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chapter_searching/binary_search/index.html
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</head>
<link href="../../assets/stylesheets/glightbox.min.css" rel="stylesheet"/><style>
html.glightbox-open { overflow: initial; height: 100%; }
.gslide-title { margin-top: 0px; user-select: text; }
.gslide-desc { color: #666; user-select: text; }
.gslide-image img { background: white; }
.gscrollbar-fixer { padding-right: 15px; }
.gdesc-inner { font-size: 0.75rem; }
body[data-md-color-scheme="slate"] .gdesc-inner { background: var(--md-default-bg-color);}
body[data-md-color-scheme="slate"] .gslide-title { color: var(--md-default-fg-color);}
body[data-md-color-scheme="slate"] .gslide-desc { color: var(--md-default-fg-color);}
</style> <script src="../../assets/javascripts/glightbox.min.js"></script></head>
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10.2 &nbsp; 二分查找插入点
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10.3 &nbsp; 二分查找边界
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15.1 &nbsp; 贪心算法
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<p class="admonition-title">Question</p>
<p>给定一个长度为 <span class="arithmatex">\(n\)</span> 的数组 <code>nums</code> ，元素按从小到大的顺序排列，数组不包含重复元素。请查找并返回元素 <code>target</code> 在该数组中的索引。若数组不包含该元素，则返回 <span class="arithmatex">\(-1\)</span> 。</p>
</div>
<p><img alt="二分查找示例数据" src="../binary_search.assets/binary_search_example.png" /></p>
<p><a class="glightbox" href="../binary_search.assets/binary_search_example.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="二分查找示例数据" src="../binary_search.assets/binary_search_example.png" /></a></p>
<p align="center"> 图 10-1 &nbsp; 二分查找示例数据 </p>
<p>如图 10-2 所示，我们先初始化指针 <span class="arithmatex">\(i = 0\)</span> 和 <span class="arithmatex">\(j = n - 1\)</span> ，分别指向数组首元素和尾元素，代表搜索区间 <span class="arithmatex">\([0, n - 1]\)</span> 。请注意，中括号表示闭区间，其包含边界值本身。</p>
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<div class="tabbed-set tabbed-alternate" data-tabs="1:7"><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" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label><label for="__tabbed_1_5">&lt;5&gt;</label><label for="__tabbed_1_6">&lt;6&gt;</label><label for="__tabbed_1_7">&lt;7&gt;</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
<p><img alt="二分查找流程" src="../binary_search.assets/binary_search_step1.png" /></p>
<p><a class="glightbox" href="../binary_search.assets/binary_search_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="二分查找流程" src="../binary_search.assets/binary_search_step1.png" /></a></p>
</div>
<div class="tabbed-block">
<p><img alt="binary_search_step2" src="../binary_search.assets/binary_search_step2.png" /></p>
<p><a class="glightbox" href="../binary_search.assets/binary_search_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_step2" src="../binary_search.assets/binary_search_step2.png" /></a></p>
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<p><img alt="binary_search_step3" src="../binary_search.assets/binary_search_step3.png" /></p>
<p><a class="glightbox" href="../binary_search.assets/binary_search_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_step3" src="../binary_search.assets/binary_search_step3.png" /></a></p>
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<p><img alt="binary_search_step4" src="../binary_search.assets/binary_search_step4.png" /></p>
<p><a class="glightbox" href="../binary_search.assets/binary_search_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_step4" src="../binary_search.assets/binary_search_step4.png" /></a></p>
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<p><img alt="binary_search_step5" src="../binary_search.assets/binary_search_step5.png" /></p>
