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chapter_searching/replace_linear_by_hashing/index.html
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<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w"> </span><span class="nx">size</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">nums</span><span class="p">)</span>
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w"> </span><span class="c1">// 两层循环，时间复杂度为 O(n^2)</span>
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></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="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">size</span><span class="o">-</span><span class="mi">1</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-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="nx">j</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="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">size</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</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="nx">j</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="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">size</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</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">if</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="o">+</span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">target</span><span class="w"> </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="k">return</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">{</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">}</span>
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w"> </span><span class="p">}</span>

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<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a>
<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a> <span class="k">def</span> <span class="nf">is_empty</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;判断栈是否为空&quot;&quot;&quot;</span>
<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="mi">0</span>
<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a> <span class="k">return</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">0</span>
<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a>
<a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></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">item</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
<a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;入栈&quot;&quot;&quot;</span>

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<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a>
<a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a> <span class="k">def</span> <span class="nf">is_empty</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;判断栈是否为空&quot;&quot;&quot;</span>
<a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="mi">0</span>
<a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a> <span class="k">return</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">0</span>
<a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a>
<a id="__codelineno-27-16" name="__codelineno-27-16" href="#__codelineno-27-16"></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">item</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
<a id="__codelineno-27-17" name="__codelineno-27-17" href="#__codelineno-27-17"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;入栈&quot;&quot;&quot;</span>

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<h3 id="2">2. &nbsp; 平行計算最佳化<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
<p>我們知道，分治生成的子問題是相互獨立的，<strong>因此通常可以並行解決</strong>。也就是說，分治不僅可以降低演算法的時間複雜度，<strong>還有利於作業系統的並行最佳化</strong>。</p>
<p>並行最佳化在多核或多處理器的環境中尤其有效，因為系統可以同時處理多個子問題，更加充分地利用計算資源，從而顯著減少總體的執行時間。</p>
<p>比如在圖 12-3 所示的“桶排序”中，我們將海量的資料平均分配到各個桶中，則可所有桶的排序任務分散到各個計算單元，完成後再合併結果。</p>
<p>比如在圖 12-3 所示的“桶排序”中，我們將海量的資料平均分配到各個桶中，則可將所有桶的排序任務分散到各個計算單元，完成後再合併結果。</p>
<p><a class="glightbox" href="../divide_and_conquer.assets/divide_and_conquer_parallel_computing.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="桶排序的平行計算" class="animation-figure" src="../divide_and_conquer.assets/divide_and_conquer_parallel_computing.png" /></a></p>
<p align="center"> 圖 12-3 &nbsp; 桶排序的平行計算 </p>

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<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=import%20heapq%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%B0%8F%E9%A0%82%E5%A0%86%E7%A9%8D%0A%20%20%20%20min_heap%2C%20flag%20%3D%20%5B%5D%2C%201%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%A4%A7%E9%A0%82%E5%A0%86%E7%A9%8D%0A%20%20%20%20max_heap%2C%20flag%20%3D%20%5B%5D%2C%20-1%0A%20%20%20%20%0A%20%20%20%20%23%20Python%20%E7%9A%84%20heapq%20%E6%A8%A1%E7%B5%84%E9%A0%90%E8%A8%AD%E5%AF%A6%E7%8F%BE%E5%B0%8F%E9%A0%82%E5%A0%86%E7%A9%8D%0A%20%20%20%20%23%20%E8%80%83%E6%85%AE%E5%B0%87%E2%80%9C%E5%85%83%E7%B4%A0%E5%8F%96%E8%B2%A0%E2%80%9D%E5%BE%8C%E5%86%8D%E5%85%A5%E5%A0%86%E7%A9%8D%EF%BC%8C%E9%80%99%E6%A8%A3%E5%B0%B1%E5%8F%AF%E4%BB%A5%E5%B0%87%E5%A4%A7%E5%B0%8F%E9%97%9C%E4%BF%82%E9%A1%9B%E5%80%92%EF%BC%8C%E5%BE%9E%E8%80%8C%E5%AF%A6%E7%8F%BE%E5%A4%A7%E9%A0%82%E5%A0%86%E7%A9%8D%0A%20%20%20%20%23%20%E5%9C%A8%E6%9C%AC%E7%A4%BA%E4%BE%8B%E4%B8%AD%EF%BC%8Cflag%20%3D%201%20%E6%99%82%E5%B0%8D%E6%87%89%E5%B0%8F%E9%A0%82%E5%A0%86%E7%A9%8D%EF%BC%8Cflag%20%3D%20-1%20%E6%99%82%E5%B0%8D%E6%87%89%E5%A4%A7%E9%A0%82%E5%A0%86%E7%A9%8D%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%85%A5%E5%A0%86%E7%A9%8D%0A%20%20%20%20heapq.heappush%28max_heap%2C%20flag%20%2A%201%29%0A%20%20%20%20heapq.heappush%28max_heap%2C%20flag%20%2A%203%29%0A%20%20%20%20heapq.heappush%28max_heap%2C%20flag%20%2A%202%29%0A%20%20%20%20heapq.heappush%28max_heap%2C%20flag%20%2A%205%29%0A%20%20%20%20heapq.heappush%28max_heap%2C%20flag%20%2A%204%29%0A%20%20%20%20%0A%20%20%20%20%23%20%E7%8D%B2%E5%8F%96%E5%A0%86%E7%A9%8D%E9%A0%82%E5%85%83%E7%B4%A0%0A%20%20%20%20peek%20%3D%20flag%20%2A%20max_heap%5B0%5D%20%23%205%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%A0%86%E7%A9%8D%E9%A0%82%E5%85%83%E7%B4%A0%E5%87%BA%E5%A0%86%E7%A9%8D%0A%20%20%20%20%23%20%E5%87%BA%E5%A0%86%E7%A9%8D%E5%85%83%E7%B4%A0%E6%9C%83%E5%BD%A2%E6%88%90%E4%B8%80%E5%80%8B%E5%BE%9E%E5%A4%A7%E5%88%B0%E5%B0%8F%E7%9A%84%E5%BA%8F%E5%88%97%0A%20%20%20%20val%20%3D%20flag%20%2A%20heapq.heappop%28max_heap%29%20%23%205%0A%20%20%20%20val%20%3D%20flag%20%2A%20heapq.heappop%28max_heap%29%20%23%204%0A%20%20%20%20val%20%3D%20flag%20%2A%20heapq.heappop%28max_heap%29%20%23%203%0A%20%20%20%20val%20%3D%20flag%20%2A%20heapq.heappop%28max_heap%29%20%23%202%0A%20%20%20%20val%20%3D%20flag%20%2A%20heapq.heappop%28max_heap%29%20%23%201%0A%20%20%20%20%0A%20%20%20%20%23%20%E7%8D%B2%E5%8F%96%E5%A0%86%E7%A9%8D%E5%A4%A7%E5%B0%8F%0A%20%20%20%20size%20%3D%20len%28max_heap%29%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%88%A4%E6%96%B7%E5%A0%86%E7%A9%8D%E6%98%AF%E5%90%A6%E7%82%BA%E7%A9%BA%0A%20%20%20%20is_empty%20%3D%20not%20max_heap%0A%20%20%20%20%0A%20%20%20%20%23%20%E8%BC%B8%E5%85%A5%E4%B8%B2%E5%88%97%E4%B8%A6%E5%BB%BA%E5%A0%86%E7%A9%8D%0A%20%20%20%20min_heap%20%3D%20%5B1%2C%203%2C%202%2C%205%2C%204%5D%0A%20%20%20%20heapq.heapify%28min_heap%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全螢幕觀看 &gt;</a></div></p>
</details>
<h2 id="812">8.1.2 &nbsp; 堆積的實現<a class="headerlink" href="#812" title="Permanent link">&para;</a></h2>
<p>下文實現的是大頂堆積。若要將其轉換為小頂堆積，只需將所有大小邏輯判斷取逆（例如，將 <span class="arithmatex">\(\geq\)</span> 替換為 <span class="arithmatex">\(\leq\)</span> ）。感興趣的讀者可以自行實現。</p>
<p>下文實現的是大頂堆積。若要將其轉換為小頂堆積，只需將所有大小邏輯判斷進行逆轉（例如，將 <span class="arithmatex">\(\geq\)</span> 替換為 <span class="arithmatex">\(\leq\)</span> ）。感興趣的讀者可以自行實現。</p>
<h3 id="1">1. &nbsp; 堆積的儲存與表示<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
<p>“二元樹”章節講過，完全二元樹非常適合用陣列來表示。由於堆積正是一種完全二元樹，<strong>因此我們將採用陣列來儲存堆積</strong>。</p>
<p>當使用陣列表示二元樹時，元素代表節點值，索引代表節點在二元樹中的位置。<strong>節點指標透過索引對映公式來實現</strong>。</p>

