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< span > 紙質書（簡體中文版）已發行，詳情請見< a href = "/chapter_paperbook/" > 這裡< / a > < / span >
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Hello 演算法
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8.2 建堆積操作
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正在初始化搜尋引擎
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krahets/hello-algo
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< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "m13.13 22.19-1.63-3.83c1.57-.58 3.04-1.36 4.4-2.27l-2.77 6.1M5.64 12.5l-3.83-1.63 6.1-2.77C7 9.46 6.22 10.93 5.64 12.5M19.22 4c.28 0 .53 0 .74.05.17 1.39-.02 4.25-3.3 7.53-1.7 1.71-3.73 3.02-6.01 3.89l-2.15-2.1c.92-2.31 2.23-4.34 3.92-6.03C15.18 4.58 17.64 4 19.22 4m0-2c-1.98 0-4.98.69-8.22 3.93-2.19 2.19-3.5 4.6-4.35 6.71-.28.75-.09 1.57.46 2.13l2.13 2.12c.38.38.89.61 1.42.61.23 0 .47-.06.7-.15A19.1 19.1 0 0 0 18.07 13c5.66-5.66 3.54-10.61 3.54-10.61S20.7 2 19.22 2m-4.68 7.46c-.78-.78-.78-2.05 0-2.83s2.05-.78 2.83 0c.77.78.78 2.05 0 2.83-.78.78-2.05.78-2.83 0m-5.66 7.07-1.41-1.41 1.41 1.41M6.24 22l3.64-3.64c-.34-.09-.67-.24-.97-.45L4.83 22h1.41M2 22h1.41l4.77-4.76-1.42-1.41L2 20.59V22m0-2.83 4.09-4.08c-.21-.3-.36-.62-.45-.97L2 17.76v1.41Z" / > < / svg >
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序
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序
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< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z" / > < / svg >
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第 0 章 前言
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第 0 章 前言
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0.1 關於本書
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0.2 如何使用本書
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0.3 小結
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第 1 章 初識演算法
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第 1 章 初識演算法
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1.1 演算法無處不在
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1.2 演算法是什麼
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1.3 小結
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第 2 章 複雜度分析
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第 2 章 複雜度分析
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2.1 演算法效率評估
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2.2 迭代與遞迴
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2.3 時間複雜度
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2.4 空間複雜度
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2.5 小結
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< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z" / > < / svg >
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第 3 章 資料結構
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第 3 章 資料結構
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3.1 資料結構分類
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3.2 基本資料型別
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3.3 數字編碼 *
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3.4 字元編碼 *
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3.5 小結
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第 4 章 陣列與鏈結串列
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第 4 章 陣列與鏈結串列
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4.1 陣列
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4.2 鏈結串列
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4.3 串列
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4.4 記憶體與快取 *
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4.5 小結
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第 5 章 堆疊與佇列
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第 5 章 堆疊與佇列
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5.1 堆疊
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5.2 佇列
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5.3 雙向佇列
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5.4 小結
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第 6 章 雜湊表
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第 6 章 雜湊表
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6.1 雜湊表
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6.2 雜湊衝突
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6.3 雜湊演算法
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6.4 小結
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第 7 章 樹
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第 7 章 樹
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7.1 二元樹
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7.2 二元樹走訪
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7.3 二元樹陣列表示
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7.4 二元搜尋樹
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7.5 AVL *
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7.6 小結
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< a href = "../" class = "md-nav__link " >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z" / > < / svg >
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第 8 章 堆積
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第 8 章 堆積
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8.1 堆積
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8.2 建堆積操作
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8.2 建堆積操作
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目錄
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8.2.1 藉助入堆積操作實現
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8.2.2 透過走訪堆積化實現
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8.2.3 複雜度分析
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8.3 Top-k 問題
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8.4 小結
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第 9 章 圖
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第 9 章 圖
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9.1 圖
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9.2 圖基礎操作
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9.3 圖的走訪
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9.4 小結
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< a href = "../../chapter_searching/" class = "md-nav__link " >
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第 10 章 搜尋
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第 10 章 搜尋
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10.1 二分搜尋
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10.2 二分搜尋插入點
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10.3 二分搜尋邊界
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10.4 雜湊最佳化策略
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10.5 重識搜尋演算法
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10.6 小結
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第 11 章 排序
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第 11 章 排序
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11.1 排序演算法
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11.2 選擇排序
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11.3 泡沫排序
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11.4 插入排序
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11.5 快速排序
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11.6 合併排序
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11.7 堆積排序
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11.8 桶排序
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11.9 計數排序
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11.10 基數排序
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11.11 小結
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< a href = "../../chapter_divide_and_conquer/" class = "md-nav__link " >
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第 12 章 分治
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第 12 章 分治
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12.1 分治演算法
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12.5 小結
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13.2 全排列問題