<p><a class="glightbox" href="../binary_search.assets/binary_search_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_step5" src="../binary_search.assets/binary_search_step5.png" /></a></p>
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<p><img alt="binary_search_step6" src="../binary_search.assets/binary_search_step6.png" /></p>
<p><a class="glightbox" href="../binary_search.assets/binary_search_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_step6" src="../binary_search.assets/binary_search_step6.png" /></a></p>
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<p><img alt="binary_search_step7" src="../binary_search.assets/binary_search_step7.png" /></p>
<p><a class="glightbox" href="../binary_search.assets/binary_search_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_step7" src="../binary_search.assets/binary_search_step7.png" /></a></p>
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</div>
<p>如图 10-3 所示，在两种区间表示下，二分查找算法的初始化、循环条件和缩小区间操作皆有所不同。</p>
<p>由于“双闭区间”表示中的左右边界都被定义为闭区间，因此指针 <span class="arithmatex">\(i\)</span> 和 <span class="arithmatex">\(j\)</span> 缩小区间操作也是对称的。这样更不容易出错，<strong>因此一般建议采用“双闭区间”的写法</strong>。</p>
<p><img alt="两种区间定义" src="../binary_search.assets/binary_search_ranges.png" /></p>
<p><a class="glightbox" href="../binary_search.assets/binary_search_ranges.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="两种区间定义" src="../binary_search.assets/binary_search_ranges.png" /></a></p>
<p align="center"> 图 10-3 &nbsp; 两种区间定义 </p>
<h2 id="1012">10.1.2 &nbsp; 优点与局限性<a class="headerlink" href="#1012" title="Permanent link">&para;</a></h2>
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<div class="md-copyright">
<div class="md-copyright__highlight">
Copyright &copy; 2023 Krahets
Copyright &copy; 2022 - 2023 Krahets
</div>
Made with
<a href="https://squidfunk.github.io/mkdocs-material/" target="_blank" rel="noopener">
Material for MkDocs
</a>
</div>
<!-- Social links -->
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</body>
<script>document$.subscribe(() => {const lightbox = GLightbox({"touchNavigation": true, "loop": false, "zoomable": true, "draggable": false, "openEffect": "zoom", "closeEffect": "zoom", "slideEffect": "none"});})</script></body>
</html>
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</head>
<link href="../../assets/stylesheets/glightbox.min.css" rel="stylesheet"/><style>
html.glightbox-open { overflow: initial; height: 100%; }
.gslide-title { margin-top: 0px; user-select: text; }
.gslide-desc { color: #666; user-select: text; }
.gslide-image img { background: white; }
.gscrollbar-fixer { padding-right: 15px; }
.gdesc-inner { font-size: 0.75rem; }
body[data-md-color-scheme="slate"] .gdesc-inner { background: var(--md-default-bg-color);}
body[data-md-color-scheme="slate"] .gslide-title { color: var(--md-default-fg-color);}
body[data-md-color-scheme="slate"] .gslide-desc { color: var(--md-default-fg-color);}
</style> <script src="../../assets/javascripts/glightbox.min.js"></script></head>
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10.2 &nbsp; 二分查找插入点
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10.3 &nbsp; 二分查找边界
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第 12 章 &nbsp; 分治
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12.2 &nbsp; 分治搜索策略
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12.3 &nbsp; 构建树问题
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12.4 &nbsp; 汉诺塔问题
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12.5 &nbsp; 小结
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第 14 章 &nbsp; 动态规划
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15.1 &nbsp; 贪心算法
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15.2 &nbsp; 分数背包问题
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15.3 &nbsp; 最大容量问题
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15.4 &nbsp; 最大切分乘积问题
