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<p>最直接的方法是借助“元素入堆操作”实现，首先创建一个空堆，然后将列表元素依次添加到堆中。</p>
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<p>设元素数量为 <span class="arithmatex">\(n\)</span> ，则最后一个元素入堆的时间复杂度为 <span class="arithmatex">\(O(\log n)\)</span> 。在依次添加元素时，堆的平均长度为 <span class="arithmatex">\(\frac{n}{2}\)</span> ，因此该方法的总体时间复杂度为 <span class="arithmatex">\(O(n \log n)\)</span> 。</p>
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<h3 id="_2">基于堆化操作实现<a class="headerlink" href="#_2" title="Permanent link">¶</a></h3>
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<p>有趣的是，存在一种更高效的建堆方法，其时间复杂度仅为 <span class="arithmatex">\(O(n)\)</span> 。我们先将列表所有元素原封不动添加到堆中，<strong>然后迭代地对各个结点执行“从顶至底堆化”</strong>。当然，<strong>我们不需要对叶结点执行堆化操作</strong>，因为它们没有子结点。</p>
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<p>有趣的是，存在一种更高效的建堆方法，其时间复杂度仅为 <span class="arithmatex">\(O(n)\)</span> 。我们先将列表所有元素原封不动添加到堆中，<strong>然后迭代地对各个节点执行“从顶至底堆化”</strong>。当然，<strong>我们不需要对叶节点执行堆化操作</strong>，因为它们没有子节点。</p>
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@@ -1794,7 +1794,7 @@
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<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="n">MaxHeap</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="w"> </span><span class="c1">// 将列表元素原封不动添加进堆</span>
|
||||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="w"> </span><span class="n">maxHeap</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">ArrayList</span><span class="o"><></span><span class="p">(</span><span class="n">nums</span><span class="p">);</span>
|
||||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="w"> </span><span class="c1">// 堆化除叶结点以外的其他所有结点</span>
|
||||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="w"> </span><span class="c1">// 堆化除叶节点以外的其他所有节点</span>
|
||||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></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="n">parent</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="mi">1</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="mi">0</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-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="w"> </span><span class="n">siftDown</span><span class="p">(</span><span class="n">i</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="p">}</span>
|
||||
@@ -1806,7 +1806,7 @@
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<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="n">MaxHeap</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w"> </span><span class="c1">// 将列表元素原封不动添加进堆</span>
|
||||
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w"> </span><span class="n">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
|
||||
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w"> </span><span class="c1">// 堆化除叶结点以外的其他所有结点</span>
|
||||
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w"> </span><span class="c1">// 堆化除叶节点以外的其他所有节点</span>
|
||||
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></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="n">parent</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="mi">1</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="mi">0</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-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w"> </span><span class="n">siftDown</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
|
||||
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w"> </span><span class="p">}</span>
|
||||
@@ -1818,7 +1818,7 @@
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<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="w"> </span><span class="sd">""" 构造方法 """</span>
|
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<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a> <span class="c1"># 将列表元素原封不动添加进堆</span>
|
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<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span> <span class="o">=</span> <span class="n">nums</span>
|
||||
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a> <span class="c1"># 堆化除叶结点以外的其他所有结点</span>
|
||||
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a> <span class="c1"># 堆化除叶节点以外的其他所有节点</span>
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<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></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">parent</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">),</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
|
||||
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a> <span class="bp">self</span><span class="o">.</span><span class="n">sift_down</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
|
||||
</code></pre></div>
|
||||
@@ -1829,7 +1829,7 @@
|
||||
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="c1">// 将列表元素原封不动添加进堆</span>
|
||||
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="nx">h</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="o">&</span><span class="nx">maxHeap</span><span class="p">{</span><span class="nx">data</span><span class="p">:</span><span class="w"> </span><span class="nx">nums</span><span class="p">}</span>
|
||||
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">)</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="nx">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="nx">i</span><span class="o">--</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="c1">// 堆化除叶结点以外的其他所有结点</span>
|
||||
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="c1">// 堆化除叶节点以外的其他所有节点</span>
|
||||
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">siftDown</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span>
|
||||
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">h</span>
|
||||
@@ -1841,7 +1841,7 @@
|
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<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kr">constructor</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w"> </span><span class="c1">// 将列表元素原封不动添加进堆</span>
|
||||
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="p">[]</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="p">[...</span><span class="nx">nums</span><span class="p">];</span>
|
||||
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w"> </span><span class="c1">// 堆化除叶结点以外的其他所有结点</span>
|
||||
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w"> </span><span class="c1">// 堆化除叶节点以外的其他所有节点</span>
|
||||
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">parent</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">siftDown</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
|
||||
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="p">}</span>
|
||||
@@ -1853,7 +1853,7 @@
|
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<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kr">constructor</span><span class="p">(</span><span class="nx">nums?</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w"> </span><span class="c1">// 将列表元素原封不动添加进堆</span>
|
||||
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="p">[]</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="p">[...</span><span class="nx">nums</span><span class="p">];</span>
|
||||
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w"> </span><span class="c1">// 堆化除叶结点以外的其他所有结点</span>
|
||||
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w"> </span><span class="c1">// 堆化除叶节点以外的其他所有节点</span>
|
||||
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</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">parent</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">siftDown</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
|
||||
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w"> </span><span class="p">}</span>
|
||||
@@ -1870,7 +1870,7 @@
|
||||
<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">{</span>
|
||||
<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w"> </span><span class="c1">// 将列表元素原封不动添加进堆</span>
|
||||
<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w"> </span><span class="n">maxHeap</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">List</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="p">(</span><span class="n">nums</span><span class="p">);</span>
|
||||
<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w"> </span><span class="c1">// 堆化除叶结点以外的其他所有结点</span>
|
||||
<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w"> </span><span class="c1">// 堆化除叶节点以外的其他所有节点</span>
|
||||
<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w"> </span><span class="kt">var</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">parent</span><span class="p">(</span><span class="k">this</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="m">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></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="n">size</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="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span>
|
||||
<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w"> </span><span class="p">{</span>
|
||||
@@ -1884,7 +1884,7 @@
|
||||
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">init</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">])</span> <span class="p">{</span>
|
||||
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a> <span class="c1">// 将列表元素原封不动添加进堆</span>
|
||||
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a> <span class="n">maxHeap</span> <span class="p">=</span> <span class="n">nums</span>
|
||||
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a> <span class="c1">// 堆化除叶结点以外的其他所有结点</span>
|
||||
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a> <span class="c1">// 堆化除叶节点以外的其他所有节点</span>
|
||||
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">),</span> <span class="n">through</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a> <span class="n">siftDown</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">)</span>
|
||||
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a> <span class="p">}</span>
|
||||
@@ -1898,7 +1898,7 @@
|
||||
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">.</span><span class="n">ArrayList</span><span class="p">(</span><span class="n">T</span><span class="p">).</span><span class="n">init</span><span class="p">(</span><span class="n">allocator</span><span class="p">);</span>
|
||||
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w"> </span><span class="c1">// 将列表元素原封不动添加进堆</span>
|
||||
<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">appendSlice</span><span class="p">(</span><span class="n">nums</span><span class="p">);</span>
|
||||
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w"> </span><span class="c1">// 堆化除叶结点以外的其他所有结点</span>
|
||||
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w"> </span><span class="c1">// 堆化除叶节点以外的其他所有节点</span>
|
||||
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">self</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="mi">1</span><span class="p">)</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-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w"> </span><span class="k">while</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="o">:</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">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">siftDown</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">1</span><span class="p">);</span>
|
||||
@@ -1911,15 +1911,15 @@
|
||||
<h2 id="822">8.2.2. 复杂度分析<a class="headerlink" href="#822" title="Permanent link">¶</a></h2>
|
||||
<p>为什么第二种建堆方法的时间复杂度是 <span class="arithmatex">\(O(n)\)</span> ？我们来展开推算一下。</p>
|
||||
<ul>
|
||||
<li>完全二叉树中，设结点总数为 <span class="arithmatex">\(n\)</span> ，则叶结点数量为 <span class="arithmatex">\((n + 1) / 2\)</span> ，其中 <span class="arithmatex">\(/\)</span> 为向下整除。因此，在排除叶结点后，需要堆化的结点数量为 <span class="arithmatex">\((n - 1)/2\)</span> ，复杂度为 <span class="arithmatex">\(O(n)\)</span> ；</li>
|
||||
<li>在从顶至底堆化的过程中，每个结点最多堆化到叶结点，因此最大迭代次数为二叉树高度 <span class="arithmatex">\(O(\log n)\)</span> ；</li>
|
||||
<li>完全二叉树中，设节点总数为 <span class="arithmatex">\(n\)</span> ，则叶节点数量为 <span class="arithmatex">\((n + 1) / 2\)</span> ，其中 <span class="arithmatex">\(/\)</span> 为向下整除。因此，在排除叶节点后，需要堆化的节点数量为 <span class="arithmatex">\((n - 1)/2\)</span> ，复杂度为 <span class="arithmatex">\(O(n)\)</span> ；</li>
|
||||
<li>在从顶至底堆化的过程中，每个节点最多堆化到叶节点，因此最大迭代次数为二叉树高度 <span class="arithmatex">\(O(\log n)\)</span> ；</li>
|
||||
</ul>
|
||||
<p>将上述两者相乘，可得到建堆过程的时间复杂度为 <span class="arithmatex">\(O(n \log n)\)</span>。<strong>然而，这个估算结果并不准确，因为我们没有考虑到二叉树底层结点数量远多于顶层结点的特性</strong>。</p>
|
||||
<p>接下来我们来进行更为详细的计算。为了减小计算难度，我们假设树是一个“完美二叉树”，该假设不会影响计算结果的正确性。设二叉树（即堆）结点数量为 <span class="arithmatex">\(n\)</span> ，树高度为 <span class="arithmatex">\(h\)</span> 。上文提到，<strong>结点堆化最大迭代次数等于该结点到叶结点的距离，而该距离正是“结点高度”</strong>。</p>
|
||||
<p><img alt="完美二叉树的各层结点数量" src="../build_heap.assets/heapify_operations_count.png" /></p>
|
||||
<p align="center"> Fig. 完美二叉树的各层结点数量 </p>
|
||||
<p>将上述两者相乘，可得到建堆过程的时间复杂度为 <span class="arithmatex">\(O(n \log n)\)</span>。<strong>然而，这个估算结果并不准确，因为我们没有考虑到二叉树底层节点数量远多于顶层节点的特性</strong>。</p>
|
||||
<p>接下来我们来进行更为详细的计算。为了减小计算难度，我们假设树是一个“完美二叉树”，该假设不会影响计算结果的正确性。设二叉树（即堆）节点数量为 <span class="arithmatex">\(n\)</span> ，树高度为 <span class="arithmatex">\(h\)</span> 。上文提到，<strong>节点堆化最大迭代次数等于该节点到叶节点的距离，而该距离正是“节点高度”</strong>。</p>
|
||||
<p><img alt="完美二叉树的各层节点数量" src="../build_heap.assets/heapify_operations_count.png" /></p>
|
||||
<p align="center"> Fig. 完美二叉树的各层节点数量 </p>
|
||||
|
||||