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13.3 子集和問題
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13.4 N 皇后問題
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13.5 小結
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第 14 章 動態規劃
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第 14 章 動態規劃
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14.1 初探動態規劃
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14.2 DP 問題特性
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14.3 DP 解題思路
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14.4 0-1 背包問題
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14.5 完全背包問題
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14.6 編輯距離問題
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14.7 小結
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第 15 章 貪婪
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第 15 章 貪婪
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15.1 貪婪演算法
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15.2 分數背包問題
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15.3 最大容量問題
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15.4 最大切分乘積問題
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15.5 小結
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第 16 章 附錄
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第 16 章 附錄
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16.1 程式設計環境安裝
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8.2.1 藉助入堆積操作實現
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8.2.2 透過走訪堆積化實現
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8.2.3 複雜度分析
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< h1 id = "82" > 8.2 建堆積操作< a class = "headerlink" href = "#82" title = "Permanent link" > ¶ < / a > < / h1 >
< p > 在某些情況下，我們希望使用一個串列的所有元素來構建一個堆積，這個過程被稱為“建堆積操作”。< / p >
< h2 id = "821" > 8.2.1 藉助入堆積操作實現< a class = "headerlink" href = "#821" title = "Permanent link" > ¶ < / a > < / h2 >
< p > 我們首先建立一個空堆積，然後走訪串列，依次對每個元素執行“入堆積操作”，即先將元素新增至堆積的尾部，再對該元素執行“從底至頂”堆積化。< / p >
< p > 每當一個元素入堆積，堆積的長度就加一。由於節點是從頂到底依次被新增進二元樹的，因此堆積是“自上而下”構建的。< / p >
< p > 設元素數量為 < span class = "arithmatex" > \(n\)< / span > ，每個元素的入堆積操作使用 < span class = "arithmatex" > \(O(\log{n})\)< / span > 時間，因此該建堆積方法的時間複雜度為 < span class = "arithmatex" > \(O(n \log n)\)< / span > 。< / p >
< h2 id = "822" > 8.2.2 透過走訪堆積化實現< a class = "headerlink" href = "#822" title = "Permanent link" > ¶ < / a > < / h2 >
< p > 實際上，我們可以實現一種更為高效的建堆積方法，共分為兩步。< / p >
< ol >
< li > 將串列所有元素原封不動地新增到堆積中，此時堆積的性質尚未得到滿足。< / li >
< li > 倒序走訪堆積（層序走訪的倒序），依次對每個非葉節點執行“從頂至底堆積化”。< / li >
< / ol >
< p > < strong > 每當堆積化一個節點後，以該節點為根節點的子樹就形成一個合法的子堆積< / strong > 。而由於是倒序走訪，因此堆積是“自下而上”構建的。< / p >
< p > 之所以選擇倒序走訪，是因為這樣能夠保證當前節點之下的子樹已經是合法的子堆積，這樣堆積化當前節點才是有效的。< / p >
< p > 值得說明的是，< strong > 由於葉節點沒有子節點，因此它們天然就是合法的子堆積，無須堆積化< / strong > 。如以下程式碼所示，最後一個非葉節點是最後一個節點的父節點，我們從它開始倒序走訪並執行堆積化：< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "1:14" > < input checked = "checked" id = "__tabbed_1_1" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_2" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_3" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_4" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_5" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_6" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_7" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_8" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_9" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_10" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_11" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_12" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_13" name = "__tabbed_1" type = "radio" / > < input id = "__tabbed_1_14" name = "__tabbed_1" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_1_1" > Python< / label > < label for = "__tabbed_1_2" > C++< / label > < label for = "__tabbed_1_3" > Java< / label > < label for = "__tabbed_1_4" > C#< / label > < label for = "__tabbed_1_5" > Go< / label > < label for = "__tabbed_1_6" > Swift< / label > < label for = "__tabbed_1_7" > JS< / label > < label for = "__tabbed_1_8" > TS< / label > < label for = "__tabbed_1_9" > Dart< / label > < label for = "__tabbed_1_10" > Rust< / label > < label for = "__tabbed_1_11" > C< / label > < label for = "__tabbed_1_12" > Kotlin< / label > < label for = "__tabbed_1_13" > Ruby< / label > < label for = "__tabbed_1_14" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-0-1" name = "__codelineno-0-1" href = "#__codelineno-0-1" > < / a > < span class = "k" > def< / span > < span class = "fm" > __init__< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "p" > ,< / span > < span class = "n" > nums< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ]):< / span >
< a id = "__codelineno-0-2" name = "__codelineno-0-2" href = "#__codelineno-0-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 建構子，根據輸入串列建堆積" " " < / span >
< a id = "__codelineno-0-3" name = "__codelineno-0-3" href = "#__codelineno-0-3" > < / a > < span class = "c1" > # 將串列元素原封不動新增進堆積< / span >
< a id = "__codelineno-0-4" name = "__codelineno-0-4" href = "#__codelineno-0-4" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > max_heap< / span > < span class = "o" > =< / span > < span class = "n" > nums< / span >
< a id = "__codelineno-0-5" name = "__codelineno-0-5" href = "#__codelineno-0-5" > < / a > < span class = "c1" > # 堆積化除葉節點以外的其他所有節點< / span >
< a id = "__codelineno-0-6" name = "__codelineno-0-6" href = "#__codelineno-0-6" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > parent< / span > < span class = "p" > (< / span > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > size< / span > < span class = "p" > ()< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ),< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-0-7" name = "__codelineno-0-7" href = "#__codelineno-0-7" > < / a > < span class = "bp" > self< / span > < span class = "o" > .< / span > < span class = "n" > sift_down< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > )< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-1-1" name = "__codelineno-1-1" href = "#__codelineno-1-1" > < / a > < span class = "cm" > /* 建構子，根據輸入串列建堆積 */< / span >
< a id = "__codelineno-1-2" name = "__codelineno-1-2" href = "#__codelineno-1-2" > < / a > < span class = "n" > MaxHeap< / span > < span class = "p" > (< / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-3" name = "__codelineno-1-3" href = "#__codelineno-1-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 將串列元素原封不動新增進堆積< / span >
< a id = "__codelineno-1-4" name = "__codelineno-1-4" href = "#__codelineno-1-4" > < / a > < span class = "w" > < / span > < span class = "n" > maxHeap< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-5" name = "__codelineno-1-5" href = "#__codelineno-1-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 堆積化除葉節點以外的其他所有節點< / span >
< a id = "__codelineno-1-6" name = "__codelineno-1-6" href = "#__codelineno-1-6" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > parent< / span > < span class = "p" > (< / span > < span class = "n" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > --< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-7" name = "__codelineno-1-7" href = "#__codelineno-1-7" > < / a > < span class = "w" > < / span > < span class = "n" > siftDown< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-1-8" name = "__codelineno-1-8" href = "#__codelineno-1-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-9" name = "__codelineno-1-9" href = "#__codelineno-1-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-2-1" name = "__codelineno-2-1" href = "#__codelineno-2-1" > < / a > < span class = "cm" > /* 建構子，根據輸入串列建堆積 */< / span >
< a id = "__codelineno-2-2" name = "__codelineno-2-2" href = "#__codelineno-2-2" > < / a > < span class = "n" > MaxHeap< / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-3" name = "__codelineno-2-3" href = "#__codelineno-2-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 將串列元素原封不動新增進堆積< / span >