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<h3 id="1">1. &nbsp; 复用查找左边界<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
<p>实际上，我们可以利用查找最左元素的函数来查找最右元素，具体方法为：<strong>将查找最右一个 <code>target</code> 转化为查找最左一个 <code>target + 1</code></strong>。</p>
<p>如图 10-7 所示，查找完成后，指针 <span class="arithmatex">\(i\)</span> 指向最左一个 <code>target + 1</code>（如果存在），而 <span class="arithmatex">\(j\)</span> 指向最右一个 <code>target</code> ，<strong>因此返回 <span class="arithmatex">\(j\)</span> 即可</strong>。</p>
<p><img alt="将查找右边界转化为查找左边界" src="../binary_search_edge.assets/binary_search_right_edge_by_left_edge.png" /></p>
<p><a class="glightbox" href="../binary_search_edge.assets/binary_search_right_edge_by_left_edge.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="将查找右边界转化为查找左边界" src="../binary_search_edge.assets/binary_search_right_edge_by_left_edge.png" /></a></p>
<p align="center"> 图 10-7 &nbsp; 将查找右边界转化为查找左边界 </p>
<p>请注意，返回的插入点是 <span class="arithmatex">\(i\)</span> ，因此需要将其减 <span class="arithmatex">\(1\)</span> ，从而获得 <span class="arithmatex">\(j\)</span> 。</p>
@@ -3893,7 +3720,7 @@
<li>查找最左一个 <code>target</code> ：可以转化为查找 <code>target - 0.5</code> ，并返回指针 <span class="arithmatex">\(i\)</span> 。</li>
<li>查找最右一个 <code>target</code> ：可以转化为查找 <code>target + 0.5</code> ，并返回指针 <span class="arithmatex">\(j\)</span> 。</li>
</ul>
<p><img alt="将查找边界转化为查找元素" src="../binary_search_edge.assets/binary_search_edge_by_element.png" /></p>
<p><a class="glightbox" href="../binary_search_edge.assets/binary_search_edge_by_element.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="将查找边界转化为查找元素" src="../binary_search_edge.assets/binary_search_edge_by_element.png" /></a></p>
<p align="center"> 图 10-8 &nbsp; 将查找边界转化为查找元素 </p>
<p>代码在此省略，值得注意以下两点。</p>
@@ -4064,10 +3891,15 @@ aria-label="页脚"
<div class="md-copyright">
<div class="md-copyright__highlight">
Copyright &copy; 2023 Krahets
Copyright &copy; 2022 - 2023 Krahets
</div>
Made with
<a href="https://squidfunk.github.io/mkdocs-material/" target="_blank" rel="noopener">
Material for MkDocs
</a>
</div>
<!-- Social links -->
@@ -4136,5 +3968,5 @@ aria-label="页脚"
</body>
<script>document$.subscribe(() => {const lightbox = GLightbox({"touchNavigation": true, "loop": false, "zoomable": true, "draggable": false, "openEffect": "zoom", "closeEffect": "zoom", "slideEffect": "none"});})</script></body>
</html>
chapter_searching/binary_search_insertion/index.html
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</head>
<link href="../../assets/stylesheets/glightbox.min.css" rel="stylesheet"/><style>
html.glightbox-open { overflow: initial; height: 100%; }
.gslide-title { margin-top: 0px; user-select: text; }
.gslide-desc { color: #666; user-select: text; }
.gslide-image img { background: white; }
.gscrollbar-fixer { padding-right: 15px; }
.gdesc-inner { font-size: 0.75rem; }
body[data-md-color-scheme="slate"] .gdesc-inner { background: var(--md-default-bg-color);}
body[data-md-color-scheme="slate"] .gslide-title { color: var(--md-default-fg-color);}
body[data-md-color-scheme="slate"] .gslide-desc { color: var(--md-default-fg-color);}
</style> <script src="../../assets/javascripts/glightbox.min.js"></script></head>
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10.2 &nbsp; 二分查找插入点
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</label>
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10.2 &nbsp; 二分查找插入点
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
@@ -1967,14 +1962,6 @@
10.3 &nbsp; 二分查找边界
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2394,14 +2381,6 @@
第 12 章 &nbsp; 分治
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
@@ -2433,14 +2412,6 @@
12.1 &nbsp; 分治算法
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2461,14 +2432,6 @@
12.2 &nbsp; 分治搜索策略
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2489,14 +2452,6 @@
12.3 &nbsp; 构建树问题