<p>因此，我们可以将各层的“结点数量 <span class="arithmatex">\(\times\)</span> 结点高度”求和，<strong>从而得到所有结点的堆化迭代次数的总和</strong>。</p>
|
||||
<p>因此，我们可以将各层的“节点数量 <span class="arithmatex">\(\times\)</span> 节点高度”求和，<strong>从而得到所有节点的堆化迭代次数的总和</strong>。</p>
|
||||
<div class="arithmatex">\[
|
||||
T(h) = 2^0h + 2^1(h-1) + 2^2(h-2) + \cdots + 2^{(h-1)}\times1
|
||||
\]</div>
|
||||
@@ -1942,7 +1942,7 @@ T(h) & = 2 \frac{1 - 2^h}{1 - 2} - h \newline
|
||||
& = O(2^h)
|
||||
\end{aligned}
|
||||
\]</div>
|
||||
<p>进一步地，高度为 <span class="arithmatex">\(h\)</span> 的完美二叉树的结点数量为 <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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@@ -1838,17 +1838,17 @@
|
||||
<h1 id="81">8.1. 堆<a class="headerlink" href="#81" title="Permanent link">¶</a></h1>
|
||||
<p>「堆 Heap」是一棵限定条件下的「完全二叉树」。根据成立条件，堆主要分为两种类型：</p>
|
||||
<ul>
|
||||
<li>「大顶堆 Max Heap」，任意结点的值 <span class="arithmatex">\(\geq\)</span> 其子结点的值；</li>
|
||||
<li>「小顶堆 Min Heap」，任意结点的值 <span class="arithmatex">\(\leq\)</span> 其子结点的值；</li>
|
||||
<li>「大顶堆 Max Heap」，任意节点的值 <span class="arithmatex">\(\geq\)</span> 其子节点的值；</li>
|
||||
<li>「小顶堆 Min Heap」，任意节点的值 <span class="arithmatex">\(\leq\)</span> 其子节点的值；</li>
|
||||
</ul>
|
||||
<p><img alt="小顶堆与大顶堆" src="../heap.assets/min_heap_and_max_heap.png" /></p>
|
||||
<p align="center"> Fig. 小顶堆与大顶堆 </p>
|
||||
|
||||
<h2 id="811">8.1.1. 堆术语与性质<a class="headerlink" href="#811" title="Permanent link">¶</a></h2>
|
||||
<ul>
|
||||
<li>由于堆是完全二叉树，因此最底层结点靠左填充，其它层结点皆被填满。</li>
|
||||
<li>二叉树中的根结点对应「堆顶」，底层最靠右结点对应「堆底」。</li>
|
||||
<li>对于大顶堆 / 小顶堆，其堆顶元素（即根结点）的值最大 / 最小。</li>
|
||||
<li>由于堆是完全二叉树，因此最底层节点靠左填充，其它层节点皆被填满。</li>
|
||||
<li>二叉树中的根节点对应「堆顶」，底层最靠右节点对应「堆底」。</li>
|
||||
<li>对于大顶堆 / 小顶堆，其堆顶元素（即根节点）的值最大 / 最小。</li>
|
||||
</ul>
|
||||
<h2 id="812">8.1.2. 堆常用操作<a class="headerlink" href="#812" title="Permanent link">¶</a></h2>
|
||||
<p>值得说明的是，多数编程语言提供的是「优先队列 Priority Queue」，其是一种抽象数据结构，<strong>定义为具有出队优先级的队列</strong>。</p>
|
||||
@@ -2146,8 +2146,8 @@
|
||||
<p>下文实现的是「大顶堆」，若想转换为「小顶堆」，将所有大小逻辑判断取逆（例如将 <span class="arithmatex">\(\geq\)</span> 替换为 <span class="arithmatex">\(\leq\)</span> ）即可，有兴趣的同学可自行实现。</p>
|
||||
<h3 id="_1">堆的存储与表示<a class="headerlink" href="#_1" title="Permanent link">¶</a></h3>
|
||||
<p>在二叉树章节我们学过，「完全二叉树」非常适合使用「数组」来表示，而堆恰好是一棵完全二叉树，<strong>因而我们采用「数组」来存储「堆」</strong>。</p>
|
||||
<p><strong>二叉树指针</strong>。使用数组表示二叉树时，元素代表结点值，索引代表结点在二叉树中的位置，<strong>而结点指针通过索引映射公式来实现</strong>。</p>
|
||||
<p>具体地，给定索引 <span class="arithmatex">\(i\)</span> ，那么其左子结点索引为 <span class="arithmatex">\(2i + 1\)</span> 、右子结点索引为 <span class="arithmatex">\(2i + 2\)</span> 、父结点索引为 <span class="arithmatex">\((i - 1) / 2\)</span> （向下整除）。当索引越界时，代表空结点或结点不存在。</p>
|
||||
<p><strong>二叉树指针</strong>。使用数组表示二叉树时，元素代表节点值，索引代表节点在二叉树中的位置，<strong>而节点指针通过索引映射公式来实现</strong>。</p>
|
||||
<p>具体地，给定索引 <span class="arithmatex">\(i\)</span> ，那么其左子节点索引为 <span class="arithmatex">\(2i + 1\)</span> 、右子节点索引为 <span class="arithmatex">\(2i + 2\)</span> 、父节点索引为 <span class="arithmatex">\((i - 1) / 2\)</span> （向下整除）。当索引越界时，代表空节点或节点不存在。</p>
|
||||
<p><img alt="堆的表示与存储" src="../heap.assets/representation_of_heap.png" /></p>
|
||||
<p align="center"> Fig. 堆的表示与存储 </p>
|
||||
|
||||
@@ -2155,34 +2155,34 @@
|
||||
<div class="tabbed-set tabbed-alternate" data-tabs="2:10"><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" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Java</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Python</label><label for="__tabbed_2_4">Go</label><label for="__tabbed_2_5">JavaScript</label><label for="__tabbed_2_6">TypeScript</label><label for="__tabbed_2_7">C</label><label for="__tabbed_2_8">C#</label><label for="__tabbed_2_9">Swift</label><label for="__tabbed_2_10">Zig</label></div>
|
||||
<div class="tabbed-content">
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 获取左子结点索引 */</span>
|
||||
<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 获取左子节点索引 */</span>
|
||||
<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</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">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="p">}</span>
|
||||
<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a>
|
||||
<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="cm">/* 获取右子结点索引 */</span>
|
||||
<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="cm">/* 获取右子节点索引 */</span>
|
||||
<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="kt">int</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</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">2</span><span class="p">;</span>
|
||||
<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="p">}</span>
|
||||
<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a>
|
||||
<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="cm">/* 获取父结点索引 */</span>
|
||||
<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="cm">/* 获取父节点索引 */</span>
|
||||
<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w"> </span><span class="k">return</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">1</span><span class="p">)</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">// 向下整除</span>
|
||||
<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 获取左子结点索引 */</span>
|
||||
<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 获取左子节点索引 */</span>
|
||||
<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</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">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="p">}</span>
|
||||
<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a>
|
||||
<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="cm">/* 获取右子结点索引 */</span>
|
||||
<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="cm">/* 获取右子节点索引 */</span>
|
||||
<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="kt">int</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</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">2</span><span class="p">;</span>
|
||||
<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="p">}</span><span class="w"> </span>
|
||||
<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a>
|
||||
<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="cm">/* 获取父结点索引 */</span>
|
||||
<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="cm">/* 获取父节点索引 */</span>
|
||||
<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w"> </span><span class="k">return</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">1</span><span class="p">)</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">// 向下取整</span>
|
||||
<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="p">}</span>
|
||||
@@ -2190,30 +2190,30 @@
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">my_heap.py</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="k">def</span> <span class="nf">left</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</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>
|
||||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="w"> </span><span class="sd">""" 获取左子结点索引 """</span>
|
||||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="w"> </span><span class="sd">""" 获取左子节点索引 """</span>
|
||||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a> <span class="k">return</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span>
|
||||
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
|
||||
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="k">def</span> <span class="nf">right</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</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>
|
||||
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="sd">""" 获取右子结点索引 """</span>
|
||||
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="sd">""" 获取右子节点索引 """</span>
|
||||
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a> <span class="k">return</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">2</span>
|
||||
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a>
|
||||
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="k">def</span> <span class="nf">parent</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</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>
|
||||
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="sd">""" 获取父结点索引 """</span>
|
||||
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="sd">""" 获取父节点索引 """</span>
|
||||
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a> <span class="k">return</span> <span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span> <span class="c1"># 向下整除</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="cm">/* 获取左子结点索引 */</span>
|
||||
<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="cm">/* 获取左子节点索引 */</span>
|
||||
<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="o">*</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
|
||||
<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="p">}</span>
|
||||
<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>
|
||||
<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="cm">/* 获取右子结点索引 */</span>
|
||||
<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="cm">/* 获取右子节点索引 */</span>
|
||||
<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="o">*</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span>
|
||||
<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="p">}</span>
|
||||
<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>
|
||||
<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="cm">/* 获取父结点索引 */</span>
|
||||
<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="cm">/* 获取父节点索引 */</span>
|
||||
<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</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="c1">// 向下整除</span>
|
||||
<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="nx">i</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="mi">2</span>
|
||||
@@ -2221,34 +2221,34 @@
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 获取左子结点索引 */</span>
|
||||
<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 获取左子节点索引 */</span>
|
||||
<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="err">#</span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="p">)</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="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="p">}</span>
|
||||
<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>
|
||||
<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="cm">/* 获取右子结点索引 */</span>
|
||||
<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="cm">/* 获取右子节点索引 */</span>
|
||||
<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="err">#</span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
|
||||
<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="p">}</span>
|
||||
<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a>
|
||||
<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="cm">/* 获取父结点索引 */</span>
|
||||
<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="cm">/* 获取父节点索引 */</span>
|
||||
<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="err">#</span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </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="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">((</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// 向下整除</span>
|
||||
<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 获取左子结点索引 */</span>
|
||||
<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 获取左子节点索引 */</span>
|
||||
<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="p">}</span>
|
||||
<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a>
|
||||
<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="cm">/* 获取右子结点索引 */</span>
|
||||
<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="cm">/* 获取右子节点索引 */</span>
|
||||
<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
|
||||
<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="p">}</span>
|
||||
<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a>
|
||||
<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="cm">/* 获取父结点索引 */</span>
|
||||
<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="cm">/* 获取父节点索引 */</span>
|
||||
<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">((</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// 向下整除</span>
|
||||
<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="p">}</span>
|
||||
@@ -2263,19 +2263,19 @@
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 获取左子结点索引 */</span>
|
||||
<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 获取左子节点索引 */</span>
|
||||
<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
|
||||
<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="p">{</span>
|
||||
<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="p">}</span>
|
||||
<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a>
|
||||
<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="cm">/* 获取右子结点索引 */</span>
|
||||
<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="cm">/* 获取右子节点索引 */</span>
|
||||
<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="kt">int</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
|
||||
<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="p">{</span>
|
||||
<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
|
||||
<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="p">}</span>
|
||||
<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a>
|
||||
<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="cm">/* 获取父结点索引 */</span>
|
||||
<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="cm">/* 获取父节点索引 */</span>
|
||||