< a id = "__codelineno-2-4" name = "__codelineno-2-4" href = "#__codelineno-2-4" > < / a > < span class = "w" > < / span > < span class = "n" > maxHeap< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > ArrayList< / span > < span class = "o" > < > < / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > );< / span >
< a id = "__codelineno-2-5" name = "__codelineno-2-5" href = "#__codelineno-2-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 堆積化除葉節點以外的其他所有節點< / span >
< a id = "__codelineno-2-6" name = "__codelineno-2-6" href = "#__codelineno-2-6" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > parent< / span > < span class = "p" > (< / span > < span class = "n" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > --< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-2-7" name = "__codelineno-2-7" href = "#__codelineno-2-7" > < / a > < span class = "w" > < / span > < span class = "n" > siftDown< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-2-8" name = "__codelineno-2-8" href = "#__codelineno-2-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-2-9" name = "__codelineno-2-9" href = "#__codelineno-2-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-3-1" name = "__codelineno-3-1" href = "#__codelineno-3-1" > < / a > < span class = "cm" > /* 建構子，根據輸入串列建堆積 */< / span >
< a id = "__codelineno-3-2" name = "__codelineno-3-2" href = "#__codelineno-3-2" > < / a > < span class = "n" > MaxHeap< / span > < span class = "p" > (< / span > < span class = "n" > IEnumerable< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-3" name = "__codelineno-3-3" href = "#__codelineno-3-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 將串列元素原封不動新增進堆積< / span >
< a id = "__codelineno-3-4" name = "__codelineno-3-4" href = "#__codelineno-3-4" > < / a > < span class = "w" > < / span > < span class = "n" > maxHeap< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > );< / span >
< a id = "__codelineno-3-5" name = "__codelineno-3-5" href = "#__codelineno-3-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 堆積化除葉節點以外的其他所有節點< / span >
< a id = "__codelineno-3-6" name = "__codelineno-3-6" href = "#__codelineno-3-6" > < / a > < span class = "w" > < / span > < span class = "kt" > var< / span > < span class = "w" > < / span > < span class = "n" > size< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > Parent< / span > < span class = "p" > (< / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "n" > Size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-3-7" name = "__codelineno-3-7" href = "#__codelineno-3-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > size< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > --< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-8" name = "__codelineno-3-8" href = "#__codelineno-3-8" > < / a > < span class = "w" > < / span > < span class = "n" > SiftDown< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-3-9" name = "__codelineno-3-9" href = "#__codelineno-3-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-10" name = "__codelineno-3-10" href = "#__codelineno-3-10" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-4-1" name = "__codelineno-4-1" href = "#__codelineno-4-1" > < / a > < span class = "cm" > /* 建構子，根據切片建堆積 */< / span >
< a id = "__codelineno-4-2" name = "__codelineno-4-2" href = "#__codelineno-4-2" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > newMaxHeap< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "kt" > any< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nx" > maxHeap< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-3" name = "__codelineno-4-3" href = "#__codelineno-4-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 將串列元素原封不動新增進堆積< / span >
< a id = "__codelineno-4-4" name = "__codelineno-4-4" href = "#__codelineno-4-4" > < / a > < span class = "w" > < / span > < span class = "nx" > h< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "o" > & < / span > < span class = "nx" > maxHeap< / span > < span class = "p" > {< / span > < span class = "nx" > data< / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > }< / span >
< a id = "__codelineno-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 = "nx" > h< / span > < span class = "p" > .< / span > < span class = "nx" > parent< / span > < span class = "p" > (< / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "nx" > h< / span > < span class = "p" > .< / span > < span class = "nx" > data< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > --< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-6" name = "__codelineno-4-6" href = "#__codelineno-4-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 堆積化除葉節點以外的其他所有節點< / span >
< a id = "__codelineno-4-7" name = "__codelineno-4-7" href = "#__codelineno-4-7" > < / a > < span class = "w" > < / span > < span class = "nx" > h< / span > < span class = "p" > .< / span > < span class = "nx" > siftDown< / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "p" > )< / span >
< a id = "__codelineno-4-8" name = "__codelineno-4-8" href = "#__codelineno-4-8" > < / a > < span class = "w" > < / 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > h< / span >
< a id = "__codelineno-4-10" name = "__codelineno-4-10" href = "#__codelineno-4-10" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-5-1" name = "__codelineno-5-1" href = "#__codelineno-5-1" > < / a > < span class = "cm" > /* 建構子，根據輸入串列建堆積 */< / span >
< a id = "__codelineno-5-2" name = "__codelineno-5-2" href = "#__codelineno-5-2" > < / a > < span class = "kd" > init< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > :< / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ])< / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-3" name = "__codelineno-5-3" href = "#__codelineno-5-3" > < / a > < span class = "c1" > // 將串列元素原封不動新增進堆積< / span >
< a id = "__codelineno-5-4" name = "__codelineno-5-4" href = "#__codelineno-5-4" > < / a > < span class = "n" > maxHeap< / span > < span class = "p" > =< / span > < span class = "n" > nums< / span >
< a id = "__codelineno-5-5" name = "__codelineno-5-5" href = "#__codelineno-5-5" > < / a > < span class = "c1" > // 堆積化除葉節點以外的其他所有節點< / span >
< a id = "__codelineno-5-6" name = "__codelineno-5-6" href = "#__codelineno-5-6" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "k" > in< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > ...< / span > < span class = "n" > parent< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > :< / span > < span class = "n" > size< / span > < span class = "p" > ()< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > )).< / span > < span class = "n" > reversed< / span > < span class = "p" > ()< / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-7" name = "__codelineno-5-7" href = "#__codelineno-5-7" > < / a > < span class = "n" > siftDown< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > :< / span > < span class = "n" > i< / span > < span class = "p" > )< / span >
< a id = "__codelineno-5-8" name = "__codelineno-5-8" href = "#__codelineno-5-8" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-9" name = "__codelineno-5-9" href = "#__codelineno-5-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-6-1" name = "__codelineno-6-1" href = "#__codelineno-6-1" > < / a > < span class = "cm" > /* 建構子，建立空堆積或根據輸入串列建堆積 */< / span >
< a id = "__codelineno-6-2" name = "__codelineno-6-2" href = "#__codelineno-6-2" > < / a > < span class = "kr" > constructor< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-6-3" name = "__codelineno-6-3" href = "#__codelineno-6-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 將串列元素原封不動新增進堆積< / span >
< a id = "__codelineno-6-4" name = "__codelineno-6-4" href = "#__codelineno-6-4" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "err" > #< / span > < span class = "nx" > maxHeap< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > undefined< / span > < span class = "w" > < / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "p" > [...< / span > < span class = "nx" > nums< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-6-5" name = "__codelineno-6-5" href = "#__codelineno-6-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 堆積化除葉節點以外的其他所有節點< / span >