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<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w"> </span><span class="nx">size</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">nums</span><span class="p">)</span>
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w"> </span><span class="c1">// 兩層迴圈，時間複雜度為 O(n^2)</span>
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></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="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">size</span><span class="o">-</span><span class="mi">1</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-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="nx">j</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="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">size</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</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="nx">j</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="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">size</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</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">if</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="o">+</span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">target</span><span class="w"> </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="k">return</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">{</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="p">}</span>
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w"> </span><span class="p">}</span>

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</details>
<h2 id="1193">11.9.3 &nbsp; 演算法特性<a class="headerlink" href="#1193" title="Permanent link">&para;</a></h2>
<ul>
<li><strong>時間複雜度為 <span class="arithmatex">\(O(n + m)\)</span></strong> ：涉及走訪 <code>nums</code> 和走訪 <code>counter</code> ，都使用線性時間。一般情況下 <span class="arithmatex">\(n \gg m\)</span> ，時間複雜度趨於 <span class="arithmatex">\(O(n)\)</span> 。</li>
<li><strong>時間複雜度為 <span class="arithmatex">\(O(n + m)\)</span>、非自適應排序</strong> ：涉及走訪 <code>nums</code> 和走訪 <code>counter</code> ，都使用線性時間。一般情況下 <span class="arithmatex">\(n \gg m\)</span> ，時間複雜度趨於 <span class="arithmatex">\(O(n)\)</span> 。</li>
<li><strong>空間複雜度為 <span class="arithmatex">\(O(n + m)\)</span>、非原地排序</strong>：藉助了長度分別為 <span class="arithmatex">\(n\)</span> 和 <span class="arithmatex">\(m\)</span> 的陣列 <code>res</code> 和 <code>counter</code> 。</li>
<li><strong>穩定排序</strong>：由於向 <code>res</code> 中填充元素的順序是“從右向左”的，因此倒序走訪 <code>nums</code> 可以避免改變相等元素之間的相對位置，從而實現穩定排序。實際上，正序走訪 <code>nums</code> 也可以得到正確的排序結果，但結果是非穩定的。</li>
</ul>

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@ -4323,7 +4323,7 @@ x_k = \lfloor\frac{x}{d^{k-1}}\rfloor \bmod d
<h2 id="11102">11.10.2 &nbsp; 演算法特性<a class="headerlink" href="#11102" title="Permanent link">&para;</a></h2>
<p>相較於計數排序，基數排序適用於數值範圍較大的情況，<strong>但前提是資料必須可以表示為固定位數的格式，且位數不能過大</strong>。例如，浮點數不適合使用基數排序，因為其位數 <span class="arithmatex">\(k\)</span> 過大，可能導致時間複雜度 <span class="arithmatex">\(O(nk) \gg O(n^2)\)</span> 。</p>
<ul>
<li><strong>時間複雜度為 <span class="arithmatex">\(O(nk)\)</span></strong>：設資料量為 <span class="arithmatex">\(n\)</span>、資料為 <span class="arithmatex">\(d\)</span> 進位制、最大位數為 <span class="arithmatex">\(k\)</span> ，則對某一位執行計數排序使用 <span class="arithmatex">\(O(n + d)\)</span> 時間，排序所有 <span class="arithmatex">\(k\)</span> 位使用 <span class="arithmatex">\(O((n + d)k)\)</span> 時間。通常情況下，<span class="arithmatex">\(d\)</span> 和 <span class="arithmatex">\(k\)</span> 都相對較小，時間複雜度趨向 <span class="arithmatex">\(O(n)\)</span> 。</li>
<li><strong>時間複雜度為 <span class="arithmatex">\(O(nk)\)</span>、非自適應排序</strong>：設資料量為 <span class="arithmatex">\(n\)</span>、資料為 <span class="arithmatex">\(d\)</span> 進位制、最大位數為 <span class="arithmatex">\(k\)</span> ，則對某一位執行計數排序使用 <span class="arithmatex">\(O(n + d)\)</span> 時間，排序所有 <span class="arithmatex">\(k\)</span> 位使用 <span class="arithmatex">\(O((n + d)k)\)</span> 時間。通常情況下，<span class="arithmatex">\(d\)</span> 和 <span class="arithmatex">\(k\)</span> 都相對較小，時間複雜度趨向 <span class="arithmatex">\(O(n)\)</span> 。</li>
<li><strong>空間複雜度為 <span class="arithmatex">\(O(n + d)\)</span>、非原地排序</strong>：與計數排序相同，基數排序需要藉助長度為 <span class="arithmatex">\(n\)</span> 和 <span class="arithmatex">\(d\)</span> 的陣列 <code>res</code> 和 <code>counter</code> 。</li>
<li><strong>穩定排序</strong>：當計數排序穩定時，基數排序也穩定；當計數排序不穩定時，基數排序無法保證得到正確的排序結果。</li>
</ul>