<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="kt">int</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
|
||||
<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="p">{</span>
|
||||
<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w"> </span><span class="k">return</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="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 向下整除</span>
|
||||
@@ -2283,34 +2283,34 @@
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 获取左子结点索引 */</span>
|
||||
<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 获取左子节点索引 */</span>
|
||||
<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span> <span class="nf">left</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span>
|
||||
<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="p">}</span>
|
||||
<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a>
|
||||
<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="cm">/* 获取右子结点索引 */</span>
|
||||
<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="cm">/* 获取右子节点索引 */</span>
|
||||
<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="kd">func</span> <span class="nf">right</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">2</span>
|
||||
<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="p">}</span>
|
||||
<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a>
|
||||
<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="cm">/* 获取父结点索引 */</span>
|
||||
<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="cm">/* 获取父节点索引 */</span>
|
||||
<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="kd">func</span> <span class="nf">parent</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||||
<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a> <span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span> <span class="c1">// 向下整除</span>
|
||||
<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="p">}</span>
|
||||
</code></pre></div>
|
||||
</div>
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">my_heap.zig</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="c1">// 获取左子结点索引</span>
|
||||
<div class="highlight"><span class="filename">my_heap.zig</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="c1">// 获取左子节点索引</span>
|
||||
<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</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">1</span><span class="p">;</span>
|
||||
<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="p">}</span>
|
||||
<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a>
|
||||
<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="c1">// 获取右子结点索引</span>
|
||||
<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="c1">// 获取右子节点索引</span>
|
||||
<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="k">fn</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</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">2</span><span class="p">;</span>
|
||||
<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="p">}</span>
|
||||
<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a>
|
||||
<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="c1">// 获取父结点索引</span>
|
||||
<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="c1">// 获取父节点索引</span>
|
||||
<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="k">fn</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w"> </span><span class="c1">// return (i - 1) / 2; // 向下整除</span>
|
||||
<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">@divFloor</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">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
|
||||
@@ -2320,7 +2320,7 @@
|
||||
</div>
|
||||
</div>
|
||||
<h3 id="_2">访问堆顶元素<a class="headerlink" href="#_2" title="Permanent link">¶</a></h3>
|
||||
<p>堆顶元素是二叉树的根结点，即列表首元素。</p>
|
||||
<p>堆顶元素是二叉树的根节点，即列表首元素。</p>
|
||||
<div class="tabbed-set tabbed-alternate" data-tabs="3:10"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Java</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Python</label><label for="__tabbed_3_4">Go</label><label for="__tabbed_3_5">JavaScript</label><label for="__tabbed_3_6">TypeScript</label><label for="__tabbed_3_7">C</label><label for="__tabbed_3_8">C#</label><label for="__tabbed_3_9">Swift</label><label for="__tabbed_3_10">Zig</label></div>
|
||||
<div class="tabbed-content">
|
||||
<div class="tabbed-block">
|
||||
@@ -2393,8 +2393,8 @@
|
||||
</div>
|
||||
</div>
|
||||
<h3 id="_3">元素入堆<a class="headerlink" href="#_3" title="Permanent link">¶</a></h3>
|
||||
<p>给定元素 <code>val</code> ，我们先将其添加到堆底。添加后，由于 <code>val</code> 可能大于堆中其它元素，此时堆的成立条件可能已经被破坏，<strong>因此需要修复从插入结点到根结点这条路径上的各个结点</strong>，该操作被称为「堆化 Heapify」。</p>
|
||||
<p>考虑从入堆结点开始，<strong>从底至顶执行堆化</strong>。具体地，比较插入结点与其父结点的值，若插入结点更大则将它们交换；并循环以上操作，从底至顶地修复堆中的各个结点；直至越过根结点时结束，或当遇到无需交换的结点时提前结束。</p>
|
||||
<p>给定元素 <code>val</code> ，我们先将其添加到堆底。添加后，由于 <code>val</code> 可能大于堆中其它元素，此时堆的成立条件可能已经被破坏，<strong>因此需要修复从插入节点到根节点这条路径上的各个节点</strong>，该操作被称为「堆化 Heapify」。</p>
|
||||
<p>考虑从入堆节点开始，<strong>从底至顶执行堆化</strong>。具体地，比较插入节点与其父节点的值，若插入节点更大则将它们交换；并循环以上操作，从底至顶地修复堆中的各个节点；直至越过根节点时结束，或当遇到无需交换的节点时提前结束。</p>
|
||||
<div class="tabbed-set tabbed-alternate" data-tabs="4:6"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1"><1></label><label for="__tabbed_4_2"><2></label><label for="__tabbed_4_3"><3></label><label for="__tabbed_4_4"><4></label><label for="__tabbed_4_5"><5></label><label for="__tabbed_4_6"><6></label></div>
|
||||
<div class="tabbed-content">
|
||||
<div class="tabbed-block">
|
||||
@@ -2417,27 +2417,27 @@
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p>设结点总数为 <span class="arithmatex">\(n\)</span> ，则树的高度为 <span class="arithmatex">\(O(\log n)\)</span> ，易得堆化操作的循环轮数最多为 <span class="arithmatex">\(O(\log n)\)</span> ，<strong>因而元素入堆操作的时间复杂度为 <span class="arithmatex">\(O(\log n)\)</span></strong> 。</p>
|
||||
<p>设节点总数为 <span class="arithmatex">\(n\)</span> ，则树的高度为 <span class="arithmatex">\(O(\log n)\)</span> ，易得堆化操作的循环轮数最多为 <span class="arithmatex">\(O(\log n)\)</span> ，<strong>因而元素入堆操作的时间复杂度为 <span class="arithmatex">\(O(\log n)\)</span></strong> 。</p>
|
||||
<div class="tabbed-set tabbed-alternate" data-tabs="5:10"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Java</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Python</label><label for="__tabbed_5_4">Go</label><label for="__tabbed_5_5">JavaScript</label><label for="__tabbed_5_6">TypeScript</label><label for="__tabbed_5_7">C</label><label for="__tabbed_5_8">C#</label><label for="__tabbed_5_9">Swift</label><label for="__tabbed_5_10">Zig</label></div>
|
||||
<div class="tabbed-content">
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 元素入堆 */</span>
|
||||
<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</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-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w"> </span><span class="c1">// 添加结点</span>
|
||||
<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
|
||||
<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
|
||||
<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
|
||||
<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w"> </span><span class="n">siftUp</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="mi">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="p">}</span>
|
||||
<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a>
|
||||
<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="cm">/* 从结点 i 开始，从底至顶堆化 */</span>
|
||||
<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
|
||||
<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftUp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w"> </span><span class="c1">// 获取结点 i 的父结点</span>
|
||||
<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
|
||||
<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
|
||||
<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w"> </span><span class="c1">// 当“越过根结点”或“结点无需修复”时，结束堆化</span>
|
||||
<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无需修复”时，结束堆化</span>
|
||||
<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</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">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">p</span><span class="p">))</span>
|
||||
<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||||
<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="w"> </span><span class="c1">// 交换两结点</span>
|
||||
<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||||
<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
|
||||
<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
|
||||
<a id="__codelineno-30-20" name="__codelineno-30-20" href="#__codelineno-30-20"></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">p</span><span class="p">;</span>
|
||||
@@ -2448,21 +2448,21 @@
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* 元素入堆 */</span>
|
||||
<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</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-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w"> </span><span class="c1">// 添加结点</span>
|
||||
<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
|
||||
<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
|
||||
<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
|
||||
<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="w"> </span><span class="n">siftUp</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="mi">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="p">}</span>
|
||||
<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a>
|
||||
<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="cm">/* 从结点 i 开始，从底至顶堆化 */</span>
|
||||
<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
|
||||
<a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftUp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></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-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="w"> </span><span class="c1">// 获取结点 i 的父结点</span>
|
||||
<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
|
||||
<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
|
||||
<a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a><span class="w"> </span><span class="c1">// 当“越过根结点”或“结点无需修复”时，结束堆化</span>
|
||||
<a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无需修复”时，结束堆化</span>
|
||||
<a id="__codelineno-31-15" name="__codelineno-31-15" href="#__codelineno-31-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</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">i</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">p</span><span class="p">])</span>
|
||||
<a id="__codelineno-31-16" name="__codelineno-31-16" href="#__codelineno-31-16"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||||
<a id="__codelineno-31-17" name="__codelineno-31-17" href="#__codelineno-31-17"></a><span class="w"> </span><span class="c1">// 交换两结点</span>
|
||||
<a id="__codelineno-31-17" name="__codelineno-31-17" href="#__codelineno-31-17"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||||
<a id="__codelineno-31-18" name="__codelineno-31-18" href="#__codelineno-31-18"></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">p</span><span class="p">]);</span>
|
||||
<a id="__codelineno-31-19" name="__codelineno-31-19" href="#__codelineno-31-19"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
|
||||
<a id="__codelineno-31-20" name="__codelineno-31-20" href="#__codelineno-31-20"></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">p</span><span class="p">;</span>
|
||||
@@ -2473,20 +2473,20 @@
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">my_heap.py</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="k">def</span> <span class="nf">push</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-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="w"> </span><span class="sd">""" 元素入堆 """</span>
|
||||
<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a> <span class="c1"># 添加结点</span>
|
||||
<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a> <span class="c1"># 添加节点</span>
|
||||
<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
|
||||
<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a> <span class="c1"># 从底至顶堆化</span>
|
||||
<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a> <span class="bp">self</span><span class="o">.</span><span class="n">sift_up</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a>
|
||||
<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="k">def</span> <span class="nf">sift_up</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||||
<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="w"> </span><span class="sd">""" 从结点 i 开始，从底至顶堆化 """</span>
|
||||
<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="w"> </span><span class="sd">""" 从节点 i 开始，从底至顶堆化 """</span>
|
||||
<a id="__codelineno-32-10" name="__codelineno-32-10" href="#__codelineno-32-10"></a> <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
|
||||
<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a> <span class="c1"># 获取结点 i 的父结点</span>
|
||||
<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a> <span class="c1"># 获取节点 i 的父节点</span>
|
||||
<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a> <span class="n">p</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
|
||||
<a id="__codelineno-32-13" name="__codelineno-32-13" href="#__codelineno-32-13"></a> <span class="c1"># 当“越过根结点”或“结点无需修复”时，结束堆化</span>
|
||||
<a id="__codelineno-32-13" name="__codelineno-32-13" href="#__codelineno-32-13"></a> <span class="c1"># 当“越过根节点”或“节点无需修复”时，结束堆化</span>
