Permanent link">¶</a></h1>
|
||||||
<p>在二叉搜索树章节中，我们提到了在多次插入和删除操作后，二叉搜索树可能退化为链表。这种情况下，所有操作的时间复杂度将从 <span class="arithmatex">\(O(\log n)\)</span> 恶化为 <span class="arithmatex">\(O(n)\)</span> 。</p>
|
<p>在二叉搜索树章节中，我们提到了在多次插入和删除操作后，二叉搜索树可能退化为链表。这种情况下，所有操作的时间复杂度将从 <span class="arithmatex">\(O(\log n)\)</span> 恶化为 <span class="arithmatex">\(O(n)\)</span> 。</p>
|
||||||
<p>如图 7-24 所示，经过两次删除节点操作，这个二叉搜索树便会退化为链表。</p>
|
<p>如图 7-24 所示，经过两次删除节点操作，这个二叉搜索树便会退化为链表。</p>
|
||||||
@@ -3666,10 +3698,10 @@
|
|||||||
<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span> <span class="nc">TreeNode</span><span class="p">:</span>
|
<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span> <span class="nc">TreeNode</span><span class="p">:</span>
|
||||||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w"> </span><span class="sd">"""AVL 树节点类"""</span>
|
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w"> </span><span class="sd">"""AVL 树节点类"""</span>
|
||||||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||||||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">val</span> <span class="c1"># 节点值</span>
|
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">val</span> <span class="c1"># 节点值</span>
|
||||||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="bp">self</span><span class="o">.</span><span class="n">height</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span> <span class="c1"># 节点高度</span>
|
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="bp">self</span><span class="o">.</span><span class="n">height</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span> <span class="c1"># 节点高度</span>
|
||||||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="bp">self</span><span class="o">.</span><span class="n">left</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 左子节点引用</span>
|
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="bp">self</span><span class="o">.</span><span class="n">left</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 左子节点引用</span>
|
||||||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="bp">self</span><span class="o">.</span><span class="n">right</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 右子节点引用</span>
|
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="bp">self</span><span class="o">.</span><span class="n">right</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 右子节点引用</span>
|
||||||
</code></pre></div>
|
</code></pre></div>
|
||||||
</div>
|
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|
||||||
<div class="tabbed-block">
|
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|
||||||
@@ -5907,11 +5939,73 @@
|
|||||||
<li>红黑树在许多应用中比 AVL 树更受欢迎。这是因为红黑树的平衡条件相对宽松，在红黑树中插入与删除节点所需的旋转操作相对较少，其节点增删操作的平均效率更高。</li>
|
<li>红黑树在许多应用中比 AVL 树更受欢迎。这是因为红黑树的平衡条件相对宽松，在红黑树中插入与删除节点所需的旋转操作相对较少，其节点增删操作的平均效率更高。</li>
|
||||||
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|
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|
||||||
|
|
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|
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<h1 id="74">7.4 二叉搜索树<a class="headerlink" href="#74" title="Permanent link">¶</a></h1>
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<h1 id="74">7.4 二叉搜索树<a class="headerlink" href="#74" title="Permanent link">¶</a></h1>
|
||||||
<p>如图 7-16 所示，「二叉搜索树 binary search tree」满足以下条件。</p>
|
<p>如图 7-16 所示，「二叉搜索树 binary search tree」满足以下条件。</p>
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<li>用于存储数据流，以保持其有序状态。</li>
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|
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FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
|
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_tree/binary_tree.md" title="编辑此页" class="md-content__button md-icon">
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<h1 id="71">7.1 二叉树<a class="headerlink" href="#71" title="Permanent link">¶</a></h1>
|
<h1 id="71">7.1 二叉树<a class="headerlink" href="#71" title="Permanent link">¶</a></h1>
|
||||||
<p>「二叉树 binary tree」是一种非线性数据结构，代表着祖先与后代之间的派生关系，体现着“一分为二”的分治逻辑。与链表类似，二叉树的基本单元是节点，每个节点包含：值、左子节点引用、右子节点引用。</p>
|
<p>「二叉树 binary tree」是一种非线性数据结构，代表着祖先与后代之间的派生关系，体现着“一分为二”的分治逻辑。与链表类似，二叉树的基本单元是节点，每个节点包含：值、左子节点引用、右子节点引用。</p>
|
||||||
<div class="tabbed-set tabbed-alternate" data-tabs="1:12"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Zig</label></div>
|
<div class="tabbed-set tabbed-alternate" data-tabs="1:12"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Zig</label></div>
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|
|||||||
<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span> <span class="nc">TreeNode</span><span class="p">:</span>
|
<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span> <span class="nc">TreeNode</span><span class="p">:</span>
|
||||||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w"> </span><span class="sd">"""二叉树节点类"""</span>
|
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w"> </span><span class="sd">"""二叉树节点类"""</span>
|
||||||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||||||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">val</span> <span class="c1"># 节点值</span>
|
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">val</span> <span class="c1"># 节点值</span>
|
||||||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="bp">self</span><span class="o">.</span><span class="n">left</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 左子节点引用</span>
|
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="bp">self</span><span class="o">.</span><span class="n">left</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 左子节点引用</span>
|
||||||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="bp">self</span><span class="o">.</span><span class="n">right</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 右子节点引用</span>
|
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="bp">self</span><span class="o">.</span><span class="n">right</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 右子节点引用</span>
|
||||||
</code></pre></div>
|
</code></pre></div>
|
||||||
</div>
|
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|
||||||
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@@ -4095,11 +4127,73 @@
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Some files were not shown because too many files have changed in this diff Show More
Reference in New Issue
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