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@ -4924,7 +4924,7 @@
<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a>
<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a> <span class="k">def</span> <span class="nf">is_empty</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;判斷堆疊是否為空&quot;&quot;&quot;</span>
<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="mi">0</span>
<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a> <span class="k">return</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">0</span>
<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a>
<a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></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">item</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
<a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;入堆疊&quot;&quot;&quot;</span>

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@ -3708,7 +3708,9 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a>
<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 二元樹的陣列表示 ###</span>
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="c1"># 使用 nil 來表示空位</span>
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="kp">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="kp">nil</span><span class="p">,</span><span class="w"> </span><span class="kp">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">12</span><span class="p">,</span><span class="w"> </span><span class="kp">nil</span><span class="p">,</span><span class="w"> </span><span class="kp">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">15</span><span class="o">]</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -4805,7 +4807,87 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_binary_tree.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">ArrayBinaryTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
<div class="highlight"><span class="filename">array_binary_tree.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1">### 陣列表示下的二元樹類別 ###</span>
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayBinaryTree</span>
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="c1">### 建構子 ###</span>
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w"> </span><span class="vi">@tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="o">.</span><span class="n">to_a</span>
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a>
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="w"> </span><span class="c1">### 串列容量 ###</span>
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">size</span>
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="w"> </span><span class="vi">@tree</span><span class="o">.</span><span class="n">length</span>
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a>
<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="w"> </span><span class="c1">### 獲取索引為 i 節點的值 ###</span>
<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="w"> </span><span class="c1"># 若索引越界，則返回 nil ，代表空位</span>
<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</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">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span>
<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a>
<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a><span class="w"> </span><span class="vi">@tree</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a>
<a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a><span class="w"> </span><span class="c1">### 獲取索引為 i 節點的左子節點的索引 ###</span>
<a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<a id="__codelineno-26-23" name="__codelineno-26-23" href="#__codelineno-26-23"></a><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>
<a id="__codelineno-26-24" name="__codelineno-26-24" href="#__codelineno-26-24"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-25" name="__codelineno-26-25" href="#__codelineno-26-25"></a>
<a id="__codelineno-26-26" name="__codelineno-26-26" href="#__codelineno-26-26"></a><span class="w"> </span><span class="c1">### 獲取索引為 i 節點的右子節點的索引 ###</span>
<a id="__codelineno-26-27" name="__codelineno-26-27" href="#__codelineno-26-27"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<a id="__codelineno-26-28" name="__codelineno-26-28" href="#__codelineno-26-28"></a><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>
<a id="__codelineno-26-29" name="__codelineno-26-29" href="#__codelineno-26-29"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-30" name="__codelineno-26-30" href="#__codelineno-26-30"></a>
<a id="__codelineno-26-31" name="__codelineno-26-31" href="#__codelineno-26-31"></a><span class="w"> </span><span class="c1">### 獲取索引為 i 節點的父節點的索引 ###</span>
<a id="__codelineno-26-32" name="__codelineno-26-32" href="#__codelineno-26-32"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<a id="__codelineno-26-33" name="__codelineno-26-33" href="#__codelineno-26-33"></a><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>
<a id="__codelineno-26-34" name="__codelineno-26-34" href="#__codelineno-26-34"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-35" name="__codelineno-26-35" href="#__codelineno-26-35"></a>
<a id="__codelineno-26-36" name="__codelineno-26-36" href="#__codelineno-26-36"></a><span class="w"> </span><span class="c1">### 層序走訪 ###</span>
<a id="__codelineno-26-37" name="__codelineno-26-37" href="#__codelineno-26-37"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">level_order</span>
<a id="__codelineno-26-38" name="__codelineno-26-38" href="#__codelineno-26-38"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a id="__codelineno-26-39" name="__codelineno-26-39" href="#__codelineno-26-39"></a>
<a id="__codelineno-26-40" name="__codelineno-26-40" href="#__codelineno-26-40"></a><span class="w"> </span><span class="c1"># 直接走訪陣列</span>
<a id="__codelineno-26-41" name="__codelineno-26-41" href="#__codelineno-26-41"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">size</span>
<a id="__codelineno-26-42" name="__codelineno-26-42" href="#__codelineno-26-42"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-26-43" name="__codelineno-26-43" href="#__codelineno-26-43"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-44" name="__codelineno-26-44" href="#__codelineno-26-44"></a>
<a id="__codelineno-26-45" name="__codelineno-26-45" href="#__codelineno-26-45"></a><span class="w"> </span><span class="vi">@res</span>
<a id="__codelineno-26-46" name="__codelineno-26-46" href="#__codelineno-26-46"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-47" name="__codelineno-26-47" href="#__codelineno-26-47"></a>
<a id="__codelineno-26-48" name="__codelineno-26-48" href="#__codelineno-26-48"></a><span class="w"> </span><span class="c1">### 深度優先走訪 ###</span>
<a id="__codelineno-26-49" name="__codelineno-26-49" href="#__codelineno-26-49"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">order</span><span class="p">)</span>
<a id="__codelineno-26-50" name="__codelineno-26-50" href="#__codelineno-26-50"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-26-51" name="__codelineno-26-51" href="#__codelineno-26-51"></a><span class="w"> </span><span class="c1"># 前序走訪</span>
<a id="__codelineno-26-52" name="__codelineno-26-52" href="#__codelineno-26-52"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="ss">:pre</span>
<a id="__codelineno-26-53" name="__codelineno-26-53" href="#__codelineno-26-53"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</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">order</span><span class="p">)</span>
<a id="__codelineno-26-54" name="__codelineno-26-54" href="#__codelineno-26-54"></a><span class="w"> </span><span class="c1"># 中序走訪</span>
<a id="__codelineno-26-55" name="__codelineno-26-55" href="#__codelineno-26-55"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="ss">:in</span>
<a id="__codelineno-26-56" name="__codelineno-26-56" href="#__codelineno-26-56"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</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">order</span><span class="p">)</span>
<a id="__codelineno-26-57" name="__codelineno-26-57" href="#__codelineno-26-57"></a><span class="w"> </span><span class="c1"># 後序走訪</span>
<a id="__codelineno-26-58" name="__codelineno-26-58" href="#__codelineno-26-58"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="ss">:post</span>
<a id="__codelineno-26-59" name="__codelineno-26-59" href="#__codelineno-26-59"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-60" name="__codelineno-26-60" href="#__codelineno-26-60"></a>
<a id="__codelineno-26-61" name="__codelineno-26-61" href="#__codelineno-26-61"></a><span class="w"> </span><span class="c1">### 前序走訪 ###</span>
<a id="__codelineno-26-62" name="__codelineno-26-62" href="#__codelineno-26-62"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span>
<a id="__codelineno-26-63" name="__codelineno-26-63" href="#__codelineno-26-63"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a id="__codelineno-26-64" name="__codelineno-26-64" href="#__codelineno-26-64"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="ss">:pre</span><span class="p">)</span>
<a id="__codelineno-26-65" name="__codelineno-26-65" href="#__codelineno-26-65"></a><span class="w"> </span><span class="vi">@res</span>
<a id="__codelineno-26-66" name="__codelineno-26-66" href="#__codelineno-26-66"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-67" name="__codelineno-26-67" href="#__codelineno-26-67"></a>
<a id="__codelineno-26-68" name="__codelineno-26-68" href="#__codelineno-26-68"></a><span class="w"> </span><span class="c1">### 中序走訪 ###</span>
<a id="__codelineno-26-69" name="__codelineno-26-69" href="#__codelineno-26-69"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">in_order</span>
<a id="__codelineno-26-70" name="__codelineno-26-70" href="#__codelineno-26-70"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a id="__codelineno-26-71" name="__codelineno-26-71" href="#__codelineno-26-71"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="ss">:in</span><span class="p">)</span>
<a id="__codelineno-26-72" name="__codelineno-26-72" href="#__codelineno-26-72"></a><span class="w"> </span><span class="vi">@res</span>
<a id="__codelineno-26-73" name="__codelineno-26-73" href="#__codelineno-26-73"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-74" name="__codelineno-26-74" href="#__codelineno-26-74"></a>
<a id="__codelineno-26-75" name="__codelineno-26-75" href="#__codelineno-26-75"></a><span class="w"> </span><span class="c1">### 後序走訪 ###</span>
<a id="__codelineno-26-76" name="__codelineno-26-76" href="#__codelineno-26-76"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">post_order</span>
<a id="__codelineno-26-77" name="__codelineno-26-77" href="#__codelineno-26-77"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a id="__codelineno-26-78" name="__codelineno-26-78" href="#__codelineno-26-78"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="ss">:post</span><span class="p">)</span>
<a id="__codelineno-26-79" name="__codelineno-26-79" href="#__codelineno-26-79"></a><span class="w"> </span><span class="vi">@res</span>
<a id="__codelineno-26-80" name="__codelineno-26-80" href="#__codelineno-26-80"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-81" name="__codelineno-26-81" href="#__codelineno-26-81"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">