|
||||
<a id="__codelineno-32-14" name="__codelineno-32-14" href="#__codelineno-32-14"></a> <span class="k">if</span> <span class="n">p</span> <span class="o"><</span> <span class="mi">0</span> <span class="ow">or</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</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">max_heap</span><span class="p">[</span><span class="n">p</span><span class="p">]:</span>
|
||||
<a id="__codelineno-32-15" name="__codelineno-32-15" href="#__codelineno-32-15"></a> <span class="k">break</span>
|
||||
<a id="__codelineno-32-16" name="__codelineno-32-16" href="#__codelineno-32-16"></a> <span class="c1"># 交换两结点</span>
|
||||
<a id="__codelineno-32-16" name="__codelineno-32-16" href="#__codelineno-32-16"></a> <span class="c1"># 交换两节点</span>
|
||||
<a id="__codelineno-32-17" name="__codelineno-32-17" href="#__codelineno-32-17"></a> <span class="bp">self</span><span class="o">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">p</span><span class="p">)</span>
|
||||
<a id="__codelineno-32-18" name="__codelineno-32-18" href="#__codelineno-32-18"></a> <span class="c1"># 循环向上堆化</span>
|
||||
<a id="__codelineno-32-19" name="__codelineno-32-19" href="#__codelineno-32-19"></a> <span class="n">i</span> <span class="o">=</span> <span class="n">p</span>
|
||||
@@ -2495,22 +2495,22 @@
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* 元素入堆 */</span>
|
||||
<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="kt">any</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w"> </span><span class="c1">// 添加结点</span>
|
||||
<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
|
||||
<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">)</span>
|
||||
<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
|
||||
<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">siftUp</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">)</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-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="p">}</span>
|
||||
<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a>
|
||||
<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="cm">/* 从结点 i 开始，从底至顶堆化 */</span>
|
||||
<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
|
||||
<a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">siftUp</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="kc">true</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="w"> </span><span class="c1">// 获取结点 i 的父结点</span>
|
||||
<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
|
||||
<a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a><span class="w"> </span><span class="nx">p</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span>
|
||||
<a id="__codelineno-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></a><span class="w"> </span><span class="c1">// 当“越过根结点”或“结点无需修复”时，结束堆化</span>
|
||||
<a id="__codelineno-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无需修复”时，结束堆化</span>
|
||||
<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">p</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">i</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">p</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-33-16" name="__codelineno-33-16" href="#__codelineno-33-16"></a><span class="w"> </span><span class="k">break</span>
|
||||
<a id="__codelineno-33-17" name="__codelineno-33-17" href="#__codelineno-33-17"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-33-18" name="__codelineno-33-18" href="#__codelineno-33-18"></a><span class="w"> </span><span class="c1">// 交换两结点</span>
|
||||
<a id="__codelineno-33-18" name="__codelineno-33-18" href="#__codelineno-33-18"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||||
<a id="__codelineno-33-19" name="__codelineno-33-19" href="#__codelineno-33-19"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">p</span><span class="p">)</span>
|
||||
<a id="__codelineno-33-20" name="__codelineno-33-20" href="#__codelineno-33-20"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
|
||||
<a id="__codelineno-33-21" name="__codelineno-33-21" href="#__codelineno-33-21"></a><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">p</span>
|
||||
@@ -2521,20 +2521,20 @@
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* 元素入堆 */</span>
|
||||
<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w"> </span><span class="c1">// 添加结点</span>
|
||||
<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
|
||||
<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="p">);</span>
|
||||
<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
|
||||
<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">siftUp</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="p">}</span>
|
||||
<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a>
|
||||
<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="cm">/* 从结点 i 开始，从底至顶堆化 */</span>
|
||||
<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
|
||||
<a id="__codelineno-34-10" name="__codelineno-34-10" href="#__codelineno-34-10"></a><span class="err">#</span><span class="nx">siftUp</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-34-11" name="__codelineno-34-11" href="#__codelineno-34-11"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-34-12" name="__codelineno-34-12" href="#__codelineno-34-12"></a><span class="w"> </span><span class="c1">// 获取结点 i 的父结点</span>
|
||||
<a id="__codelineno-34-12" name="__codelineno-34-12" href="#__codelineno-34-12"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
|
||||
<a id="__codelineno-34-13" name="__codelineno-34-13" href="#__codelineno-34-13"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
|
||||
<a id="__codelineno-34-14" name="__codelineno-34-14" href="#__codelineno-34-14"></a><span class="w"> </span><span class="c1">// 当“越过根结点”或“结点无需修复”时，结束堆化</span>
|
||||
<a id="__codelineno-34-14" name="__codelineno-34-14" href="#__codelineno-34-14"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无需修复”时，结束堆化</span>
|
||||
<a id="__codelineno-34-15" name="__codelineno-34-15" href="#__codelineno-34-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">p</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">p</span><span class="p">])</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||||
<a id="__codelineno-34-16" name="__codelineno-34-16" href="#__codelineno-34-16"></a><span class="w"> </span><span class="c1">// 交换两结点</span>
|
||||
<a id="__codelineno-34-16" name="__codelineno-34-16" href="#__codelineno-34-16"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||||
<a id="__codelineno-34-17" name="__codelineno-34-17" href="#__codelineno-34-17"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">p</span><span class="p">);</span>
|
||||
<a id="__codelineno-34-18" name="__codelineno-34-18" href="#__codelineno-34-18"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
|
||||
<a id="__codelineno-34-19" name="__codelineno-34-19" href="#__codelineno-34-19"></a><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">p</span><span class="p">;</span>
|
||||
@@ -2545,20 +2545,20 @@
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* 元素入堆 */</span>
|
||||
<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w"> </span><span class="c1">// 添加结点</span>
|
||||
<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
|
||||
<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="p">);</span>
|
||||
<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
|
||||
<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">siftUp</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="p">}</span>
|
||||
<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a>
|
||||
<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="cm">/* 从结点 i 开始，从底至顶堆化 */</span>
|
||||
<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
|
||||
<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a><span class="nx">siftUp</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-35-11" name="__codelineno-35-11" href="#__codelineno-35-11"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-35-12" name="__codelineno-35-12" href="#__codelineno-35-12"></a><span class="w"> </span><span class="c1">// 获取结点 i 的父结点</span>
|
||||
<a id="__codelineno-35-12" name="__codelineno-35-12" href="#__codelineno-35-12"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
|
||||
<a id="__codelineno-35-13" name="__codelineno-35-13" href="#__codelineno-35-13"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">p</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">parent</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
|
||||
<a id="__codelineno-35-14" name="__codelineno-35-14" href="#__codelineno-35-14"></a><span class="w"> </span><span class="c1">// 当“越过根结点”或“结点无需修复”时，结束堆化</span>
|
||||
<a id="__codelineno-35-14" name="__codelineno-35-14" href="#__codelineno-35-14"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无需修复”时，结束堆化</span>
|
||||
<a id="__codelineno-35-15" name="__codelineno-35-15" href="#__codelineno-35-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">p</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mf">0</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">maxHeap</span><span class="p">[</span><span class="nx">i</span><span class="p">]</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">maxHeap</span><span class="p">[</span><span class="nx">p</span><span class="p">])</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||||
<a id="__codelineno-35-16" name="__codelineno-35-16" href="#__codelineno-35-16"></a><span class="w"> </span><span class="c1">// 交换两结点</span>
|
||||
<a id="__codelineno-35-16" name="__codelineno-35-16" href="#__codelineno-35-16"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||||
<a id="__codelineno-35-17" name="__codelineno-35-17" href="#__codelineno-35-17"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">p</span><span class="p">);</span>
|
||||
<a id="__codelineno-35-18" name="__codelineno-35-18" href="#__codelineno-35-18"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
|
||||
<a id="__codelineno-35-19" name="__codelineno-35-19" href="#__codelineno-35-19"></a><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">p</span><span class="p">;</span>
|
||||
@@ -2576,23 +2576,23 @@
|
||||
<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* 元素入堆 */</span>
|
||||
<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
|
||||
<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="p">{</span>
|
||||
<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w"> </span><span class="c1">// 添加结点</span>
|
||||
<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w"> </span><span class="c1">// 添加节点</span>
|
||||
<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
|
||||
<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
|
||||
<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w"> </span><span class="n">siftUp</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="m">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="p">}</span>
|
||||
<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a>
|
||||
<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a><span class="cm">/* 从结点 i 开始，从底至顶堆化 */</span>
|
||||
<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
|
||||
<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a><span class="k">void</span><span class="w"> </span><span class="nf">siftUp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
|
||||
<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></a><span class="p">{</span>
|
||||
<a id="__codelineno-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="k">true</span><span class="p">)</span>
|
||||
<a id="__codelineno-37-14" name="__codelineno-37-14" href="#__codelineno-37-14"></a><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-37-15" name="__codelineno-37-15" href="#__codelineno-37-15"></a><span class="w"> </span><span class="c1">// 获取结点 i 的父结点</span>
|
||||
<a id="__codelineno-37-15" name="__codelineno-37-15" href="#__codelineno-37-15"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
|
||||
<a id="__codelineno-37-16" name="__codelineno-37-16" href="#__codelineno-37-16"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
|
||||
<a id="__codelineno-37-17" name="__codelineno-37-17" href="#__codelineno-37-17"></a><span class="w"> </span><span class="c1">// 若“越过根结点”或“结点无需修复”，则结束堆化</span>
|
||||
<a id="__codelineno-37-17" name="__codelineno-37-17" href="#__codelineno-37-17"></a><span class="w"> </span><span class="c1">// 若“越过根节点”或“节点无需修复”，则结束堆化</span>
|
||||
<a id="__codelineno-37-18" name="__codelineno-37-18" href="#__codelineno-37-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="m">0</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">i</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">p</span><span class="p">])</span>
|
||||
<a id="__codelineno-37-19" name="__codelineno-37-19" href="#__codelineno-37-19"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||||
<a id="__codelineno-37-20" name="__codelineno-37-20" href="#__codelineno-37-20"></a><span class="w"> </span><span class="c1">// 交换两结点</span>
|
||||
<a id="__codelineno-37-20" name="__codelineno-37-20" href="#__codelineno-37-20"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||||
<a id="__codelineno-37-21" name="__codelineno-37-21" href="#__codelineno-37-21"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
|
||||
<a id="__codelineno-37-22" name="__codelineno-37-22" href="#__codelineno-37-22"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