< a id = "__codelineno-6-6" name = "__codelineno-6-6" href = "#__codelineno-6-6" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "err" > #< / span > < span class = "nx" > parent< / span > < span class = "p" > (< / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > --< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-6-7" name = "__codelineno-6-7" href = "#__codelineno-6-7" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "err" > #< / span > < span class = "nx" > siftDown< / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-6-8" name = "__codelineno-6-8" href = "#__codelineno-6-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-6-9" name = "__codelineno-6-9" href = "#__codelineno-6-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-7-1" name = "__codelineno-7-1" href = "#__codelineno-7-1" > < / a > < span class = "cm" > /* 建構子，建立空堆積或根據輸入串列建堆積 */< / span >
< a id = "__codelineno-7-2" name = "__codelineno-7-2" href = "#__codelineno-7-2" > < / a > < span class = "kr" > constructor< / span > < span class = "p" > (< / span > < span class = "nx" > nums?< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > [])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-3" name = "__codelineno-7-3" href = "#__codelineno-7-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 將串列元素原封不動新增進堆積< / span >
< a id = "__codelineno-7-4" name = "__codelineno-7-4" href = "#__codelineno-7-4" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > maxHeap< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "w" > < / span > < span class = "o" > ===< / span > < span class = "w" > < / span > < span class = "kc" > undefined< / span > < span class = "w" > < / span > < span class = "o" > ?< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "p" > [...< / span > < span class = "nx" > nums< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-7-5" name = "__codelineno-7-5" href = "#__codelineno-7-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 堆積化除葉節點以外的其他所有節點< / span >
< a id = "__codelineno-7-6" name = "__codelineno-7-6" href = "#__codelineno-7-6" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > parent< / span > < span class = "p" > (< / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "mf" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > --< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-7" name = "__codelineno-7-7" href = "#__codelineno-7-7" > < / a > < span class = "w" > < / span > < span class = "k" > this< / span > < span class = "p" > .< / span > < span class = "nx" > siftDown< / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-7-8" name = "__codelineno-7-8" href = "#__codelineno-7-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-9" name = "__codelineno-7-9" href = "#__codelineno-7-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-8-1" name = "__codelineno-8-1" href = "#__codelineno-8-1" > < / a > < span class = "cm" > /* 建構子，根據輸入串列建堆積 */< / span >
< a id = "__codelineno-8-2" name = "__codelineno-8-2" href = "#__codelineno-8-2" > < / a > < span class = "n" > MaxHeap< / span > < span class = "p" > (< / span > < span class = "n" > List< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-3" name = "__codelineno-8-3" href = "#__codelineno-8-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 將串列元素原封不動新增進堆積< / span >
< a id = "__codelineno-8-4" name = "__codelineno-8-4" href = "#__codelineno-8-4" > < / a > < span class = "w" > < / span > < span class = "n" > _maxHeap< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-8-5" name = "__codelineno-8-5" href = "#__codelineno-8-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 堆積化除葉節點以外的其他所有節點< / span >
< a id = "__codelineno-8-6" name = "__codelineno-8-6" href = "#__codelineno-8-6" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > _parent< / span > < span class = "p" > (< / span > < span class = "n" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > --< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-7" name = "__codelineno-8-7" href = "#__codelineno-8-7" > < / a > < span class = "w" > < / span > < span class = "n" > siftDown< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-8-8" name = "__codelineno-8-8" href = "#__codelineno-8-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-8-9" name = "__codelineno-8-9" href = "#__codelineno-8-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.rs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-9-1" name = "__codelineno-9-1" href = "#__codelineno-9-1" > < / a > < span class = "cm" > /* 建構子，根據輸入串列建堆積 */< / span >
< a id = "__codelineno-9-2" name = "__codelineno-9-2" href = "#__codelineno-9-2" > < / a > < span class = "k" > fn< / span > < span class = "nf" > new< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > : < span class = "nb" > Vec< / span > < span class = "o" > < < / span > < span class = "kt" > i32< / span > < span class = "o" > > < / span > < span class = "p" > )< / span > < span class = "w" > < / span > -> < span class = "nc" > Self< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-3" name = "__codelineno-9-3" href = "#__codelineno-9-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 將串列元素原封不動新增進堆積< / span >
< a id = "__codelineno-9-4" name = "__codelineno-9-4" href = "#__codelineno-9-4" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "k" > mut< / span > < span class = "w" > < / span > < span class = "n" > heap< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > MaxHeap< / span > < span class = "w" > < / span > < span class = "p" > {< / span > < span class = "w" > < / span > < span class = "n" > max_heap< / span > : < span class = "nc" > nums< / span > < span class = "w" > < / span > < span class = "p" > };< / span >
< a id = "__codelineno-9-5" name = "__codelineno-9-5" href = "#__codelineno-9-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 堆積化除葉節點以外的其他所有節點< / span >
< a id = "__codelineno-9-6" name = "__codelineno-9-6" href = "#__codelineno-9-6" > < / 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 = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "o" > ..=< / span > < span class = "bp" > Self< / span > ::< span class = "n" > parent< / span > < span class = "p" > (< / span > < span class = "n" > heap< / span > < span class = "p" > .< / span > < span class = "n" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )).< / span > < span class = "n" > rev< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-9-7" name = "__codelineno-9-7" href = "#__codelineno-9-7" > < / a > < span class = "w" > < / span > < span class = "n" > heap< / span > < span class = "p" > .< / span > < span class = "n" > sift_down< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-9-8" name = "__codelineno-9-8" href = "#__codelineno-9-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-9-9" name = "__codelineno-9-9" href = "#__codelineno-9-9" > < / a > < span class = "w" > < / span > < span class = "n" > heap< / span >
< a id = "__codelineno-9-10" name = "__codelineno-9-10" href = "#__codelineno-9-10" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-10-1" name = "__codelineno-10-1" href = "#__codelineno-10-1" > < / a > < span class = "cm" > /* 建構子，根據切片建堆積 */< / span >
< a id = "__codelineno-10-2" name = "__codelineno-10-2" href = "#__codelineno-10-2" > < / a > < span class = "n" > MaxHeap< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "nf" > newMaxHeap< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > [],< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > size< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-3" name = "__codelineno-10-3" href = "#__codelineno-10-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 所有元素入堆積< / span >