164
zh-hant/chapter_tree/avl_tree/index.html
View File

@ -3960,9 +3960,9 @@
<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w"> </span><span class="nx">right</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右子節點指標</span>
<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w"> </span><span class="kr">constructor</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="w"> </span><span class="nx">height?</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">left?</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="nx">right?</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</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="nx">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">val</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="k">this</span><span class="p">.</span><span class="nx">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">height</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="nx">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">height</span><span class="p">;</span><span class="w"> </span>
<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</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="nx">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">left</span><span class="p">;</span><span class="w"> </span>
<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">right</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="nx">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">right</span><span class="p">;</span><span class="w"> </span>
<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">height</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="nx">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">height</span><span class="p">;</span>
<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</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="nx">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">left</span><span class="p">;</span>
<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">right</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="nx">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">right</span><span class="p">;</span>
<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="p">}</span>
</code></pre></div>
@ -4035,7 +4035,18 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a>
<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### AVL 樹節點類別 ###</span>
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">TreeNode</span>
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:val</span><span class="w"> </span><span class="c1"># 節點值</span>
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:height</span><span class="w"> </span><span class="c1"># 節點高度</span>
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:left</span><span class="w"> </span><span class="c1"># 左子節點引用</span>
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:right</span><span class="w"> </span><span class="c1"># 右子節點引用</span>
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a>
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="vi">@val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span>
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="vi">@height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -4243,9 +4254,19 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">height</span><span class="p">}</span>
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a>
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">update_height</span><span class="p">}</span>
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1">### 獲取節點高度 ###</span>
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="c1"># 空節點高度為 -1 ，葉節點高度為 0</span>
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">height</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a>
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="k">end</span>
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a>
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="c1">### 更新節點高度 ###</span>
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="k">def</span><span class="w"> </span><span class="nf">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w"> </span><span class="c1"># 節點高度等於最高子樹高度 + 1</span>
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">),</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span><span class="o">].</span><span class="n">max</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -4400,7 +4421,14 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">balance_factor</span><span class="p">}</span>
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="c1">### 獲取平衡因子 ###</span>
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w"> </span><span class="c1"># 空節點平衡因子為 0</span>
<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a>
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w"> </span><span class="c1"># 節點平衡因子 = 左子樹高度 - 右子樹高度</span>
<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -4647,7 +4675,19 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">right_rotate</span><span class="p">}</span>
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="c1">### 右旋操作 ###</span>
<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">right_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span>
<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w"> </span><span class="n">grand_child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w"> </span><span class="c1"># 以 child 為原點，將 node 向右旋轉</span>
<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w"> </span><span class="n">child</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
<a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grand_child</span>
<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w"> </span><span class="c1"># 更新節點高度</span>
<a id="__codelineno-54-9" name="__codelineno-54-9" href="#__codelineno-54-9"></a><span class="w"> </span><span class="n">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-54-10" name="__codelineno-54-10" href="#__codelineno-54-10"></a><span class="w"> </span><span class="n">update_height</span><span class="p">(</span><span class="n">child</span><span class="p">)</span>
<a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a><span class="w"> </span><span class="c1"># 返回旋轉後子樹的根節點</span>
<a id="__codelineno-54-12" name="__codelineno-54-12" href="#__codelineno-54-12"></a><span class="w"> </span><span class="n">child</span>
<a id="__codelineno-54-13" name="__codelineno-54-13" href="#__codelineno-54-13"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -4878,7 +4918,19 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">left_rotate</span><span class="p">}</span>
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="c1">### 左旋操作 ###</span>
<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">left_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-68-3" name="__codelineno-68-3" href="#__codelineno-68-3"></a><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-68-4" name="__codelineno-68-4" href="#__codelineno-68-4"></a><span class="w"> </span><span class="n">grand_child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">.</span><span class="n">left</span>
<a id="__codelineno-68-5" name="__codelineno-68-5" href="#__codelineno-68-5"></a><span class="w"> </span><span class="c1"># 以 child 為原點，將 node 向左旋轉</span>
<a id="__codelineno-68-6" name="__codelineno-68-6" href="#__codelineno-68-6"></a><span class="w"> </span><span class="n">child</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