|
||||
<a id="__codelineno-37-23" name="__codelineno-37-23" href="#__codelineno-37-23"></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">p</span><span class="p">;</span>
|
||||
@@ -2603,23 +2603,23 @@
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="cm">/* 元素入堆 */</span>
|
||||
<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="kd">func</span> <span class="nf">push</span><span class="p">(</span><span class="n">val</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a> <span class="c1">// 添加结点</span>
|
||||
<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a> <span class="c1">// 添加节点</span>
|
||||
<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a> <span class="n">maxHeap</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
|
||||
<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a> <span class="c1">// 从底至顶堆化</span>
|
||||
<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a> <span class="n">siftUp</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="p">}</span>
|
||||
<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a>
|
||||
<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="cm">/* 从结点 i 开始，从底至顶堆化 */</span>
|
||||
<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
|
||||
<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a><span class="kd">func</span> <span class="nf">siftUp</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a> <span class="kd">var</span> <span class="nv">i</span> <span class="p">=</span> <span class="n">i</span>
|
||||
<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a> <span class="k">while</span> <span class="kc">true</span> <span class="p">{</span>
|
||||
<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a> <span class="c1">// 获取结点 i 的父结点</span>
|
||||
<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a> <span class="c1">// 获取节点 i 的父节点</span>
|
||||
<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a> <span class="kd">let</span> <span class="nv">p</span> <span class="p">=</span> <span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">)</span>
|
||||
<a id="__codelineno-38-15" name="__codelineno-38-15" href="#__codelineno-38-15"></a> <span class="c1">// 当“越过根结点”或“结点无需修复”时，结束堆化</span>
|
||||
<a id="__codelineno-38-15" name="__codelineno-38-15" href="#__codelineno-38-15"></a> <span class="c1">// 当“越过根节点”或“节点无需修复”时，结束堆化</span>
|
||||
<a id="__codelineno-38-16" name="__codelineno-38-16" href="#__codelineno-38-16"></a> <span class="k">if</span> <span class="n">p</span> <span class="o"><</span> <span class="mi">0</span> <span class="o">||</span> <span class="n">maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o"><=</span> <span class="n">maxHeap</span><span class="p">[</span><span class="n">p</span><span class="p">]</span> <span class="p">{</span>
|
||||
<a id="__codelineno-38-17" name="__codelineno-38-17" href="#__codelineno-38-17"></a> <span class="k">break</span>
|
||||
<a id="__codelineno-38-18" name="__codelineno-38-18" href="#__codelineno-38-18"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-38-19" name="__codelineno-38-19" href="#__codelineno-38-19"></a> <span class="c1">// 交换两结点</span>
|
||||
<a id="__codelineno-38-19" name="__codelineno-38-19" href="#__codelineno-38-19"></a> <span class="c1">// 交换两节点</span>
|
||||
<a id="__codelineno-38-20" name="__codelineno-38-20" href="#__codelineno-38-20"></a> <span class="bp">swap</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="n">p</span><span class="p">)</span>
|
||||
<a id="__codelineno-38-21" name="__codelineno-38-21" href="#__codelineno-38-21"></a> <span class="c1">// 循环向上堆化</span>
|
||||
<a id="__codelineno-38-22" name="__codelineno-38-22" href="#__codelineno-38-22"></a> <span class="n">i</span> <span class="p">=</span> <span class="n">p</span>
|
||||
@@ -2630,21 +2630,21 @@
|
||||
<div class="tabbed-block">
|
||||
<div class="highlight"><span class="filename">my_heap.zig</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="c1">// 元素入堆</span>
|
||||
<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="o">:</span><span class="w"> </span><span class="n">T</span><span class="p">)</span><span class="w"> </span><span class="o">!</span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a><span class="w"> </span><span class="c1">// 添加结点</span>
|
||||
<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
|
||||
<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
|
||||
<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
|
||||
<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">siftUp</span><span class="p">(</span><span class="n">self</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="mi">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a><span class="p">}</span><span class="w"> </span>
|
||||
<a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a>
|
||||
<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a><span class="c1">// 从结点 i 开始，从底至顶堆化</span>
|
||||
<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a><span class="c1">// 从节点 i 开始，从底至顶堆化</span>
|
||||
<a id="__codelineno-39-10" name="__codelineno-39-10" href="#__codelineno-39-10"></a><span class="k">fn</span><span class="w"> </span><span class="n">siftUp</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">i_</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="o">!</span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-39-11" name="__codelineno-39-11" href="#__codelineno-39-11"></a><span class="w"> </span><span class="kr">var</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">i_</span><span class="p">;</span>
|
||||
<a id="__codelineno-39-12" name="__codelineno-39-12" href="#__codelineno-39-12"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-39-13" name="__codelineno-39-13" href="#__codelineno-39-13"></a><span class="w"> </span><span class="c1">// 获取结点 i 的父结点</span>
|
||||
<a id="__codelineno-39-13" name="__codelineno-39-13" href="#__codelineno-39-13"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
|
||||
<a id="__codelineno-39-14" name="__codelineno-39-14" href="#__codelineno-39-14"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
|
||||
<a id="__codelineno-39-15" name="__codelineno-39-15" href="#__codelineno-39-15"></a><span class="w"> </span><span class="c1">// 当“越过根结点”或“结点无需修复”时，结束堆化</span>
|
||||
<a id="__codelineno-39-15" name="__codelineno-39-15" href="#__codelineno-39-15"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无需修复”时，结束堆化</span>
|
||||
<a id="__codelineno-39-16" name="__codelineno-39-16" href="#__codelineno-39-16"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="k">or</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</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">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</span><span class="p">[</span><span class="n">p</span><span class="p">])</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||||
<a id="__codelineno-39-17" name="__codelineno-39-17" href="#__codelineno-39-17"></a><span class="w"> </span><span class="c1">// 交换两结点</span>
|
||||
<a id="__codelineno-39-17" name="__codelineno-39-17" href="#__codelineno-39-17"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||||
<a id="__codelineno-39-18" name="__codelineno-39-18" href="#__codelineno-39-18"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
|
||||
<a id="__codelineno-39-19" name="__codelineno-39-19" href="#__codelineno-39-19"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
|
||||
<a id="__codelineno-39-20" name="__codelineno-39-20" href="#__codelineno-39-20"></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">p</span><span class="p">;</span>
|
||||
@@ -2655,13 +2655,13 @@
|
||||
</div>
|
||||
</div>
|
||||
<h3 id="_4">堆顶元素出堆<a class="headerlink" href="#_4" title="Permanent link">¶</a></h3>
|
||||
<p>堆顶元素是二叉树根结点，即列表首元素，如果我们直接将首元素从列表中删除，则二叉树中所有结点都会随之发生移位（索引发生变化），这样后续使用堆化修复就很麻烦了。为了尽量减少元素索引变动，采取以下操作步骤：</p>
|
||||
<p>堆顶元素是二叉树根节点，即列表首元素，如果我们直接将首元素从列表中删除，则二叉树中所有节点都会随之发生移位（索引发生变化），这样后续使用堆化修复就很麻烦了。为了尽量减少元素索引变动，采取以下操作步骤：</p>
|
||||
<ol>
|
||||
<li>交换堆顶元素与堆底元素（即交换根结点与最右叶结点）；</li>
|
||||
<li>交换堆顶元素与堆底元素（即交换根节点与最右叶节点）；</li>
|
||||
<li>交换完成后，将堆底从列表中删除（注意，因为已经交换，实际上删除的是原来的堆顶元素）；</li>
|
||||
<li>从根结点开始，<strong>从顶至底执行堆化</strong>；</li>
|
||||
<li>从根节点开始，<strong>从顶至底执行堆化</strong>；</li>
|
||||
</ol>
|
||||
<p>顾名思义，<strong>从顶至底堆化的操作方向与从底至顶堆化相反</strong>，我们比较根结点的值与其两个子结点的值，将最大的子结点与根结点执行交换，并循环以上操作，直到越过叶结点时结束，或当遇到无需交换的结点时提前结束。</p>
|
||||
<p>顾名思义，<strong>从顶至底堆化的操作方向与从底至顶堆化相反</strong>，我们比较根节点的值与其两个子节点的值，将最大的子节点与根节点执行交换，并循环以上操作，直到越过叶节点时结束，或当遇到无需交换的节点时提前结束。</p>
|
||||
<div class="tabbed-set tabbed-alternate" data-tabs="6:10"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1"><1></label><label for="__tabbed_6_2"><2></label><label for="__tabbed_6_3"><3></label><label for="__tabbed_6_4"><4></label><label for="__tabbed_6_5"><5></label><label for="__tabbed_6_6"><6></label><label for="__tabbed_6_7"><7></label><label for="__tabbed_6_8"><8></label><label for="__tabbed_6_9"><9></label><label for="__tabbed_6_10"><10></label></div>
|
||||
<div class="tabbed-content">
|
||||
<div class="tabbed-block">
|
||||
@@ -2705,9 +2705,9 @@
|
||||
<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
|
||||
<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
|
||||
<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">EmptyStackException</span><span class="p">();</span>
|
||||
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w"> </span><span class="c1">// 交换根结点与最右叶结点（即交换首元素与尾元素）</span>
|
||||
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（即交换首元素与尾元素）</span>
|
||||
<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</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="mi">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w"> </span><span class="c1">// 删除结点</span>
|
||||
<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w"> </span><span class="c1">// 删除节点</span>
|
||||
<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">remove</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="mi">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
|
||||
<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w"> </span><span class="n">siftDown</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
|
||||
@@ -2715,18 +2715,18 @@
|
||||
<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
|
||||
<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="p">}</span>
|
||||
<a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a>
|
||||
<a id="__codelineno-40-16" name="__codelineno-40-16" href="#__codelineno-40-16"></a><span class="cm">/* 从结点 i 开始，从顶至底堆化 */</span>
|
||||
<a id="__codelineno-40-16" name="__codelineno-40-16" href="#__codelineno-40-16"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
|
||||
<a id="__codelineno-40-17" name="__codelineno-40-17" href="#__codelineno-40-17"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-40-18" name="__codelineno-40-18" href="#__codelineno-40-18"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-40-19" name="__codelineno-40-19" href="#__codelineno-40-19"></a><span class="w"> </span><span class="c1">// 判断结点 i, l, r 中值最大的结点，记为 ma</span>
|
||||
<a id="__codelineno-40-19" name="__codelineno-40-19" href="#__codelineno-40-19"></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-40-20" name="__codelineno-40-20" href="#__codelineno-40-20"></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-40-21" name="__codelineno-40-21" href="#__codelineno-40-21"></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="na">get</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="na">get</span><span class="p">(</span><span class="n">ma</span><span class="p">))</span>
|
||||
<a id="__codelineno-40-22" name="__codelineno-40-22" href="#__codelineno-40-22"></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-40-23" name="__codelineno-40-23" href="#__codelineno-40-23"></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="na">get</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="na">get</span><span class="p">(</span><span class="n">ma</span><span class="p">))</span>
|
||||
<a id="__codelineno-40-24" name="__codelineno-40-24" href="#__codelineno-40-24"></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-40-25" name="__codelineno-40-25" href="#__codelineno-40-25"></a><span class="w"> </span><span class="c1">// 若结点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
|
||||
<a id="__codelineno-40-25" name="__codelineno-40-25" href="#__codelineno-40-25"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
|
||||
<a id="__codelineno-40-26" name="__codelineno-40-26" href="#__codelineno-40-26"></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><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||||
<a id="__codelineno-40-27" name="__codelineno-40-27" href="#__codelineno-40-27"></a><span class="w"> </span><span class="c1">// 交换两结点</span>
|
||||
<a id="__codelineno-40-27" name="__codelineno-40-27" href="#__codelineno-40-27"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||||
<a id="__codelineno-40-28" name="__codelineno-40-28" href="#__codelineno-40-28"></a><span class="w"> </span><span class="n">swap</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="p">);</span>
|
||||
<a id="__codelineno-40-29" name="__codelineno-40-29" href="#__codelineno-40-29"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
|
||||
<a id="__codelineno-40-30" name="__codelineno-40-30" href="#__codelineno-40-30"></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>
|
||||
@@ -2741,25 +2741,25 @@