< a id = "__codelineno-10-4" name = "__codelineno-10-4" href = "#__codelineno-10-4" > < / a > < span class = "w" > < / span > < span class = "n" > MaxHeap< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > maxHeap< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > MaxHeap< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "p" > )< / span > < span class = "n" > malloc< / span > < span class = "p" > (< / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "n" > MaxHeap< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-10-5" name = "__codelineno-10-5" href = "#__codelineno-10-5" > < / a > < span class = "w" > < / span > < span class = "n" > maxHeap< / span > < span class = "o" > -> < / span > < span class = "n" > size< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > size< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-6" name = "__codelineno-10-6" href = "#__codelineno-10-6" > < / a > < span class = "w" > < / span > < span class = "n" > memcpy< / span > < span class = "p" > (< / span > < span class = "n" > maxHeap< / span > < span class = "o" > -> < / span > < span class = "n" > data< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > size< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "k" > sizeof< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > ));< / span >
< a id = "__codelineno-10-7" name = "__codelineno-10-7" href = "#__codelineno-10-7" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > parent< / span > < span class = "p" > (< / span > < span class = "n" > maxHeap< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > size< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > --< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-10-8" name = "__codelineno-10-8" href = "#__codelineno-10-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 堆積化除葉節點以外的其他所有節點< / span >
< a id = "__codelineno-10-9" name = "__codelineno-10-9" href = "#__codelineno-10-9" > < / a > < span class = "w" > < / span > < span class = "n" > siftDown< / span > < span class = "p" > (< / span > < span class = "n" > maxHeap< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > );< / span >
< a id = "__codelineno-10-10" name = "__codelineno-10-10" href = "#__codelineno-10-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-11" name = "__codelineno-10-11" href = "#__codelineno-10-11" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > maxHeap< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-10-12" name = "__codelineno-10-12" href = "#__codelineno-10-12" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.kt< / span > < pre > < span > < / span > < code > < a id = "__codelineno-11-1" name = "__codelineno-11-1" href = "#__codelineno-11-1" > < / a > < span class = "cm" > /* 大頂堆積 */< / span >
< a id = "__codelineno-11-2" name = "__codelineno-11-2" href = "#__codelineno-11-2" > < / a > < span class = "kd" > class< / span > < span class = "w" > < / span > < span class = "nc" > MaxHeap< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "n" > MutableList< / span > < span class = "o" > < < / span > < span class = "kt" > Int< / span > < span class = "o" > > ?< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-3" name = "__codelineno-11-3" href = "#__codelineno-11-3" > < / a > < span class = "w" > < / span > < span class = "c1" > // 使用串列而非陣列，這樣無須考慮擴容問題< / span >
< a id = "__codelineno-11-4" name = "__codelineno-11-4" href = "#__codelineno-11-4" > < / a > < span class = "w" > < / span > < span class = "kd" > private< / span > < span class = "w" > < / span > < span class = "kd" > val< / span > < span class = "w" > < / span > < span class = "nv" > maxHeap< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > mutableListOf< / span > < span class = "o" > < < / span > < span class = "kt" > Int< / span > < span class = "o" > > < / span > < span class = "p" > ()< / span >
< a id = "__codelineno-11-5" name = "__codelineno-11-5" href = "#__codelineno-11-5" > < / a >
< a id = "__codelineno-11-6" name = "__codelineno-11-6" href = "#__codelineno-11-6" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 建構子，根據輸入串列建堆積 */< / span >
< a id = "__codelineno-11-7" name = "__codelineno-11-7" href = "#__codelineno-11-7" > < / a > < span class = "w" > < / span > < span class = "k" > init< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-8" name = "__codelineno-11-8" href = "#__codelineno-11-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 將串列元素原封不動新增進堆積< / span >
< a id = "__codelineno-11-9" name = "__codelineno-11-9" href = "#__codelineno-11-9" > < / a > < span class = "w" > < / span > < span class = "n" > maxHeap< / span > < span class = "p" > .< / span > < span class = "na" > addAll< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "o" > !!< / span > < span class = "p" > )< / span >
< a id = "__codelineno-11-10" name = "__codelineno-11-10" href = "#__codelineno-11-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 堆積化除葉節點以外的其他所有節點< / span >
< a id = "__codelineno-11-11" name = "__codelineno-11-11" href = "#__codelineno-11-11" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "k" > in< / span > < span class = "w" > < / span > < span class = "n" > parent< / span > < span class = "p" > (< / span > < span class = "n" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "n" > downTo< / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-12" name = "__codelineno-11-12" href = "#__codelineno-11-12" > < / a > < span class = "w" > < / span > < span class = "n" > siftDown< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > )< / span >
< a id = "__codelineno-11-13" name = "__codelineno-11-13" href = "#__codelineno-11-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-14" name = "__codelineno-11-14" href = "#__codelineno-11-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-15" name = "__codelineno-11-15" href = "#__codelineno-11-15" > < / a >
< a id = "__codelineno-11-16" name = "__codelineno-11-16" href = "#__codelineno-11-16" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 獲取左子節點的索引 */< / span >
< a id = "__codelineno-11-17" name = "__codelineno-11-17" href = "#__codelineno-11-17" > < / a > < span class = "w" > < / span > < span class = "kd" > private< / span > < span class = "w" > < / span > < span class = "kd" > fun< / span > < span class = "w" > < / span > < span class = "nf" > left< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "kt" > Int< / span > < span class = "p" > ):< / span > < span class = "w" > < / span > < span class = "kt" > Int< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-18" name = "__codelineno-11-18" href = "#__codelineno-11-18" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "m" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "m" > 1< / span >
< a id = "__codelineno-11-19" name = "__codelineno-11-19" href = "#__codelineno-11-19" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-20" name = "__codelineno-11-20" href = "#__codelineno-11-20" > < / a >
< a id = "__codelineno-11-21" name = "__codelineno-11-21" href = "#__codelineno-11-21" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 獲取右子節點的索引 */< / span >
< a id = "__codelineno-11-22" name = "__codelineno-11-22" href = "#__codelineno-11-22" > < / a > < span class = "w" > < / span > < span class = "kd" > private< / span > < span class = "w" > < / span > < span class = "kd" > fun< / span > < span class = "w" > < / span > < span class = "nf" > right< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "kt" > Int< / span > < span class = "p" > ):< / span > < span class = "w" > < / span > < span class = "kt" > Int< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-23" name = "__codelineno-11-23" href = "#__codelineno-11-23" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "m" > 2< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "m" > 2< / span >
< a id = "__codelineno-11-24" name = "__codelineno-11-24" href = "#__codelineno-11-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-25" name = "__codelineno-11-25" href = "#__codelineno-11-25" > < / a >