<a id="__codelineno-68-7" name="__codelineno-68-7" href="#__codelineno-68-7"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grand_child</span>
<a id="__codelineno-68-8" name="__codelineno-68-8" href="#__codelineno-68-8"></a><span class="w"> </span><span class="c1"># 更新節點高度</span>
<a id="__codelineno-68-9" name="__codelineno-68-9" href="#__codelineno-68-9"></a><span class="w"> </span><span class="n">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-68-10" name="__codelineno-68-10" href="#__codelineno-68-10"></a><span class="w"> </span><span class="n">update_height</span><span class="p">(</span><span class="n">child</span><span class="p">)</span>
<a id="__codelineno-68-11" name="__codelineno-68-11" href="#__codelineno-68-11"></a><span class="w"> </span><span class="c1"># 返回旋轉後子樹的根節點</span>
<a id="__codelineno-68-12" name="__codelineno-68-12" href="#__codelineno-68-12"></a><span class="w"> </span><span class="n">child</span>
<a id="__codelineno-68-13" name="__codelineno-68-13" href="#__codelineno-68-13"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -5339,7 +5391,34 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">rotate</span><span class="p">}</span>
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="c1">### 執行旋轉操作，使該子樹重新恢復平衡 ###</span>
<a id="__codelineno-82-2" name="__codelineno-82-2" href="#__codelineno-82-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-82-3" name="__codelineno-82-3" href="#__codelineno-82-3"></a><span class="w"> </span><span class="c1"># 獲取節點 node 的平衡因子</span>
<a id="__codelineno-82-4" name="__codelineno-82-4" href="#__codelineno-82-4"></a><span class="w"> </span><span class="n">balance_factor</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-82-5" name="__codelineno-82-5" href="#__codelineno-82-5"></a><span class="w"> </span><span class="c1"># 左遍樹</span>
<a id="__codelineno-82-6" name="__codelineno-82-6" href="#__codelineno-82-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">balance_factor</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-82-7" name="__codelineno-82-7" href="#__codelineno-82-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-82-8" name="__codelineno-82-8" href="#__codelineno-82-8"></a><span class="w"> </span><span class="c1"># 右旋</span>
<a id="__codelineno-82-9" name="__codelineno-82-9" href="#__codelineno-82-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">right_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-82-10" name="__codelineno-82-10" href="#__codelineno-82-10"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-82-11" name="__codelineno-82-11" href="#__codelineno-82-11"></a><span class="w"> </span><span class="c1"># 先左旋後右旋</span>
<a id="__codelineno-82-12" name="__codelineno-82-12" href="#__codelineno-82-12"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left_rotate</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
<a id="__codelineno-82-13" name="__codelineno-82-13" href="#__codelineno-82-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">right_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-82-14" name="__codelineno-82-14" href="#__codelineno-82-14"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-82-15" name="__codelineno-82-15" href="#__codelineno-82-15"></a><span class="w"> </span><span class="c1"># 右遍樹</span>
<a id="__codelineno-82-16" name="__codelineno-82-16" href="#__codelineno-82-16"></a><span class="w"> </span><span class="k">elsif</span><span class="w"> </span><span class="n">balance_factor</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
<a id="__codelineno-82-17" name="__codelineno-82-17" href="#__codelineno-82-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-82-18" name="__codelineno-82-18" href="#__codelineno-82-18"></a><span class="w"> </span><span class="c1"># 左旋</span>
<a id="__codelineno-82-19" name="__codelineno-82-19" href="#__codelineno-82-19"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">left_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-82-20" name="__codelineno-82-20" href="#__codelineno-82-20"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-82-21" name="__codelineno-82-21" href="#__codelineno-82-21"></a><span class="w"> </span><span class="c1"># 先右旋後左旋</span>
<a id="__codelineno-82-22" name="__codelineno-82-22" href="#__codelineno-82-22"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right_rotate</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
<a id="__codelineno-82-23" name="__codelineno-82-23" href="#__codelineno-82-23"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">left_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-82-24" name="__codelineno-82-24" href="#__codelineno-82-24"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-82-25" name="__codelineno-82-25" href="#__codelineno-82-25"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-82-26" name="__codelineno-82-26" href="#__codelineno-82-26"></a><span class="w"> </span><span class="c1"># 平衡樹，無須旋轉，直接返回</span>
<a id="__codelineno-82-27" name="__codelineno-82-27" href="#__codelineno-82-27"></a><span class="w"> </span><span class="n">node</span>
<a id="__codelineno-82-28" name="__codelineno-82-28" href="#__codelineno-82-28"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -5703,9 +5782,28 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-96-1" name="__codelineno-96-1" href="#__codelineno-96-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert</span><span class="p">}</span>
<a id="__codelineno-96-2" name="__codelineno-96-2" href="#__codelineno-96-2"></a>
<a id="__codelineno-96-3" name="__codelineno-96-3" href="#__codelineno-96-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert_helper</span><span class="p">}</span>
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-96-1" name="__codelineno-96-1" href="#__codelineno-96-1"></a><span class="c1">### 插入節點 ###</span>
<a id="__codelineno-96-2" name="__codelineno-96-2" href="#__codelineno-96-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-96-3" name="__codelineno-96-3" href="#__codelineno-96-3"></a><span class="w"> </span><span class="vi">@root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insert_helper</span><span class="p">(</span><span class="vi">@root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-96-4" name="__codelineno-96-4" href="#__codelineno-96-4"></a><span class="k">end</span>
<a id="__codelineno-96-5" name="__codelineno-96-5" href="#__codelineno-96-5"></a>
<a id="__codelineno-96-6" name="__codelineno-96-6" href="#__codelineno-96-6"></a><span class="c1">### 遞迴插入節點（輔助方法）###</span>
<a id="__codelineno-96-7" name="__codelineno-96-7" href="#__codelineno-96-7"></a><span class="k">def</span><span class="w"> </span><span class="nf">insert_helper</span><span class="p">(</span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-96-8" name="__codelineno-96-8" href="#__codelineno-96-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-96-9" name="__codelineno-96-9" href="#__codelineno-96-9"></a><span class="w"> </span><span class="c1"># 1. 查詢插入位置並插入節點</span>
<a id="__codelineno-96-10" name="__codelineno-96-10" href="#__codelineno-96-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">val</span>
<a id="__codelineno-96-11" name="__codelineno-96-11" href="#__codelineno-96-11"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insert_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-96-12" name="__codelineno-96-12" href="#__codelineno-96-12"></a><span class="w"> </span><span class="k">elsif</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">val</span>