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2517,14 +2472,6 @@
12.4 &nbsp; 汉诺塔问题
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2545,14 +2492,6 @@
12.5 &nbsp; 小结
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2784,14 +2723,6 @@
第 14 章 &nbsp; 动态规划
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
@@ -2823,14 +2754,6 @@
14.1 &nbsp; 初探动态规划
</span>
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</span>
</a>
</li>
@@ -2851,14 +2774,6 @@
14.2 &nbsp; DP 问题特性
</span>
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</span>
</a>
</li>
@@ -2879,14 +2794,6 @@
14.3 &nbsp; DP 解题思路
</span>
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</span>
</a>
</li>
@@ -2907,14 +2814,6 @@
14.4 &nbsp; 0-1 背包问题
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</span>
</a>
</li>
@@ -2935,14 +2834,6 @@
14.5 &nbsp; 完全背包问题
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2963,14 +2854,6 @@
14.6 &nbsp; 编辑距离问题
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2991,14 +2874,6 @@
14.7 &nbsp; 小结
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -3057,14 +2932,6 @@
第 15 章 &nbsp; 贪心
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
@@ -3096,14 +2963,6 @@
15.1 &nbsp; 贪心算法
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -3124,14 +2983,6 @@
15.2 &nbsp; 分数背包问题
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -3152,14 +3003,6 @@
15.3 &nbsp; 最大容量问题
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -3180,14 +3023,6 @@
15.4 &nbsp; 最大切分乘积问题
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -3208,14 +3043,6 @@
15.5 &nbsp; 小结
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -3488,7 +3315,7 @@
<p class="admonition-title">Question</p>
<p>给定一个长度为 <span class="arithmatex">\(n\)</span> 的有序数组 <code>nums</code> 和一个元素 <code>target</code> ，数组不存在重复元素。现将 <code>target</code> 插入到数组 <code>nums</code> 中，并保持其有序性。若数组中已存在元素 <code>target</code> ，则插入到其左方。请返回插入后 <code>target</code> 在数组中的索引。</p>
</div>
<p><img alt="二分查找插入点示例数据" src="../binary_search_insertion.assets/binary_search_insertion_example.png" /></p>
<p><a class="glightbox" href="../binary_search_insertion.assets/binary_search_insertion_example.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="二分查找插入点示例数据" src="../binary_search_insertion.assets/binary_search_insertion_example.png" /></a></p>
<p align="center"> 图 10-4 &nbsp; 二分查找插入点示例数据 </p>
<p>如果想要复用上节的二分查找代码，则需要回答以下两个问题。</p>
@@ -3732,7 +3559,7 @@
<li>执行二分查找，得到任意一个 <code>target</code> 的索引，记为 <span class="arithmatex">\(k\)</span> 。</li>
<li>从索引 <span class="arithmatex">\(k\)</span> 开始，向左进行线性遍历，当找到最左边的 <code>target</code> 时返回。</li>
</ol>
<p><img alt="线性查找重复元素的插入点" src="../binary_search_insertion.assets/binary_search_insertion_naive.png" /></p>
<p><a class="glightbox" href="../binary_search_insertion.assets/binary_search_insertion_naive.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="线性查找重复元素的插入点" src="../binary_search_insertion.assets/binary_search_insertion_naive.png" /></a></p>
<p align="center"> 图 10-5 &nbsp; 线性查找重复元素的插入点 </p>
<p>此方法虽然可用，但其包含线性查找，因此时间复杂度为 <span class="arithmatex">\(O(n)\)</span> 。当数组中存在很多重复的 <code>target</code> 时，该方法效率很低。</p>
@@ -3745,28 +3572,28 @@
<div class="tabbed-set tabbed-alternate" data-tabs="2:8"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">&lt;1&gt;</label><label for="__tabbed_2_2">&lt;2&gt;</label><label for="__tabbed_2_3">&lt;3&gt;</label><label for="__tabbed_2_4">&lt;4&gt;</label><label for="__tabbed_2_5">&lt;5&gt;</label><label for="__tabbed_2_6">&lt;6&gt;</label><label for="__tabbed_2_7">&lt;7&gt;</label><label for="__tabbed_2_8">&lt;8&gt;</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
<p><img alt="二分查找重复元素的插入点的步骤" src="../binary_search_insertion.assets/binary_search_insertion_step1.png" /></p>
