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chapter_heap/build_heap/index.html

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+        
       
       
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@@ -1028,9 +1030,23 @@
   
   
   
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        8.3. &nbsp; 二叉树数组表示
+      </a>
+    </li>
+  
+
+            
+          
+            
+              
+  
+  
+  
     <li class="md-nav__item">
       <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
-        8.3. &nbsp; 二叉搜索树
+        8.4. &nbsp; 二叉搜索树
       </a>
     </li>
   
@@ -1044,7 +1060,7 @@
   
     <li class="md-nav__item">
       <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
-        8.4. &nbsp; AVL 树 *
+        8.5. &nbsp; AVL 树 *
       </a>
     </li>
   
@@ -1058,7 +1074,7 @@
   
     <li class="md-nav__item">
       <a href="../../chapter_tree/summary/" class="md-nav__link">
-        8.5. &nbsp; 小结
+        8.6. &nbsp; 小结
       </a>
     </li>
   
@@ -1167,34 +1183,21 @@
       
         <li class="md-nav__item">
   <a href="#921" class="md-nav__link">
-    9.2.1. &nbsp; 两种建堆方法
+    9.2.1. &nbsp; 借助入堆方法实现
   </a>
   
-    <nav class="md-nav" aria-label="9.2.1. &nbsp; 两种建堆方法">
-      <ul class="md-nav__list">
-        
-          <li class="md-nav__item">
-  <a href="#_1" class="md-nav__link">
-    借助入堆方法实现
-  </a>
-  
-</li>
-        
-          <li class="md-nav__item">
-  <a href="#_2" class="md-nav__link">
-    基于堆化操作实现
-  </a>
-  
-</li>
-        
-      </ul>
-    </nav>
-  
 </li>
       
         <li class="md-nav__item">
   <a href="#922" class="md-nav__link">
-    9.2.2. &nbsp; 复杂度分析
+    9.2.2. &nbsp; 基于堆化操作实现
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#923" class="md-nav__link">
+    9.2.3. &nbsp; 复杂度分析
   </a>
   
 </li>
@@ -1802,34 +1805,21 @@
       
         <li class="md-nav__item">
   <a href="#921" class="md-nav__link">
-    9.2.1. &nbsp; 两种建堆方法
+    9.2.1. &nbsp; 借助入堆方法实现
   </a>
   
-    <nav class="md-nav" aria-label="9.2.1. &nbsp; 两种建堆方法">
-      <ul class="md-nav__list">
-        
-          <li class="md-nav__item">
-  <a href="#_1" class="md-nav__link">
-    借助入堆方法实现
-  </a>
-  
-</li>
-        
-          <li class="md-nav__item">
-  <a href="#_2" class="md-nav__link">
-    基于堆化操作实现
-  </a>
-  
-</li>
-        
-      </ul>
-    </nav>
-  
 </li>
       
         <li class="md-nav__item">
   <a href="#922" class="md-nav__link">
-    9.2.2. &nbsp; 复杂度分析
+    9.2.2. &nbsp; 基于堆化操作实现
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#923" class="md-nav__link">
+    9.2.3. &nbsp; 复杂度分析
   </a>
   
 </li>
@@ -1859,11 +1849,10 @@
 
 <h1 id="92">9.2. &nbsp; 建堆操作 *<a class="headerlink" href="#92" title="Permanent link">&para;</a></h1>
 <p>如果我们想要根据输入列表生成一个堆，这个过程被称为「建堆」。</p>
-<h2 id="921">9.2.1. &nbsp; 两种建堆方法<a class="headerlink" href="#921" title="Permanent link">&para;</a></h2>
-<h3 id="_1">借助入堆方法实现<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h3>
+<h2 id="921">9.2.1. &nbsp; 借助入堆方法实现<a class="headerlink" href="#921" title="Permanent link">&para;</a></h2>
 <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>
 <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>
-<h3 id="_2">基于堆化操作实现<a class="headerlink" href="#_2" title="Permanent link">&para;</a></h3>
+<h2 id="922">9.2.2. &nbsp; 基于堆化操作实现<a class="headerlink" href="#922" title="Permanent link">&para;</a></h2>
 <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>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:10"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Java</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Python</label><label for="__tabbed_1_4">Go</label><label for="__tabbed_1_5">JavaScript</label><label for="__tabbed_1_6">TypeScript</label><label for="__tabbed_1_7">C</label><label for="__tabbed_1_8">C#</label><label for="__tabbed_1_9">Swift</label><label for="__tabbed_1_10">Zig</label></div>
 <div class="tabbed-content">
@@ -1986,7 +1975,7 @@
 </div>
 </div>
 </div>
-<h2 id="922">9.2.2. &nbsp; 复杂度分析<a class="headerlink" href="#922" title="Permanent link">&para;</a></h2>
+<h2 id="923">9.2.3. &nbsp; 复杂度分析<a class="headerlink" href="#923" title="Permanent link">&para;</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>

chapter_heap/heap/index.html

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+          
+        
       
       
         <label class="md-nav__link" for="__nav_9" id="__nav_9_label" tabindex="0">
@@ -1028,9 +1030,23 @@
   
   
   
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        8.3. &nbsp; 二叉树数组表示
+      </a>
+    </li>
+  
+
+            
+          
+            
+              
+  
+  
+  
     <li class="md-nav__item">
       <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
-        8.3. &nbsp; 二叉搜索树
+        8.4. &nbsp; 二叉搜索树
       </a>
     </li>
   
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     <li class="md-nav__item">
       <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
-        8.4. &nbsp; AVL 树 *
+        8.5. &nbsp; AVL 树 *
       </a>
     </li>
   
@@ -1058,7 +1074,7 @@
   
     <li class="md-nav__item">
       <a href="../../chapter_tree/summary/" class="md-nav__link">
-        8.5. &nbsp; 小结
+        8.6. &nbsp; 小结
       </a>
     </li>
   
@@ -3186,7 +3202,7 @@
       <nav class="md-footer__inner md-grid" aria-label="页脚" >
         
           
-          <a href="../../chapter_tree/summary/" class="md-footer__link md-footer__link--prev" aria-label="上一页: 8.5. &amp;nbsp; 小结" rel="prev">
+          <a href="../../chapter_tree/summary/" class="md-footer__link md-footer__link--prev" aria-label="上一页: 8.6. &amp;nbsp; 小结" rel="prev">
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                 上一页
               </span>
               <div class="md-ellipsis">
-                8.5. &nbsp; 小结
+                8.6. &nbsp; 小结
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chapter_heap/summary/index.html

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+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        8.3. &nbsp; 二叉树数组表示
+      </a>
+    </li>
+  
+
+            
+          
+            
+              
+  
+  
+  
     <li class="md-nav__item">
       <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
-        8.3. &nbsp; 二叉搜索树
+        8.4. &nbsp; 二叉搜索树
       </a>
     </li>
   
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     <li class="md-nav__item">
       <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
-        8.4. &nbsp; AVL 树 *
+        8.5. &nbsp; AVL 树 *
       </a>
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     <li class="md-nav__item">
       <a href="../../chapter_tree/summary/" class="md-nav__link">
-        8.5. &nbsp; 小结
+        8.6. &nbsp; 小结
       </a>
     </li>