<a id="__codelineno-96-13" name="__codelineno-96-13" href="#__codelineno-96-13"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insert_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-96-14" name="__codelineno-96-14" href="#__codelineno-96-14"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-96-15" name="__codelineno-96-15" href="#__codelineno-96-15"></a><span class="w"> </span><span class="c1"># 重複節點不插入，直接返回</span>
<a id="__codelineno-96-16" name="__codelineno-96-16" href="#__codelineno-96-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span>
<a id="__codelineno-96-17" name="__codelineno-96-17" href="#__codelineno-96-17"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-96-18" name="__codelineno-96-18" href="#__codelineno-96-18"></a><span class="w"> </span><span class="c1"># 更新節點高度</span>
<a id="__codelineno-96-19" name="__codelineno-96-19" href="#__codelineno-96-19"></a><span class="w"> </span><span class="n">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-96-20" name="__codelineno-96-20" href="#__codelineno-96-20"></a><span class="w"> </span><span class="c1"># 2. 執行旋轉操作，使該子樹重新恢復平衡</span>
<a id="__codelineno-96-21" name="__codelineno-96-21" href="#__codelineno-96-21"></a><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-96-22" name="__codelineno-96-22" href="#__codelineno-96-22"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -6278,9 +6376,41 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-110-1" name="__codelineno-110-1" href="#__codelineno-110-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove</span><span class="p">}</span>
<a id="__codelineno-110-2" name="__codelineno-110-2" href="#__codelineno-110-2"></a>
<a id="__codelineno-110-3" name="__codelineno-110-3" href="#__codelineno-110-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove_helper</span><span class="p">}</span>
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-110-1" name="__codelineno-110-1" href="#__codelineno-110-1"></a><span class="c1">### 刪除節點 ###</span>
<a id="__codelineno-110-2" name="__codelineno-110-2" href="#__codelineno-110-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-110-3" name="__codelineno-110-3" href="#__codelineno-110-3"></a><span class="w"> </span><span class="vi">@root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">remove_helper</span><span class="p">(</span><span class="vi">@root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-110-4" name="__codelineno-110-4" href="#__codelineno-110-4"></a><span class="k">end</span>
<a id="__codelineno-110-5" name="__codelineno-110-5" href="#__codelineno-110-5"></a>
<a id="__codelineno-110-6" name="__codelineno-110-6" href="#__codelineno-110-6"></a><span class="c1">### 遞迴刪除節點（輔助方法）###</span>
<a id="__codelineno-110-7" name="__codelineno-110-7" href="#__codelineno-110-7"></a><span class="k">def</span><span class="w"> </span><span class="nf">remove_helper</span><span class="p">(</span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-110-8" name="__codelineno-110-8" href="#__codelineno-110-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-110-9" name="__codelineno-110-9" href="#__codelineno-110-9"></a><span class="w"> </span><span class="c1"># 1. 查詢節點並刪除</span>
<a id="__codelineno-110-10" name="__codelineno-110-10" href="#__codelineno-110-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">val</span>
<a id="__codelineno-110-11" name="__codelineno-110-11" href="#__codelineno-110-11"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">remove_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-110-12" name="__codelineno-110-12" href="#__codelineno-110-12"></a><span class="w"> </span><span class="k">elsif</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">val</span>
<a id="__codelineno-110-13" name="__codelineno-110-13" href="#__codelineno-110-13"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">remove_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-110-14" name="__codelineno-110-14" href="#__codelineno-110-14"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-110-15" name="__codelineno-110-15" href="#__codelineno-110-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="o">.</span><span class="n">nil?</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-110-16" name="__codelineno-110-16" href="#__codelineno-110-16"></a><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-110-17" name="__codelineno-110-17" href="#__codelineno-110-17"></a><span class="w"> </span><span class="c1"># 子節點數量 = 0 ，直接刪除 node 並返回</span>
<a id="__codelineno-110-18" name="__codelineno-110-18" href="#__codelineno-110-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">child</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-110-19" name="__codelineno-110-19" href="#__codelineno-110-19"></a><span class="w"> </span><span class="c1"># 子節點數量 = 1 ，直接刪除 node</span>
<a id="__codelineno-110-20" name="__codelineno-110-20" href="#__codelineno-110-20"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span>
<a id="__codelineno-110-21" name="__codelineno-110-21" href="#__codelineno-110-21"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-110-22" name="__codelineno-110-22" href="#__codelineno-110-22"></a><span class="w"> </span><span class="c1"># 子節點數量 = 2 ，則將中序走訪的下個節點刪除，並用該節點替換當前節點</span>
<a id="__codelineno-110-23" name="__codelineno-110-23" href="#__codelineno-110-23"></a><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-110-24" name="__codelineno-110-24" href="#__codelineno-110-24"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">temp</span><span class="o">.</span><span class="n">left</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-110-25" name="__codelineno-110-25" href="#__codelineno-110-25"></a><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="o">.</span><span class="n">left</span>
<a id="__codelineno-110-26" name="__codelineno-110-26" href="#__codelineno-110-26"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-110-27" name="__codelineno-110-27" href="#__codelineno-110-27"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">remove_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">temp</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-110-28" name="__codelineno-110-28" href="#__codelineno-110-28"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="o">.</span><span class="n">val</span>
<a id="__codelineno-110-29" name="__codelineno-110-29" href="#__codelineno-110-29"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-110-30" name="__codelineno-110-30" href="#__codelineno-110-30"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-110-31" name="__codelineno-110-31" href="#__codelineno-110-31"></a><span class="w"> </span><span class="c1"># 更新節點高度</span>
<a id="__codelineno-110-32" name="__codelineno-110-32" href="#__codelineno-110-32"></a><span class="w"> </span><span class="n">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-110-33" name="__codelineno-110-33" href="#__codelineno-110-33"></a><span class="w"> </span><span class="c1"># 2. 執行旋轉操作，使該子樹重新恢復平衡</span>
<a id="__codelineno-110-34" name="__codelineno-110-34" href="#__codelineno-110-34"></a><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-110-35" name="__codelineno-110-35" href="#__codelineno-110-35"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">