<p><a class="glightbox" href="../binary_search_insertion.assets/binary_search_insertion_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="二分查找重复元素的插入点的步骤" src="../binary_search_insertion.assets/binary_search_insertion_step1.png" /></a></p>
</div>
<div class="tabbed-block">
<p><img alt="binary_search_insertion_step2" src="../binary_search_insertion.assets/binary_search_insertion_step2.png" /></p>
<p><a class="glightbox" href="../binary_search_insertion.assets/binary_search_insertion_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_insertion_step2" src="../binary_search_insertion.assets/binary_search_insertion_step2.png" /></a></p>
</div>
<div class="tabbed-block">
<p><img alt="binary_search_insertion_step3" src="../binary_search_insertion.assets/binary_search_insertion_step3.png" /></p>
<p><a class="glightbox" href="../binary_search_insertion.assets/binary_search_insertion_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_insertion_step3" src="../binary_search_insertion.assets/binary_search_insertion_step3.png" /></a></p>
</div>
<div class="tabbed-block">
<p><img alt="binary_search_insertion_step4" src="../binary_search_insertion.assets/binary_search_insertion_step4.png" /></p>
<p><a class="glightbox" href="../binary_search_insertion.assets/binary_search_insertion_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_insertion_step4" src="../binary_search_insertion.assets/binary_search_insertion_step4.png" /></a></p>
</div>
<div class="tabbed-block">
<p><img alt="binary_search_insertion_step5" src="../binary_search_insertion.assets/binary_search_insertion_step5.png" /></p>
<p><a class="glightbox" href="../binary_search_insertion.assets/binary_search_insertion_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_insertion_step5" src="../binary_search_insertion.assets/binary_search_insertion_step5.png" /></a></p>
</div>
<div class="tabbed-block">
<p><img alt="binary_search_insertion_step6" src="../binary_search_insertion.assets/binary_search_insertion_step6.png" /></p>
<p><a class="glightbox" href="../binary_search_insertion.assets/binary_search_insertion_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_insertion_step6" src="../binary_search_insertion.assets/binary_search_insertion_step6.png" /></a></p>
</div>
<div class="tabbed-block">
<p><img alt="binary_search_insertion_step7" src="../binary_search_insertion.assets/binary_search_insertion_step7.png" /></p>
<p><a class="glightbox" href="../binary_search_insertion.assets/binary_search_insertion_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_insertion_step7" src="../binary_search_insertion.assets/binary_search_insertion_step7.png" /></a></p>
</div>
<div class="tabbed-block">
<p><img alt="binary_search_insertion_step8" src="../binary_search_insertion.assets/binary_search_insertion_step8.png" /></p>
<p><a class="glightbox" href="../binary_search_insertion.assets/binary_search_insertion_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_insertion_step8" src="../binary_search_insertion.assets/binary_search_insertion_step8.png" /></a></p>
</div>
</div>
</div>
@@ -4164,10 +3991,15 @@ aria-label="页脚"
<div class="md-copyright">
<div class="md-copyright__highlight">
Copyright &copy; 2023 Krahets
Copyright &copy; 2022 - 2023 Krahets
</div>
Made with
<a href="https://squidfunk.github.io/mkdocs-material/" target="_blank" rel="noopener">
Material for MkDocs
</a>
</div>
<!-- Social links -->
@@ -4236,5 +4068,5 @@ aria-label="页脚"
</body>
<script>document$.subscribe(() => {const lightbox = GLightbox({"touchNavigation": true, "loop": false, "zoomable": true, "draggable": false, "openEffect": "zoom", "closeEffect": "zoom", "slideEffect": "none"});})</script></body>
</html>
chapter_searching/index.html
+20 -180
View File
@@ -60,7 +60,18 @@
</head>
<link href="../assets/stylesheets/glightbox.min.css" rel="stylesheet"/><style>
html.glightbox-open { overflow: initial; height: 100%; }