< a id = "__codelineno-11-26" name = "__codelineno-11-26" href = "#__codelineno-11-26" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 獲取父節點的索引 */< / span >
< a id = "__codelineno-11-27" name = "__codelineno-11-27" href = "#__codelineno-11-27" > < / a > < span class = "w" > < / span > < span class = "kd" > private< / span > < span class = "w" > < / span > < span class = "kd" > fun< / span > < span class = "w" > < / span > < span class = "nf" > parent< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "kt" > Int< / span > < span class = "p" > ):< / span > < span class = "w" > < / span > < span class = "kt" > Int< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-28" name = "__codelineno-11-28" href = "#__codelineno-11-28" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "m" > 2< / span > < span class = "w" > < / span > < span class = "c1" > // 向下整除< / span >
< a id = "__codelineno-11-29" name = "__codelineno-11-29" href = "#__codelineno-11-29" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-30" name = "__codelineno-11-30" href = "#__codelineno-11-30" > < / a >
< a id = "__codelineno-11-31" name = "__codelineno-11-31" href = "#__codelineno-11-31" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 交換元素 */< / span >
< a id = "__codelineno-11-32" name = "__codelineno-11-32" href = "#__codelineno-11-32" > < / a > < span class = "w" > < / span > < span class = "kd" > private< / span > < span class = "w" > < / span > < span class = "kd" > fun< / span > < span class = "w" > < / span > < span class = "nf" > swap< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "kt" > Int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "kt" > Int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-33" name = "__codelineno-11-33" href = "#__codelineno-11-33" > < / a > < span class = "w" > < / span > < span class = "kd" > val< / span > < span class = "w" > < / span > < span class = "nv" > temp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > maxHeap< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span >
< a id = "__codelineno-11-34" name = "__codelineno-11-34" href = "#__codelineno-11-34" > < / a > < span class = "w" > < / span > < span class = "n" > maxHeap< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > maxHeap< / span > < span class = "o" > [< / span > < span class = "n" > j< / span > < span class = "o" > ]< / span >
< a id = "__codelineno-11-35" name = "__codelineno-11-35" href = "#__codelineno-11-35" > < / a > < span class = "w" > < / span > < span class = "n" > maxHeap< / span > < span class = "o" > [< / span > < span class = "n" > j< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > temp< / span >
< a id = "__codelineno-11-36" name = "__codelineno-11-36" href = "#__codelineno-11-36" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-37" name = "__codelineno-11-37" href = "#__codelineno-11-37" > < / a >
< a id = "__codelineno-11-38" name = "__codelineno-11-38" href = "#__codelineno-11-38" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 獲取堆積大小 */< / span >
< a id = "__codelineno-11-39" name = "__codelineno-11-39" href = "#__codelineno-11-39" > < / a > < span class = "w" > < / span > < span class = "kd" > fun< / span > < span class = "w" > < / span > < span class = "nf" > size< / span > < span class = "p" > ():< / span > < span class = "w" > < / span > < span class = "kt" > Int< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-40" name = "__codelineno-11-40" href = "#__codelineno-11-40" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > maxHeap< / span > < span class = "p" > .< / span > < span class = "na" > size< / span >
< a id = "__codelineno-11-41" name = "__codelineno-11-41" href = "#__codelineno-11-41" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-42" name = "__codelineno-11-42" href = "#__codelineno-11-42" > < / a >
< a id = "__codelineno-11-43" name = "__codelineno-11-43" href = "#__codelineno-11-43" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 判斷堆積是否為空 */< / span >
< a id = "__codelineno-11-44" name = "__codelineno-11-44" href = "#__codelineno-11-44" > < / a > < span class = "w" > < / span > < span class = "kd" > fun< / span > < span class = "w" > < / span > < span class = "nf" > isEmpty< / span > < span class = "p" > ():< / span > < span class = "w" > < / span > < span class = "kt" > Boolean< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-45" name = "__codelineno-11-45" href = "#__codelineno-11-45" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 判斷堆積是否為空 */< / span >
< a id = "__codelineno-11-46" name = "__codelineno-11-46" href = "#__codelineno-11-46" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "m" > 0< / span >
< a id = "__codelineno-11-47" name = "__codelineno-11-47" href = "#__codelineno-11-47" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-48" name = "__codelineno-11-48" href = "#__codelineno-11-48" > < / a >
< a id = "__codelineno-11-49" name = "__codelineno-11-49" href = "#__codelineno-11-49" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 訪問堆積頂元素 */< / span >
< a id = "__codelineno-11-50" name = "__codelineno-11-50" href = "#__codelineno-11-50" > < / a > < span class = "w" > < / span > < span class = "kd" > fun< / span > < span class = "w" > < / span > < span class = "nf" > peek< / span > < span class = "p" > ():< / span > < span class = "w" > < / span > < span class = "kt" > Int< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-51" name = "__codelineno-11-51" href = "#__codelineno-11-51" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > maxHeap< / span > < span class = "o" > [< / span > < span class = "m" > 0< / span > < span class = "o" > ]< / span >
< a id = "__codelineno-11-52" name = "__codelineno-11-52" href = "#__codelineno-11-52" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-53" name = "__codelineno-11-53" href = "#__codelineno-11-53" > < / a >
< a id = "__codelineno-11-54" name = "__codelineno-11-54" href = "#__codelineno-11-54" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 元素入堆積 */< / span >
< a id = "__codelineno-11-55" name = "__codelineno-11-55" href = "#__codelineno-11-55" > < / a > < span class = "w" > < / span > < span class = "kd" > fun< / span > < span class = "w" > < / span > < span class = "nf" > push< / span > < span class = "p" > (< / span > < span class = "n" > _val< / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "kt" > Int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-56" name = "__codelineno-11-56" href = "#__codelineno-11-56" > < / a > < span class = "w" > < / span > < span class = "c1" > // 新增節點< / span >
< a id = "__codelineno-11-57" name = "__codelineno-11-57" href = "#__codelineno-11-57" > < / a > < span class = "w" > < / span > < span class = "n" > maxHeap< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "n" > _val< / span > < span class = "p" > )< / span >
< a id = "__codelineno-11-58" name = "__codelineno-11-58" href = "#__codelineno-11-58" > < / a > < span class = "w" > < / span > < span class = "c1" > // 從底至頂堆積化< / span >
< a id = "__codelineno-11-59" name = "__codelineno-11-59" href = "#__codelineno-11-59" > < / a > < span class = "w" > < / span > < span class = "n" > siftUp< / span > < span class = "p" > (< / span > < span class = "n" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-11-60" name = "__codelineno-11-60" href = "#__codelineno-11-60" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-61" name = "__codelineno-11-61" href = "#__codelineno-11-61" > < / a >
< a id = "__codelineno-11-62" name = "__codelineno-11-62" href = "#__codelineno-11-62" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 從節點 i 開始，從底至頂堆積化 */< / span >