106
zh-hant/chapter_tree/binary_search_tree/index.html
View File

@ -3988,7 +3988,26 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">BinarySearchTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">search</span><span class="p">}</span>
<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 查詢節點 ###</span>
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">search</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@root</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="w"> </span><span class="c1"># 迴圈查詢，越過葉節點後跳出</span>
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">cur</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="c1"># 目標節點在 cur 的右子樹中</span>
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span>
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="c1"># 目標節點在 cur 的左子樹中</span>
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="k">elsif</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">num</span>
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">left</span>
<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w"> </span><span class="c1"># 找到目標節點，跳出迴圈</span>
<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w"> </span><span class="k">break</span>
<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a>
<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w"> </span><span class="n">cur</span>
<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -4419,7 +4438,38 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">BinarySearchTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert</span><span class="p">}</span>
<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1">### 插入節點 ###</span>
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="c1"># 若樹為空，則初始化根節點</span>
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="vi">@root</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w"> </span><span class="vi">@root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w"> </span><span class="k">return</span>
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a>
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="w"> </span><span class="c1"># 迴圈查詢，越過葉節點後跳出</span>
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="w"> </span><span class="n">cur</span><span class="p">,</span><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@root</span><span class="p">,</span><span class="w"> </span><span class="kp">nil</span>
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">cur</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="w"> </span><span class="c1"># 找到重複節點，直接返回</span>
<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span>
<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a>
<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span>
<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a><span class="w"> </span><span class="c1"># 插入位置在 cur 的右子樹中</span>
<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span>
<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a><span class="w"> </span><span class="c1"># 插入位置在 cur 的左子樹中</span>
<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">left</span>
<a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-23" name="__codelineno-26-23" href="#__codelineno-26-23"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-24" name="__codelineno-26-24" href="#__codelineno-26-24"></a>
<a id="__codelineno-26-25" name="__codelineno-26-25" href="#__codelineno-26-25"></a><span class="w"> </span><span class="c1"># 插入節點</span>
<a id="__codelineno-26-26" name="__codelineno-26-26" href="#__codelineno-26-26"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-26-27" name="__codelineno-26-27" href="#__codelineno-26-27"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">pre</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span>
<a id="__codelineno-26-28" name="__codelineno-26-28" href="#__codelineno-26-28"></a><span class="w"> </span><span class="n">pre</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
<a id="__codelineno-26-29" name="__codelineno-26-29" href="#__codelineno-26-29"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-26-30" name="__codelineno-26-30" href="#__codelineno-26-30"></a><span class="w"> </span><span class="n">pre</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
<a id="__codelineno-26-31" name="__codelineno-26-31" href="#__codelineno-26-31"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-32" name="__codelineno-26-32" href="#__codelineno-26-32"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -5162,7 +5212,57 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">BinarySearchTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove</span><span class="p">}</span>
<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="c1">### 刪除節點 ###</span>
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w"> </span><span class="c1"># 若樹為空，直接提前返回</span>
<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="vi">@root</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a>
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w"> </span><span class="c1"># 迴圈查詢，越過葉節點後跳出</span>
<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w"> </span><span class="n">cur</span><span class="p">,</span><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@root</span><span class="p">,</span><span class="w"> </span><span class="kp">nil</span>
<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">cur</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w"> </span><span class="c1"># 找到待刪除節點，跳出迴圈</span>
<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w"> </span><span class="k">break</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span>
<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a>
<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span>
<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w"> </span><span class="c1"># 待刪除節點在 cur 的右子樹中</span>
<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span>
<a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-40-16" name="__codelineno-40-16" href="#__codelineno-40-16"></a><span class="w"> </span><span class="c1"># 待刪除節點在 cur 的左子樹中</span>
<a id="__codelineno-40-17" name="__codelineno-40-17" href="#__codelineno-40-17"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-40-18" name="__codelineno-40-18" href="#__codelineno-40-18"></a><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">left</span>
<a id="__codelineno-40-19" name="__codelineno-40-19" href="#__codelineno-40-19"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-40-20" name="__codelineno-40-20" href="#__codelineno-40-20"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-40-21" name="__codelineno-40-21" href="#__codelineno-40-21"></a><span class="w"> </span><span class="c1"># 若無待刪除節點，則直接返回</span>
<a id="__codelineno-40-22" name="__codelineno-40-22" href="#__codelineno-40-22"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-40-23" name="__codelineno-40-23" href="#__codelineno-40-23"></a>
<a id="__codelineno-40-24" name="__codelineno-40-24" href="#__codelineno-40-24"></a><span class="w"> </span><span class="c1"># 子節點數量 = 0 or 1</span>
<a id="__codelineno-40-25" name="__codelineno-40-25" href="#__codelineno-40-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">left</span><span class="o">.</span><span class="n">nil?</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">right</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-40-26" name="__codelineno-40-26" href="#__codelineno-40-26"></a><span class="w"> </span><span class="c1"># 當子節點數量 = 0 / 1 時， child = null / 該子節點</span>
<a id="__codelineno-40-27" name="__codelineno-40-27" href="#__codelineno-40-27"></a><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-40-28" name="__codelineno-40-28" href="#__codelineno-40-28"></a><span class="w"> </span><span class="c1"># 刪除節點 cur</span>
<a id="__codelineno-40-29" name="__codelineno-40-29" href="#__codelineno-40-29"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="vi">@root</span>
<a id="__codelineno-40-30" name="__codelineno-40-30" href="#__codelineno-40-30"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">pre</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">cur</span>
<a id="__codelineno-40-31" name="__codelineno-40-31" href="#__codelineno-40-31"></a><span class="w"> </span><span class="n">pre</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span>
<a id="__codelineno-40-32" name="__codelineno-40-32" href="#__codelineno-40-32"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-40-33" name="__codelineno-40-33" href="#__codelineno-40-33"></a><span class="w"> </span><span class="n">pre</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span>
<a id="__codelineno-40-34" name="__codelineno-40-34" href="#__codelineno-40-34"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-40-35" name="__codelineno-40-35" href="#__codelineno-40-35"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-40-36" name="__codelineno-40-36" href="#__codelineno-40-36"></a><span class="w"> </span><span class="c1"># 若刪除節點為根節點，則重新指定根節點</span>
<a id="__codelineno-40-37" name="__codelineno-40-37" href="#__codelineno-40-37"></a><span class="w"> </span><span class="vi">@root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span>
<a id="__codelineno-40-38" name="__codelineno-40-38" href="#__codelineno-40-38"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-40-39" name="__codelineno-40-39" href="#__codelineno-40-39"></a><span class="w"> </span><span class="c1"># 子節點數量 = 2</span>
<a id="__codelineno-40-40" name="__codelineno-40-40" href="#__codelineno-40-40"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-40-41" name="__codelineno-40-41" href="#__codelineno-40-41"></a><span class="w"> </span><span class="c1"># 獲取中序走訪中 cur 的下一個節點</span>
<a id="__codelineno-40-42" name="__codelineno-40-42" href="#__codelineno-40-42"></a><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-40-43" name="__codelineno-40-43" href="#__codelineno-40-43"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">tmp</span><span class="o">.</span><span class="n">left</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-40-44" name="__codelineno-40-44" href="#__codelineno-40-44"></a><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">.</span><span class="n">left</span>
<a id="__codelineno-40-45" name="__codelineno-40-45" href="#__codelineno-40-45"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-40-46" name="__codelineno-40-46" href="#__codelineno-40-46"></a><span class="w"> </span><span class="c1"># 遞迴刪除節點 tmp</span>
<a id="__codelineno-40-47" name="__codelineno-40-47" href="#__codelineno-40-47"></a><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="n">tmp</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-40-48" name="__codelineno-40-48" href="#__codelineno-40-48"></a><span class="w"> </span><span class="c1"># 用 tmp 覆蓋 cur</span>
<a id="__codelineno-40-49" name="__codelineno-40-49" href="#__codelineno-40-49"></a><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">.</span><span class="n">val</span>
<a id="__codelineno-40-50" name="__codelineno-40-50" href="#__codelineno-40-50"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-40-51" name="__codelineno-40-51" href="#__codelineno-40-51"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">