|
||||
<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">empty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">"堆为空"</span><span class="p">);</span>
|
||||
<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="w"> </span><span class="c1">// 交换根结点与最右叶结点（即交换首元素与尾元素）</span>
|
||||
<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（即交换首元素与尾元素）</span>
|
||||
<a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></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="mi">0</span><span class="p">],</span><span class="w"> </span><span class="n">maxHeap</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="mi">1</span><span class="p">]);</span>
|
||||
<a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="w"> </span><span class="c1">// 删除结点</span>
|
||||
<a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="w"> </span><span class="c1">// 删除节点</span>
|
||||
<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
|
||||
<a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
|
||||
<a id="__codelineno-41-12" name="__codelineno-41-12" href="#__codelineno-41-12"></a><span class="w"> </span><span class="n">siftDown</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
|
||||
<a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a><span class="p">}</span>
|
||||
<a id="__codelineno-41-14" name="__codelineno-41-14" href="#__codelineno-41-14"></a>
|
||||
<a id="__codelineno-41-15" name="__codelineno-41-15" href="#__codelineno-41-15"></a><span class="cm">/* 从结点 i 开始，从顶至底堆化 */</span>
|
||||
<a id="__codelineno-41-15" name="__codelineno-41-15" href="#__codelineno-41-15"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
|
||||
<a id="__codelineno-41-16" name="__codelineno-41-16" href="#__codelineno-41-16"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-41-17" name="__codelineno-41-17" href="#__codelineno-41-17"></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-41-18" name="__codelineno-41-18" href="#__codelineno-41-18"></a><span class="w"> </span><span class="c1">// 判断结点 i, l, r 中值最大的结点，记为 ma</span>
|
||||
<a id="__codelineno-41-18" name="__codelineno-41-18" href="#__codelineno-41-18"></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-41-19" name="__codelineno-41-19" href="#__codelineno-41-19"></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-41-20" name="__codelineno-41-20" href="#__codelineno-41-20"></a><span class="w"> </span><span class="c1">// 若结点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
|
||||
<a id="__codelineno-41-20" name="__codelineno-41-20" href="#__codelineno-41-20"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
|
||||
<a id="__codelineno-41-21" name="__codelineno-41-21" href="#__codelineno-41-21"></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><span class="w"> </span>
|
||||
<a id="__codelineno-41-22" name="__codelineno-41-22" href="#__codelineno-41-22"></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-41-23" name="__codelineno-41-23" href="#__codelineno-41-23"></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-41-24" name="__codelineno-41-24" href="#__codelineno-41-24"></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-41-25" name="__codelineno-41-25" href="#__codelineno-41-25"></a><span class="w"> </span><span class="c1">// 若结点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
|
||||
<a id="__codelineno-41-25" name="__codelineno-41-25" href="#__codelineno-41-25"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
|
||||
<a id="__codelineno-41-26" name="__codelineno-41-26" href="#__codelineno-41-26"></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><span class="w"> </span>
|
||||
<a id="__codelineno-41-27" name="__codelineno-41-27" href="#__codelineno-41-27"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||||
<a id="__codelineno-41-28" name="__codelineno-41-28" href="#__codelineno-41-28"></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>
|
||||
@@ -2774,9 +2774,9 @@
|
||||
<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="w"> </span><span class="sd">""" 元素出堆 """</span>
|
||||
<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a> <span class="c1"># 判空处理</span>
|
||||
<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a> <span class="k">assert</span> <span class="ow">not</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">()</span>
|
||||
<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a> <span class="c1"># 交换根结点与最右叶结点（即交换首元素与尾元素）</span>
|
||||
<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a> <span class="c1"># 交换根节点与最右叶节点（即交换首元素与尾元素）</span>
|
||||
<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a> <span class="bp">self</span><span class="o">.</span><span class="n">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a> <span class="c1"># 删除结点</span>
|
||||
<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a> <span class="c1"># 删除节点</span>
|
||||
<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a> <span class="n">val</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
|
||||
<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a> <span class="c1"># 从顶至底堆化</span>
|
||||
<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a> <span class="bp">self</span><span class="o">.</span><span class="n">sift_down</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||||
@@ -2784,18 +2784,18 @@
|
||||
<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a> <span class="k">return</span> <span class="n">val</span>
|
||||
<a id="__codelineno-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></a>
|
||||
<a id="__codelineno-42-14" name="__codelineno-42-14" href="#__codelineno-42-14"></a><span class="k">def</span> <span class="nf">sift_down</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||||
<a id="__codelineno-42-15" name="__codelineno-42-15" href="#__codelineno-42-15"></a><span class="w"> </span><span class="sd">""" 从结点 i 开始，从顶至底堆化 """</span>
|
||||
<a id="__codelineno-42-15" name="__codelineno-42-15" href="#__codelineno-42-15"></a><span class="w"> </span><span class="sd">""" 从节点 i 开始，从顶至底堆化 """</span>
|
||||
<a id="__codelineno-42-16" name="__codelineno-42-16" href="#__codelineno-42-16"></a> <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
|
||||
<a id="__codelineno-42-17" name="__codelineno-42-17" href="#__codelineno-42-17"></a> <span class="c1"># 判断结点 i, l, r 中值最大的结点，记为 ma</span>
|
||||
<a id="__codelineno-42-17" name="__codelineno-42-17" href="#__codelineno-42-17"></a> <span class="c1"># 判断节点 i, l, r 中值最大的节点，记为 ma</span>
|
||||
<a id="__codelineno-42-18" name="__codelineno-42-18" href="#__codelineno-42-18"></a> <span class="n">l</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="n">ma</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="n">i</span>
|
||||
<a id="__codelineno-42-19" name="__codelineno-42-19" href="#__codelineno-42-19"></a> <span class="k">if</span> <span class="n">l</span> <span class="o"><</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span> <span class="o">></span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">ma</span><span class="p">]:</span>
|
||||
<a id="__codelineno-42-20" name="__codelineno-42-20" href="#__codelineno-42-20"></a> <span class="n">ma</span> <span class="o">=</span> <span class="n">l</span>
|
||||
<a id="__codelineno-42-21" name="__codelineno-42-21" href="#__codelineno-42-21"></a> <span class="k">if</span> <span class="n">r</span> <span class="o"><</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span> <span class="o">></span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">ma</span><span class="p">]:</span>
|
||||
<a id="__codelineno-42-22" name="__codelineno-42-22" href="#__codelineno-42-22"></a> <span class="n">ma</span> <span class="o">=</span> <span class="n">r</span>
|
||||
<a id="__codelineno-42-23" name="__codelineno-42-23" href="#__codelineno-42-23"></a> <span class="c1"># 若结点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
|
||||
<a id="__codelineno-42-23" name="__codelineno-42-23" href="#__codelineno-42-23"></a> <span class="c1"># 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
|
||||
<a id="__codelineno-42-24" name="__codelineno-42-24" href="#__codelineno-42-24"></a> <span class="k">if</span> <span class="n">ma</span> <span class="o">==</span> <span class="n">i</span><span class="p">:</span>
|
||||
<a id="__codelineno-42-25" name="__codelineno-42-25" href="#__codelineno-42-25"></a> <span class="k">break</span>
|
||||
<a id="__codelineno-42-26" name="__codelineno-42-26" href="#__codelineno-42-26"></a> <span class="c1"># 交换两结点</span>
|
||||
<a id="__codelineno-42-26" name="__codelineno-42-26" href="#__codelineno-42-26"></a> <span class="c1"># 交换两节点</span>
|
||||
<a id="__codelineno-42-27" name="__codelineno-42-27" href="#__codelineno-42-27"></a> <span class="bp">self</span><span class="o">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">ma</span><span class="p">)</span>
|
||||
<a id="__codelineno-42-28" name="__codelineno-42-28" href="#__codelineno-42-28"></a> <span class="c1"># 循环向下堆化</span>
|
||||
<a id="__codelineno-42-29" name="__codelineno-42-29" href="#__codelineno-42-29"></a> <span class="n">i</span> <span class="o">=</span> <span class="n">ma</span>
|
||||
@@ -2809,9 +2809,9 @@
|
||||
<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="s">"error"</span><span class="p">)</span>
|
||||
<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
|
||||
<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w"> </span><span class="c1">// 交换根结点与最右叶结点（即交换首元素与尾元素）</span>
|
||||
<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（即交换首元素与尾元素）</span>
|
||||
<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w"> </span><span class="c1">// 删除结点</span>
|
||||
<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w"> </span><span class="c1">// 删除节点</span>
|
||||
<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nb">len</span><span class="p">(</span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
|
||||
<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[:</span><span class="nb">len</span><span class="p">(</span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
|
||||
<a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
|
||||
@@ -2821,10 +2821,10 @@
|
||||
<a id="__codelineno-43-17" name="__codelineno-43-17" href="#__codelineno-43-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">val</span>
|
||||
<a id="__codelineno-43-18" name="__codelineno-43-18" href="#__codelineno-43-18"></a><span class="p">}</span>
|
||||
<a id="__codelineno-43-19" name="__codelineno-43-19" href="#__codelineno-43-19"></a>
|
||||
<a id="__codelineno-43-20" name="__codelineno-43-20" href="#__codelineno-43-20"></a><span class="cm">/* 从结点 i 开始，从顶至底堆化 */</span>
|
||||
<a id="__codelineno-43-20" name="__codelineno-43-20" href="#__codelineno-43-20"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
|
||||
<a id="__codelineno-43-21" name="__codelineno-43-21" href="#__codelineno-43-21"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">siftDown</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-43-22" name="__codelineno-43-22" href="#__codelineno-43-22"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="kc">true</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-43-23" name="__codelineno-43-23" href="#__codelineno-43-23"></a><span class="w"> </span><span class="c1">// 判断结点 i, l, r 中值最大的结点，记为 max</span>
|
||||
<a id="__codelineno-43-23" name="__codelineno-43-23" href="#__codelineno-43-23"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 max</span>
|
||||
<a id="__codelineno-43-24" name="__codelineno-43-24" href="#__codelineno-43-24"></a><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">r</span><span class="p">,</span><span class="w"> </span><span class="nx">max</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span><span class="w"> </span><span class="nx">i</span>
|
||||
<a id="__codelineno-43-25" name="__codelineno-43-25" href="#__codelineno-43-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">l</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">></span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">max</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-43-26" name="__codelineno-43-26" href="#__codelineno-43-26"></a><span class="w"> </span><span class="nx">max</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">l</span>
|
||||
@@ -2832,11 +2832,11 @@
|
||||
<a id="__codelineno-43-28" name="__codelineno-43-28" href="#__codelineno-43-28"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">r</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">></span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">max</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-43-29" name="__codelineno-43-29" href="#__codelineno-43-29"></a><span class="w"> </span><span class="nx">max</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">r</span>
|
||||
<a id="__codelineno-43-30" name="__codelineno-43-30" href="#__codelineno-43-30"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-43-31" name="__codelineno-43-31" href="#__codelineno-43-31"></a><span class="w"> </span><span class="c1">// 若结点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
|
||||
<a id="__codelineno-43-31" name="__codelineno-43-31" href="#__codelineno-43-31"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
|
||||
<a id="__codelineno-43-32" name="__codelineno-43-32" href="#__codelineno-43-32"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">max</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-43-33" name="__codelineno-43-33" href="#__codelineno-43-33"></a><span class="w"> </span><span class="k">break</span>