< a id = "__codelineno-11-63" name = "__codelineno-11-63" href = "#__codelineno-11-63" > < / a > < span class = "w" > < / span > < span class = "kd" > private< / span > < span class = "w" > < / span > < span class = "kd" > fun< / span > < span class = "w" > < / span > < span class = "nf" > siftUp< / span > < span class = "p" > (< / span > < span class = "nb" > it< / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "kt" > Int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-64" name = "__codelineno-11-64" href = "#__codelineno-11-64" > < / a > < span class = "w" > < / span > < span class = "c1" > // Kotlin的函式參數不可變， < / span >
< a id = "__codelineno-11-65" name = "__codelineno-11-65" href = "#__codelineno-11-65" > < / a > < span class = "w" > < / span > < span class = "kd" > var< / span > < span class = "w" > < / span > < span class = "nv" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > it< / span >
< a id = "__codelineno-11-66" name = "__codelineno-11-66" href = "#__codelineno-11-66" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kc" > true< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-67" name = "__codelineno-11-67" href = "#__codelineno-11-67" > < / a > < span class = "w" > < / span > < span class = "c1" > // 獲取節點 i 的父節點< / span >
< a id = "__codelineno-11-68" name = "__codelineno-11-68" href = "#__codelineno-11-68" > < / a > < span class = "w" > < / span > < span class = "kd" > val< / span > < span class = "w" > < / span > < span class = "nv" > p< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > parent< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > )< / span >
< a id = "__codelineno-11-69" name = "__codelineno-11-69" href = "#__codelineno-11-69" > < / a > < span class = "w" > < / span > < span class = "c1" > // 當“越過根節點”或“節點無須修復”時，結束堆積化< / span >
< a id = "__codelineno-11-70" name = "__codelineno-11-70" href = "#__codelineno-11-70" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > p< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "m" > 0< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "n" > maxHeap< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > maxHeap< / span > < span class = "o" > [< / span > < span class = "n" > p< / span > < span class = "o" > ]< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > break< / span >
< a id = "__codelineno-11-71" name = "__codelineno-11-71" href = "#__codelineno-11-71" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交換兩節點< / span >
< a id = "__codelineno-11-72" name = "__codelineno-11-72" href = "#__codelineno-11-72" > < / a > < span class = "w" > < / span > < span class = "n" > swap< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > p< / span > < span class = "p" > )< / span >
< a id = "__codelineno-11-73" name = "__codelineno-11-73" href = "#__codelineno-11-73" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈向上堆積化< / span >
< a id = "__codelineno-11-74" name = "__codelineno-11-74" href = "#__codelineno-11-74" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > p< / span >
< a id = "__codelineno-11-75" name = "__codelineno-11-75" href = "#__codelineno-11-75" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-76" name = "__codelineno-11-76" href = "#__codelineno-11-76" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-77" name = "__codelineno-11-77" href = "#__codelineno-11-77" > < / a >
< a id = "__codelineno-11-78" name = "__codelineno-11-78" href = "#__codelineno-11-78" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 元素出堆積 */< / span >
< a id = "__codelineno-11-79" name = "__codelineno-11-79" href = "#__codelineno-11-79" > < / a > < span class = "w" > < / span > < span class = "kd" > fun< / span > < span class = "w" > < / span > < span class = "nf" > pop< / span > < span class = "p" > ():< / span > < span class = "w" > < / span > < span class = "kt" > Int< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-80" name = "__codelineno-11-80" href = "#__codelineno-11-80" > < / a > < span class = "w" > < / span > < span class = "c1" > // 判空處理< / span >
< a id = "__codelineno-11-81" name = "__codelineno-11-81" href = "#__codelineno-11-81" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > isEmpty< / span > < span class = "p" > ())< / span > < span class = "w" > < / span > < span class = "k" > throw< / span > < span class = "w" > < / span > < span class = "n" > IndexOutOfBoundsException< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-11-82" name = "__codelineno-11-82" href = "#__codelineno-11-82" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交換根節點與最右葉節點（交換首元素與尾元素）< / span >
< a id = "__codelineno-11-83" name = "__codelineno-11-83" href = "#__codelineno-11-83" > < / a > < span class = "w" > < / span > < span class = "n" > swap< / span > < span class = "p" > (< / span > < span class = "m" > 0< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-11-84" name = "__codelineno-11-84" href = "#__codelineno-11-84" > < / a > < span class = "w" > < / span > < span class = "c1" > // 刪除節點< / span >
< a id = "__codelineno-11-85" name = "__codelineno-11-85" href = "#__codelineno-11-85" > < / a > < span class = "w" > < / span > < span class = "kd" > val< / span > < span class = "w" > < / span > < span class = "nv" > _val< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > maxHeap< / span > < span class = "p" > .< / span > < span class = "na" > removeAt< / span > < span class = "p" > (< / span > < span class = "n" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-11-86" name = "__codelineno-11-86" href = "#__codelineno-11-86" > < / a > < span class = "w" > < / span > < span class = "c1" > // 從頂至底堆積化< / span >
< a id = "__codelineno-11-87" name = "__codelineno-11-87" href = "#__codelineno-11-87" > < / a > < span class = "w" > < / span > < span class = "n" > siftDown< / span > < span class = "p" > (< / span > < span class = "m" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-11-88" name = "__codelineno-11-88" href = "#__codelineno-11-88" > < / a > < span class = "w" > < / span > < span class = "c1" > // 返回堆積頂元素< / span >
< a id = "__codelineno-11-89" name = "__codelineno-11-89" href = "#__codelineno-11-89" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > _val< / span >
< a id = "__codelineno-11-90" name = "__codelineno-11-90" href = "#__codelineno-11-90" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-91" name = "__codelineno-11-91" href = "#__codelineno-11-91" > < / a >
< a id = "__codelineno-11-92" name = "__codelineno-11-92" href = "#__codelineno-11-92" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 從節點 i 開始，從頂至底堆積化 */< / span >
< a id = "__codelineno-11-93" name = "__codelineno-11-93" href = "#__codelineno-11-93" > < / a > < span class = "w" > < / span > < span class = "kd" > private< / span > < span class = "w" > < / span > < span class = "kd" > fun< / span > < span class = "w" > < / span > < span class = "nf" > siftDown< / span > < span class = "p" > (< / span > < span class = "nb" > it< / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "kt" > Int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-94" name = "__codelineno-11-94" href = "#__codelineno-11-94" > < / a > < span class = "w" > < / span > < span class = "c1" > // Kotlin的函式參數不可變， < / span >
< a id = "__codelineno-11-95" name = "__codelineno-11-95" href = "#__codelineno-11-95" > < / a > < span class = "w" > < / span > < span class = "kd" > var< / span > < span class = "w" > < / span > < span class = "nv" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > it< / span >
< a id = "__codelineno-11-96" name = "__codelineno-11-96" href = "#__codelineno-11-96" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kc" > true< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-97" name = "__codelineno-11-97" href = "#__codelineno-11-97" > < / a > < span class = "w" > < / span > < span class = "c1" > // 判斷節點 i, l, r 中值最大的節點，記為 ma< / span >
< a id = "__codelineno-11-98" name = "__codelineno-11-98" href = "#__codelineno-11-98" > < / a > < span class = "w" > < / span > < span class = "kd" > val< / span > < span class = "w" > < / span > < span class = "nv" > l< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > )< / span >