.gslide-title { margin-top: 0px; user-select: text; }
.gslide-desc { color: #666; user-select: text; }
.gslide-image img { background: white; }
.gscrollbar-fixer { padding-right: 15px; }
.gdesc-inner { font-size: 0.75rem; }
body[data-md-color-scheme="slate"] .gdesc-inner { background: var(--md-default-bg-color);}
body[data-md-color-scheme="slate"] .gslide-title { color: var(--md-default-fg-color);}
body[data-md-color-scheme="slate"] .gslide-desc { color: var(--md-default-fg-color);}
</style> <script src="../assets/javascripts/glightbox.min.js"></script></head>
@@ -1877,14 +1888,6 @@
10.2 &nbsp; 二分查找插入点
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -1905,14 +1908,6 @@
10.3 &nbsp; 二分查找边界
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2332,14 +2327,6 @@
第 12 章 &nbsp; 分治
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
@@ -2371,14 +2358,6 @@
12.1 &nbsp; 分治算法
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2399,14 +2378,6 @@
12.2 &nbsp; 分治搜索策略
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2427,14 +2398,6 @@
12.3 &nbsp; 构建树问题
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2455,14 +2418,6 @@
12.4 &nbsp; 汉诺塔问题
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2483,14 +2438,6 @@
12.5 &nbsp; 小结
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2722,14 +2669,6 @@
第 14 章 &nbsp; 动态规划
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
@@ -2761,14 +2700,6 @@
14.1 &nbsp; 初探动态规划
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2789,14 +2720,6 @@
14.2 &nbsp; DP 问题特性
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2817,14 +2740,6 @@
14.3 &nbsp; DP 解题思路
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2845,14 +2760,6 @@
14.4 &nbsp; 0-1 背包问题
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2873,14 +2780,6 @@
14.5 &nbsp; 完全背包问题
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2901,14 +2800,6 @@
14.6 &nbsp; 编辑距离问题
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2929,14 +2820,6 @@
14.7 &nbsp; 小结
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2995,14 +2878,6 @@
第 15 章 &nbsp; 贪心
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
@@ -3034,14 +2909,6 @@
15.1 &nbsp; 贪心算法
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -3062,14 +2929,6 @@
15.2 &nbsp; 分数背包问题
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -3090,14 +2949,6 @@
15.3 &nbsp; 最大容量问题
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -3118,14 +2969,6 @@
15.4 &nbsp; 最大切分乘积问题
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -3146,14 +2989,6 @@
15.5 &nbsp; 小结
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -3414,7 +3249,7 @@
<!-- Page content -->
<h1 id="10">第 10 章 &nbsp; 搜索<a class="headerlink" href="#10" title="Permanent link">&para;</a></h1>
<div class="center-table">
<p><img alt="搜索" src="../assets/covers/chapter_searching.jpg" width="600" /></p>
<p><a class="glightbox" href="../assets/covers/chapter_searching.jpg" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="搜索" src="../assets/covers/chapter_searching.jpg" width="600" /></a></p>
</div>
<div class="admonition abstract">
<p class="admonition-title">Abstract</p>
@@ -3593,10 +3428,15 @@ aria-label="页脚"
<div class="md-copyright">
<div class="md-copyright__highlight">
Copyright &copy; 2023 Krahets
Copyright &copy; 2022 - 2023 Krahets
</div>
Made with
<a href="https://squidfunk.github.io/mkdocs-material/" target="_blank" rel="noopener">
Material for MkDocs
</a>
</div>
<!-- Social links -->
@@ -3665,5 +3505,5 @@ aria-label="页脚"
</body>
<script>document$.subscribe(() => {const lightbox = GLightbox({"touchNavigation": true, "loop": false, "zoomable": true, "draggable": false, "openEffect": "zoom", "closeEffect": "zoom", "slideEffect": "none"});})</script></body>
</html>
chapter_searching/replace_linear_by_hashing/index.html
+23 -183
View File
@@ -60,7 +60,18 @@
</head>