|
||||
<a id="__codelineno-43-34" name="__codelineno-43-34" href="#__codelineno-43-34"></a><span class="w"> </span><span class="p">}</span>
|
||||
<a id="__codelineno-43-35" name="__codelineno-43-35" href="#__codelineno-43-35"></a><span class="w"> </span><span class="c1">// 交换两结点</span>
|
||||
<a id="__codelineno-43-35" name="__codelineno-43-35" href="#__codelineno-43-35"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||||
<a id="__codelineno-43-36" name="__codelineno-43-36" href="#__codelineno-43-36"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">max</span><span class="p">)</span>
|
||||
<a id="__codelineno-43-37" name="__codelineno-43-37" href="#__codelineno-43-37"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
|
||||
<a id="__codelineno-43-38" name="__codelineno-43-38" href="#__codelineno-43-38"></a><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">max</span>
|
||||
@@ -2849,9 +2849,9 @@
|
||||
<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="nx">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
|
||||
<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s2">"堆为空"</span><span class="p">);</span>
|
||||
<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w"> </span><span class="c1">// 交换根结点与最右叶结点（即交换首元素与尾元素）</span>
|
||||
<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（即交换首元素与尾元素）</span>
|
||||
<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">swap</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w"> </span><span class="c1">// 删除结点</span>
|
||||
<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w"> </span><span class="c1">// 删除节点</span>
|
||||
<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
|
||||
<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
|
||||
<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">siftDown</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
|
||||
@@ -2859,18 +2859,18 @@
|
||||
<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span>
|
||||
<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="p">}</span>
|
||||
<a id="__codelineno-44-14" name="__codelineno-44-14" href="#__codelineno-44-14"></a>
|
||||
<a id="__codelineno-44-15" name="__codelineno-44-15" href="#__codelineno-44-15"></a><span class="cm">/* 从结点 i 开始，从顶至底堆化 */</span>
|
||||
<a id="__codelineno-44-15" name="__codelineno-44-15" href="#__codelineno-44-15"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
|
||||
<a id="__codelineno-44-16" name="__codelineno-44-16" href="#__codelineno-44-16"></a><span class="err">#</span><span class="nx">siftDown</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-44-17" name="__codelineno-44-17" href="#__codelineno-44-17"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-44-18" name="__codelineno-44-18" href="#__codelineno-44-18"></a><span class="w"> </span><span class="c1">// 判断结点 i, l, r 中值最大的结点，记为 ma</span>
|
||||
<a id="__codelineno-44-18" name="__codelineno-44-18" href="#__codelineno-44-18"></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-44-19" name="__codelineno-44-19" href="#__codelineno-44-19"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span>
|
||||
<a id="__codelineno-44-20" name="__codelineno-44-20" href="#__codelineno-44-20"></a><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
|
||||
<a id="__codelineno-44-21" name="__codelineno-44-21" href="#__codelineno-44-21"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
|
||||
<a id="__codelineno-44-22" name="__codelineno-44-22" href="#__codelineno-44-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">l</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">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">l</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">ma</span><span class="p">])</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">l</span><span class="p">;</span>
|
||||
<a id="__codelineno-44-23" name="__codelineno-44-23" href="#__codelineno-44-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">r</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">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">r</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">ma</span><span class="p">])</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">r</span><span class="p">;</span>
|
||||
<a id="__codelineno-44-24" name="__codelineno-44-24" href="#__codelineno-44-24"></a><span class="w"> </span><span class="c1">// 若结点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
|
||||
<a id="__codelineno-44-24" name="__codelineno-44-24" href="#__codelineno-44-24"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
|
||||
<a id="__codelineno-44-25" name="__codelineno-44-25" href="#__codelineno-44-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||||
<a id="__codelineno-44-26" name="__codelineno-44-26" href="#__codelineno-44-26"></a><span class="w"> </span><span class="c1">// 交换两结点</span>
|
||||
<a id="__codelineno-44-26" name="__codelineno-44-26" href="#__codelineno-44-26"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||||
<a id="__codelineno-44-27" name="__codelineno-44-27" href="#__codelineno-44-27"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">ma</span><span class="p">);</span>
|
||||
<a id="__codelineno-44-28" name="__codelineno-44-28" href="#__codelineno-44-28"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
|
||||
<a id="__codelineno-44-29" name="__codelineno-44-29" href="#__codelineno-44-29"></a><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">ma</span><span class="p">;</span>
|
||||
@@ -2883,9 +2883,9 @@
|
||||
<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="nx">pop</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
|
||||
<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">RangeError</span><span class="p">(</span><span class="s1">'Heap is empty.'</span><span class="p">);</span>
|
||||
<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w"> </span><span class="c1">// 交换根结点与最右叶结点（即交换首元素与尾元素）</span>
|
||||
<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（即交换首元素与尾元素）</span>
|
||||
<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="w"> </span><span class="c1">// 删除结点</span>
|
||||
<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="w"> </span><span class="c1">// 删除节点</span>
|
||||
<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">val</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">maxHeap</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
|
||||
<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
|
||||
<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">siftDown</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
|
||||
@@ -2893,18 +2893,18 @@
|
||||
<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span>
|
||||
<a id="__codelineno-45-13" name="__codelineno-45-13" href="#__codelineno-45-13"></a><span class="p">}</span>
|
||||
<a id="__codelineno-45-14" name="__codelineno-45-14" href="#__codelineno-45-14"></a>
|
||||
<a id="__codelineno-45-15" name="__codelineno-45-15" href="#__codelineno-45-15"></a><span class="cm">/* 从结点 i 开始，从顶至底堆化 */</span>
|
||||
<a id="__codelineno-45-15" name="__codelineno-45-15" href="#__codelineno-45-15"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
|
||||
<a id="__codelineno-45-16" name="__codelineno-45-16" href="#__codelineno-45-16"></a><span class="nx">siftDown</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-45-17" name="__codelineno-45-17" href="#__codelineno-45-17"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-45-18" name="__codelineno-45-18" href="#__codelineno-45-18"></a><span class="w"> </span><span class="c1">// 判断结点 i, l, r 中值最大的结点，记为 ma</span>
|
||||
<a id="__codelineno-45-18" name="__codelineno-45-18" href="#__codelineno-45-18"></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-45-19" name="__codelineno-45-19" href="#__codelineno-45-19"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">l</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">left</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span>
|
||||
<a id="__codelineno-45-20" name="__codelineno-45-20" href="#__codelineno-45-20"></a><span class="w"> </span><span class="nx">r</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">right</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
|
||||
<a id="__codelineno-45-21" name="__codelineno-45-21" href="#__codelineno-45-21"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
|
||||
<a id="__codelineno-45-22" name="__codelineno-45-22" href="#__codelineno-45-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">l</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">size</span><span class="p">()</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">maxHeap</span><span class="p">[</span><span class="nx">l</span><span class="p">]</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">maxHeap</span><span class="p">[</span><span class="nx">ma</span><span class="p">])</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">l</span><span class="p">;</span>
|
||||
<a id="__codelineno-45-23" name="__codelineno-45-23" href="#__codelineno-45-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">r</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">size</span><span class="p">()</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">maxHeap</span><span class="p">[</span><span class="nx">r</span><span class="p">]</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">maxHeap</span><span class="p">[</span><span class="nx">ma</span><span class="p">])</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">r</span><span class="p">;</span>
|
||||
<a id="__codelineno-45-24" name="__codelineno-45-24" href="#__codelineno-45-24"></a><span class="w"> </span><span class="c1">// 若结点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
|
||||
<a id="__codelineno-45-24" name="__codelineno-45-24" href="#__codelineno-45-24"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
|
||||
<a id="__codelineno-45-25" name="__codelineno-45-25" href="#__codelineno-45-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||||
<a id="__codelineno-45-26" name="__codelineno-45-26" href="#__codelineno-45-26"></a><span class="w"> </span><span class="c1">// 交换两结点</span>
|
||||
<a id="__codelineno-45-26" name="__codelineno-45-26" href="#__codelineno-45-26"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||||
<a id="__codelineno-45-27" name="__codelineno-45-27" href="#__codelineno-45-27"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">ma</span><span class="p">);</span>
|
||||
<a id="__codelineno-45-28" name="__codelineno-45-28" href="#__codelineno-45-28"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
|
||||
<a id="__codelineno-45-29" name="__codelineno-45-29" href="#__codelineno-45-29"></a><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">ma</span><span class="p">;</span>
|
||||
@@ -2925,9 +2925,9 @@
|
||||
<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w"> </span><span class="c1">// 判空处理</span>
|
||||
<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
|
||||
<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="nf">IndexOutOfRangeException</span><span class="p">();</span>
|
||||
<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="w"> </span><span class="c1">// 交换根结点与最右叶结点（即交换首元素与尾元素）</span>
|
||||
<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（即交换首元素与尾元素）</span>
|
||||
<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="m">0</span><span class="p">,</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="m">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="w"> </span><span class="c1">// 删除结点</span>
|
||||
<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="w"> </span><span class="c1">// 删除节点</span>
|
||||
<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</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">Last</span><span class="p">();</span>
|
||||
<a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">RemoveAt</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="m">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
|
||||
@@ -2936,20 +2936,20 @@
|
||||
<a id="__codelineno-47-15" name="__codelineno-47-15" href="#__codelineno-47-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
|
||||
<a id="__codelineno-47-16" name="__codelineno-47-16" href="#__codelineno-47-16"></a><span class="p">}</span>
|
||||
<a id="__codelineno-47-17" name="__codelineno-47-17" href="#__codelineno-47-17"></a>
|
||||
<a id="__codelineno-47-18" name="__codelineno-47-18" href="#__codelineno-47-18"></a><span class="cm">/* 从结点 i 开始，从顶至底堆化 */</span>
|
||||
<a id="__codelineno-47-18" name="__codelineno-47-18" href="#__codelineno-47-18"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
|
||||
<a id="__codelineno-47-19" name="__codelineno-47-19" href="#__codelineno-47-19"></a><span class="k">void</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
|
||||
<a id="__codelineno-47-20" name="__codelineno-47-20" href="#__codelineno-47-20"></a><span class="p">{</span>
|
||||
<a id="__codelineno-47-21" name="__codelineno-47-21" href="#__codelineno-47-21"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="k">true</span><span class="p">)</span>
|
||||
<a id="__codelineno-47-22" name="__codelineno-47-22" href="#__codelineno-47-22"></a><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-47-23" name="__codelineno-47-23" href="#__codelineno-47-23"></a><span class="w"> </span><span class="c1">// 判断结点 i, l, r 中值最大的结点，记为 ma</span>