32
zh-hant/chapter_tree/binary_tree/index.html
View File

@ -3931,7 +3931,16 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a>
<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 二元樹節點類別 ###</span>
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">TreeNode</span>
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:val</span><span class="w"> </span><span class="c1"># 節點值</span>
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:left</span><span class="w"> </span><span class="c1"># 左子節點引用</span>
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="kp">attr_accessor</span><span class="w"> </span><span class="ss">:right</span><span class="w"> </span><span class="c1"># 右子節點引用</span>
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a>
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="vi">@val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span>
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -4146,7 +4155,18 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_tree.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a>
<div class="highlight"><span class="filename">binary_tree.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1"># 初始化二元樹</span>
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="c1"># 初始化節點</span>
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="n">n5</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="c1"># 構建節點之間的引用（指標）</span>
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="n">n1</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span>
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="n">n1</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span>
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="n">n2</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span>
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="n">n2</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n5</span>
</code></pre></div>
</div>
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@ -4284,7 +4304,13 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_tree.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a>
<div class="highlight"><span class="filename">binary_tree.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="c1"># 插入與刪除節點</span>
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="n">_p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="c1"># 在 n1 -&gt; n2 中間插入節點 _p</span>
<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="n">n1</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_p</span>
<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="n">_p</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span>
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="c1"># 刪除節點</span>
<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="n">n1</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span>
</code></pre></div>
</div>
<div class="tabbed-block">

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@ -3977,7 +3977,20 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_tree_bfs.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">level_order</span><span class="p">}</span>
<div class="highlight"><span class="filename">binary_tree_bfs.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 層序走訪 ###</span>
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">level_order</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="c1"># 初始化佇列，加入根節點</span>
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="n">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">root</span><span class="o">]</span>
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="c1"># 初始化一個串列，用於儲存走訪序列</span>
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">queue</span><span class="o">.</span><span class="n">empty?</span>
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">.</span><span class="n">shift</span><span class="w"> </span><span class="c1"># 隊列出隊</span>
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="c1"># 儲存節點值</span>
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="n">queue</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="o">.</span><span class="n">nil?</span><span class="w"> </span><span class="c1"># 左子節點入列</span>
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="n">queue</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="o">.</span><span class="n">nil?</span><span class="w"> </span><span class="c1"># 右子節點入列</span>
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w"> </span><span class="n">res</span>
<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -4420,11 +4433,35 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_tree_dfs.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">pre_order</span><span class="p">}</span>
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a>
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">in_order</span><span class="p">}</span>
<div class="highlight"><span class="filename">binary_tree_dfs.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1">### 前序走訪 ###</span>
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">post_order</span><span class="p">}</span>
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w"> </span><span class="c1"># 訪問優先順序：根節點 -&gt; 左子樹 -&gt; 右子樹</span>
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w"> </span><span class="vg">$res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">val</span>
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="w"> </span><span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="k">end</span>
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a>
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="c1">### 中序走訪 ###</span>
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="k">def</span><span class="w"> </span><span class="nf">in_order</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a>
<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="w"> </span><span class="c1"># 訪問優先順序：左子樹 -&gt; 根節點 -&gt; 右子樹</span>
<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a><span class="w"> </span><span class="n">in_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a><span class="w"> </span><span class="vg">$res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">val</span>
<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a><span class="w"> </span><span class="n">in_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a><span class="k">end</span>
<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a>
<a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a><span class="c1">### 後序走訪 ###</span>
<a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a><span class="k">def</span><span class="w"> </span><span class="nf">post_order</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
<a id="__codelineno-26-23" name="__codelineno-26-23" href="#__codelineno-26-23"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-26-24" name="__codelineno-26-24" href="#__codelineno-26-24"></a>
<a id="__codelineno-26-25" name="__codelineno-26-25" href="#__codelineno-26-25"></a><span class="w"> </span><span class="c1"># 訪問優先順序：左子樹 -&gt; 右子樹 -&gt; 根節點</span>
<a id="__codelineno-26-26" name="__codelineno-26-26" href="#__codelineno-26-26"></a><span class="w"> </span><span class="n">post_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
<a id="__codelineno-26-27" name="__codelineno-26-27" href="#__codelineno-26-27"></a><span class="w"> </span><span class="n">post_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
<a id="__codelineno-26-28" name="__codelineno-26-28" href="#__codelineno-26-28"></a><span class="w"> </span><span class="vg">$res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">val</span>
<a id="__codelineno-26-29" name="__codelineno-26-29" href="#__codelineno-26-29"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">

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