<link href="../../assets/stylesheets/glightbox.min.css" rel="stylesheet"/><style>
html.glightbox-open { overflow: initial; height: 100%; }
.gslide-title { margin-top: 0px; user-select: text; }
.gslide-desc { color: #666; user-select: text; }
.gslide-image img { background: white; }
.gscrollbar-fixer { padding-right: 15px; }
.gdesc-inner { font-size: 0.75rem; }
body[data-md-color-scheme="slate"] .gdesc-inner { background: var(--md-default-bg-color);}
body[data-md-color-scheme="slate"] .gslide-title { color: var(--md-default-fg-color);}
body[data-md-color-scheme="slate"] .gslide-desc { color: var(--md-default-fg-color);}
</style> <script src="../../assets/javascripts/glightbox.min.js"></script></head>
@@ -1877,14 +1888,6 @@
10.2 &nbsp; 二分查找插入点
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -1905,14 +1908,6 @@
10.3 &nbsp; 二分查找边界
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2386,14 +2381,6 @@
第 12 章 &nbsp; 分治
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
@@ -2425,14 +2412,6 @@
12.1 &nbsp; 分治算法
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2453,14 +2432,6 @@
12.2 &nbsp; 分治搜索策略
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2481,14 +2452,6 @@
12.3 &nbsp; 构建树问题
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2509,14 +2472,6 @@
12.4 &nbsp; 汉诺塔问题
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2537,14 +2492,6 @@
12.5 &nbsp; 小结
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2776,14 +2723,6 @@
第 14 章 &nbsp; 动态规划
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
@@ -2815,14 +2754,6 @@
14.1 &nbsp; 初探动态规划
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2843,14 +2774,6 @@
14.2 &nbsp; DP 问题特性
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2871,14 +2794,6 @@
14.3 &nbsp; DP 解题思路
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2899,14 +2814,6 @@
14.4 &nbsp; 0-1 背包问题
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
</li>
@@ -2927,14 +2834,6 @@
14.5 &nbsp; 完全背包问题
</span>
<span class="md-status md-status--new" title="最近添加">
</span>
</a>
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<h2 id="1041">10.4.1 &nbsp; 线性查找：以时间换空间<a class="headerlink" href="#1041" title="Permanent link">&para;</a></h2>
<p>考虑直接遍历所有可能的组合。如图 10-9 所示，我们开启一个两层循环，在每轮中判断两个整数的和是否为 <code>target</code> ，若是则返回它们的索引。</p>
<p><img alt="线性查找求解两数之和" src="../replace_linear_by_hashing.assets/two_sum_brute_force.png" /></p>
<p><a class="glightbox" href="../replace_linear_by_hashing.assets/two_sum_brute_force.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="线性查找求解两数之和" src="../replace_linear_by_hashing.assets/two_sum_brute_force.png" /></a></p>
<p align="center"> 图 10-9 &nbsp; 线性查找求解两数之和 </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>
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<p><img alt="辅助哈希表求解两数之和" src="../replace_linear_by_hashing.assets/two_sum_hashtable_step1.png" /></p>
<p><a class="glightbox" href="../replace_linear_by_hashing.assets/two_sum_hashtable_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="辅助哈希表求解两数之和" src="../replace_linear_by_hashing.assets/two_sum_hashtable_step1.png" /></a></p>
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<h2 id="1053">10.5.3 &nbsp; 搜索方法选取<a class="headerlink" href="#1053" title="Permanent link">&para;</a></h2>
<p>给定大小为 <span class="arithmatex">\(n\)</span> 的一组数据，我们可以使用线性搜索、二分查找、树查找、哈希查找等多种方法在该数据中搜索目标元素。各个方法的工作原理如图 10-11 所示。</p>
<p><img alt="多种搜索策略" src="../searching_algorithm_revisited.assets/searching_algorithms.png" /></p>
<p><a class="glightbox" href="../searching_algorithm_revisited.assets/searching_algorithms.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="多种搜索策略" src="../searching_algorithm_revisited.assets/searching_algorithms.png" /></a></p>
<p align="center"> 图 10-11 &nbsp; 多种搜索策略 </p>
<p>上述几种方法的操作效率与特性如表 10-1 所示。</p>
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