|
||||
<a id="__codelineno-47-23" name="__codelineno-47-23" href="#__codelineno-47-23"></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-47-24" name="__codelineno-47-24" href="#__codelineno-47-24"></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-47-25" name="__codelineno-47-25" href="#__codelineno-47-25"></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-47-26" name="__codelineno-47-26" href="#__codelineno-47-26"></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-47-27" name="__codelineno-47-27" href="#__codelineno-47-27"></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-47-28" name="__codelineno-47-28" href="#__codelineno-47-28"></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-47-29" name="__codelineno-47-29" href="#__codelineno-47-29"></a><span class="w"> </span><span class="c1">// 若“结点 i 最大”或“越过叶结点”，则结束堆化</span>
|
||||
<a id="__codelineno-47-29" name="__codelineno-47-29" href="#__codelineno-47-29"></a><span class="w"> </span><span class="c1">// 若“节点 i 最大”或“越过叶节点”，则结束堆化</span>
|
||||
<a id="__codelineno-47-30" name="__codelineno-47-30" href="#__codelineno-47-30"></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><span class="w"> </span><span class="k">break</span><span class="p">;</span>
|
||||
<a id="__codelineno-47-31" name="__codelineno-47-31" href="#__codelineno-47-31"></a><span class="w"> </span><span class="c1">// 交换两结点</span>
|
||||
<a id="__codelineno-47-31" name="__codelineno-47-31" href="#__codelineno-47-31"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||||
<a id="__codelineno-47-32" name="__codelineno-47-32" href="#__codelineno-47-32"></a><span class="w"> </span><span class="n">swap</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="p">);</span>
|
||||
<a id="__codelineno-47-33" name="__codelineno-47-33" href="#__codelineno-47-33"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
|
||||
<a id="__codelineno-47-34" name="__codelineno-47-34" href="#__codelineno-47-34"></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>
|
||||
@@ -2964,9 +2964,9 @@
|
||||
<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a> <span class="k">if</span> <span class="bp">isEmpty</span><span class="p">()</span> <span class="p">{</span>
|
||||
<a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a> <span class="bp">fatalError</span><span class="p">(</span><span class="s">"堆为空"</span><span class="p">)</span>
|
||||
<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a> <span class="c1">// 交换根结点与最右叶结点（即交换首元素与尾元素）</span>
|
||||
<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a> <span class="c1">// 交换根节点与最右叶节点（即交换首元素与尾元素）</span>
|
||||
<a id="__codelineno-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a> <span class="bp">swap</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></a> <span class="c1">// 删除结点</span>
|
||||
<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></a> <span class="c1">// 删除节点</span>
|
||||
<a id="__codelineno-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a> <span class="kd">let</span> <span class="nv">val</span> <span class="p">=</span> <span class="n">maxHeap</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">at</span><span class="p">:</span> <span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<a id="__codelineno-48-11" name="__codelineno-48-11" href="#__codelineno-48-11"></a> <span class="c1">// 从顶至底堆化</span>
|
||||
<a id="__codelineno-48-12" name="__codelineno-48-12" href="#__codelineno-48-12"></a> <span class="n">siftDown</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="mi">0</span><span class="p">)</span>
|
||||
@@ -2974,11 +2974,11 @@
|
||||
<a id="__codelineno-48-14" name="__codelineno-48-14" href="#__codelineno-48-14"></a> <span class="k">return</span> <span class="n">val</span>
|
||||
<a id="__codelineno-48-15" name="__codelineno-48-15" href="#__codelineno-48-15"></a><span class="p">}</span>
|
||||
<a id="__codelineno-48-16" name="__codelineno-48-16" href="#__codelineno-48-16"></a>
|
||||
<a id="__codelineno-48-17" name="__codelineno-48-17" href="#__codelineno-48-17"></a><span class="cm">/* 从结点 i 开始，从顶至底堆化 */</span>
|
||||
<a id="__codelineno-48-17" name="__codelineno-48-17" href="#__codelineno-48-17"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
|
||||
<a id="__codelineno-48-18" name="__codelineno-48-18" href="#__codelineno-48-18"></a><span class="kd">func</span> <span class="nf">siftDown</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
|
||||
<a id="__codelineno-48-19" name="__codelineno-48-19" href="#__codelineno-48-19"></a> <span class="kd">var</span> <span class="nv">i</span> <span class="p">=</span> <span class="n">i</span>
|
||||
<a id="__codelineno-48-20" name="__codelineno-48-20" href="#__codelineno-48-20"></a> <span class="k">while</span> <span class="kc">true</span> <span class="p">{</span>
|
||||
<a id="__codelineno-48-21" name="__codelineno-48-21" href="#__codelineno-48-21"></a> <span class="c1">// 判断结点 i, l, r 中值最大的结点，记为 ma</span>
|
||||
<a id="__codelineno-48-21" name="__codelineno-48-21" href="#__codelineno-48-21"></a> <span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
|
||||
<a id="__codelineno-48-22" name="__codelineno-48-22" href="#__codelineno-48-22"></a> <span class="kd">let</span> <span class="nv">l</span> <span class="p">=</span> <span class="kr">left</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">)</span>
|
||||
<a id="__codelineno-48-23" name="__codelineno-48-23" href="#__codelineno-48-23"></a> <span class="kd">let</span> <span class="nv">r</span> <span class="p">=</span> <span class="kr">right</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">)</span>
|
||||
<a id="__codelineno-48-24" name="__codelineno-48-24" href="#__codelineno-48-24"></a> <span class="kd">var</span> <span class="nv">ma</span> <span class="p">=</span> <span class="n">i</span>
|
||||
@@ -2988,11 +2988,11 @@
|
||||
<a id="__codelineno-48-28" name="__codelineno-48-28" href="#__codelineno-48-28"></a> <span class="k">if</span> <span class="n">r</span> <span class="o"><</span> <span class="n">size</span><span class="p">(),</span> <span class="n">maxHeap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span> <span class="o">></span> <span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span> <span class="p">{</span>
|
||||
<a id="__codelineno-48-29" name="__codelineno-48-29" href="#__codelineno-48-29"></a> <span class="n">ma</span> <span class="p">=</span> <span class="n">r</span>
|
||||
<a id="__codelineno-48-30" name="__codelineno-48-30" href="#__codelineno-48-30"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-48-31" name="__codelineno-48-31" href="#__codelineno-48-31"></a> <span class="c1">// 若结点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
|
||||
<a id="__codelineno-48-31" name="__codelineno-48-31" href="#__codelineno-48-31"></a> <span class="c1">// 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
|
||||
<a id="__codelineno-48-32" name="__codelineno-48-32" href="#__codelineno-48-32"></a> <span class="k">if</span> <span class="n">ma</span> <span class="p">==</span> <span class="n">i</span> <span class="p">{</span>
|
||||
<a id="__codelineno-48-33" name="__codelineno-48-33" href="#__codelineno-48-33"></a> <span class="k">break</span>
|
||||
<a id="__codelineno-48-34" name="__codelineno-48-34" href="#__codelineno-48-34"></a> <span class="p">}</span>
|
||||
<a id="__codelineno-48-35" name="__codelineno-48-35" href="#__codelineno-48-35"></a> <span class="c1">// 交换两结点</span>
|
||||
<a id="__codelineno-48-35" name="__codelineno-48-35" href="#__codelineno-48-35"></a> <span class="c1">// 交换两节点</span>
|
||||
<a id="__codelineno-48-36" name="__codelineno-48-36" href="#__codelineno-48-36"></a> <span class="bp">swap</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="n">ma</span><span class="p">)</span>
|
||||
<a id="__codelineno-48-37" name="__codelineno-48-37" href="#__codelineno-48-37"></a> <span class="c1">// 循环向下堆化</span>
|
||||
<a id="__codelineno-48-38" name="__codelineno-48-38" href="#__codelineno-48-38"></a> <span class="n">i</span> <span class="p">=</span> <span class="n">ma</span>
|
||||
@@ -3005,9 +3005,9 @@
|
||||
<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">pop</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">)</span><span class="w"> </span><span class="o">!</span><span class="n">T</span><span class="w"> </span><span class="p">{</span>
|
||||
<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="w"> </span><span class="c1">// 判断处理</span>
|
||||
<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">self</span><span class="p">.</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">unreachable</span><span class="p">;</span>
|
||||
<a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="w"> </span><span class="c1">// 交换根结点与最右叶结点（即交换首元素与尾元素）</span>
|
||||
<a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（即交换首元素与尾元素）</span>
|
||||
<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">self</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="mi">1</span><span class="p">);</span>
|
||||
<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a><span class="w"> </span><span class="c1">// 删除结点</span>
|
||||
<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a><span class="w"> </span><span class="c1">// 删除节点</span>
|
||||
<a id="__codelineno-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
|
||||
<a id="__codelineno-49-9" name="__codelineno-49-9" href="#__codelineno-49-9"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
|
||||
<a id="__codelineno-49-10" name="__codelineno-49-10" href="#__codelineno-49-10"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">siftDown</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
|
||||
@@ -3015,19 +3015,19 @@
|
||||
<a id="__codelineno-49-12" name="__codelineno-49-12" href="#__codelineno-49-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
|
||||
<a id="__codelineno-49-13" name="__codelineno-49-13" href="#__codelineno-49-13"></a><span class="p">}</span><span class="w"> </span>
|
||||
<a id="__codelineno-49-14" name="__codelineno-49-14" href="#__codelineno-49-14"></a>
|
||||
<a id="__codelineno-49-15" name="__codelineno-49-15" href="#__codelineno-49-15"></a><span class="c1">// 从结点 i 开始，从顶至底堆化</span>
|
||||
<a id="__codelineno-49-15" name="__codelineno-49-15" href="#__codelineno-49-15"></a><span class="c1">// 从节点 i 开始，从顶至底堆化</span>
|
||||
<a id="__codelineno-49-16" name="__codelineno-49-16" href="#__codelineno-49-16"></a><span class="k">fn</span><span class="w"> </span><span class="n">siftDown</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">i_</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="o">!</span><span class="kt">void</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="kr">var</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">i_</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="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </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="c1">// 判断结点 i, l, r 中值最大的结点，记为 ma</span>
|
||||
<a id="__codelineno-49-19" name="__codelineno-49-19" href="#__codelineno-49-19"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
|
||||
<a id="__codelineno-49-20" name="__codelineno-49-20" href="#__codelineno-49-20"></a><span class="w"> </span><span class="kr">var</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>
|
||||
<a id="__codelineno-49-21" name="__codelineno-49-21" href="#__codelineno-49-21"></a><span class="w"> </span><span class="kr">var</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>
|
||||
<a id="__codelineno-49-22" name="__codelineno-49-22" href="#__codelineno-49-22"></a><span class="w"> </span><span class="kr">var</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-49-23" 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">l</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="k">and</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</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">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</span><span class="p">[</span><span class="n">ma</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">l</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="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">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="k">and</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</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">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</span><span class="p">[</span><span class="n">ma</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">r</span><span class="p">;</span>
|
||||
<a id="__codelineno-49-25" name="__codelineno-49-25" href="#__codelineno-49-25"></a><span class="w"> </span><span class="c1">// 若结点 i 最大或索引 l, r 越界，则无需继续堆化，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，则无需继续堆化，跳出</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><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="c1">// 交换两结点</span>
|
||||
<a id="__codelineno-49-27" name="__codelineno-49-27" href="#__codelineno-49-27"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
||||
<a id="__codelineno-49-28" name="__codelineno-49-28" href="#__codelineno-49-28"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">swap</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="p">);</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-49-30" 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>
|
||||
|
||||
Reference in New Issue
Block a user