< a id = "__codelineno-11-99" name = "__codelineno-11-99" href = "#__codelineno-11-99" > < / a > < span class = "w" > < / span > < span class = "kd" > val< / span > < span class = "w" > < / span > < span class = "nv" > r< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > right< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > )< / span >
< a id = "__codelineno-11-100" name = "__codelineno-11-100" href = "#__codelineno-11-100" > < / a > < span class = "w" > < / span > < span class = "kd" > var< / span > < span class = "w" > < / span > < span class = "nv" > ma< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > i< / span >
< a id = "__codelineno-11-101" name = "__codelineno-11-101" href = "#__codelineno-11-101" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > l< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "n" > maxHeap< / span > < span class = "o" > [< / span > < span class = "n" > l< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > maxHeap< / span > < span class = "o" > [< / span > < span class = "n" > ma< / span > < span class = "o" > ]< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "n" > ma< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > l< / span >
< a id = "__codelineno-11-102" name = "__codelineno-11-102" href = "#__codelineno-11-102" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > r< / span > < span class = "w" > < / span > < span class = "o" > < < / span > < span class = "w" > < / span > < span class = "n" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > & & < / span > < span class = "w" > < / span > < span class = "n" > maxHeap< / span > < span class = "o" > [< / span > < span class = "n" > r< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > maxHeap< / span > < span class = "o" > [< / span > < span class = "n" > ma< / span > < span class = "o" > ]< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "n" > ma< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > r< / span >
< a id = "__codelineno-11-103" name = "__codelineno-11-103" href = "#__codelineno-11-103" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若節點 i 最大或索引 l, r 越界，則無須繼續堆積化，跳出< / span >
< a id = "__codelineno-11-104" name = "__codelineno-11-104" href = "#__codelineno-11-104" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > ma< / span > < span class = "w" > < / span > < span class = "o" > ==< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > break< / span >
< a id = "__codelineno-11-105" name = "__codelineno-11-105" href = "#__codelineno-11-105" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交換兩節點< / span >
< a id = "__codelineno-11-106" name = "__codelineno-11-106" href = "#__codelineno-11-106" > < / a > < span class = "w" > < / span > < span class = "n" > swap< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > ma< / span > < span class = "p" > )< / span >
< a id = "__codelineno-11-107" name = "__codelineno-11-107" href = "#__codelineno-11-107" > < / a > < span class = "w" > < / span > < span class = "c1" > // 迴圈向下堆積化< / span >
< a id = "__codelineno-11-108" name = "__codelineno-11-108" href = "#__codelineno-11-108" > < / a > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > ma< / span >
< a id = "__codelineno-11-109" name = "__codelineno-11-109" href = "#__codelineno-11-109" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-110" name = "__codelineno-11-110" href = "#__codelineno-11-110" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-111" name = "__codelineno-11-111" href = "#__codelineno-11-111" > < / a >
< a id = "__codelineno-11-112" name = "__codelineno-11-112" href = "#__codelineno-11-112" > < / a > < span class = "w" > < / span > < span class = "cm" > /* 列印堆積（二元樹） */< / span >
< a id = "__codelineno-11-113" name = "__codelineno-11-113" href = "#__codelineno-11-113" > < / a > < span class = "w" > < / span > < span class = "kd" > fun< / span > < span class = "w" > < / span > < span class = "nf" > print< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-11-114" name = "__codelineno-11-114" href = "#__codelineno-11-114" > < / a > < span class = "w" > < / span > < span class = "kd" > val< / span > < span class = "w" > < / span > < span class = "nv" > queue< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > PriorityQueue< / span > < span class = "w" > < / span > < span class = "p" > {< / span > < span class = "w" > < / span > < span class = "n" > a< / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "kt" > Int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > b< / span > < span class = "p" > :< / span > < span class = "w" > < / span > < span class = "kt" > Int< / span > < span class = "w" > < / span > < span class = "o" > -> < / span > < span class = "w" > < / span > < span class = "n" > b< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > a< / span > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-115" name = "__codelineno-11-115" href = "#__codelineno-11-115" > < / a > < span class = "w" > < / span > < span class = "n" > queue< / span > < span class = "p" > .< / span > < span class = "na" > addAll< / span > < span class = "p" > (< / span > < span class = "n" > maxHeap< / span > < span class = "p" > )< / span >
< a id = "__codelineno-11-116" name = "__codelineno-11-116" href = "#__codelineno-11-116" > < / a > < span class = "w" > < / span > < span class = "n" > printHeap< / span > < span class = "p" > (< / span > < span class = "n" > queue< / span > < span class = "p" > )< / span >
< a id = "__codelineno-11-117" name = "__codelineno-11-117" href = "#__codelineno-11-117" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-118" name = "__codelineno-11-118" href = "#__codelineno-11-118" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.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" > MaxHeap< / 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" > __init__< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > my_heap.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-13-1" name = "__codelineno-13-1" href = "#__codelineno-13-1" > < / a > < span class = "c1" > // 建構子，根據輸入串列建堆積< / span >
< a id = "__codelineno-13-2" name = "__codelineno-13-2" href = "#__codelineno-13-2" > < / a > < span class = "k" > fn< / span > < span class = "w" > < / span > < span class = "n" > init< / span > < span class = "p" > (< / span > < span class = "n" > self< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "o" > *< / span > < span class = "n" > Self< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > allocator< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "n" > std< / span > < span class = "p" > .< / span > < span class = "n" > mem< / span > < span class = "p" > .< / span > < span class = "n" > Allocator< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "kr" > const< / span > < span class = "w" > < / span > < span class = "n" > T< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > !< / span > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-13-3" name = "__codelineno-13-3" href = "#__codelineno-13-3" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > self< / span > < span class = "p" > .< / span > < span class = "n" > max_heap< / 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 = "k" > return< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-13-4" name = "__codelineno-13-4" href = "#__codelineno-13-4" > < / a > < span class = "w" > < / span > < span class = "n" > self< / span > < span class = "p" > .< / span > < span class = "n" > max_heap< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > std< / span > < span class = "p" > .< / span > < span class = "n" > ArrayList< / span > < span class = "p" > (< / span > < span class = "n" > T< / span > < span class = "p" > ).< / span > < span class = "n" > init< / span > < span class = "p" > (< / span > < span class = "n" > allocator< / span > < span class = "p" > );< / span >
< a id = "__codelineno-13-5" name = "__codelineno-13-5" href = "#__codelineno-13-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 將串列元素原封不動新增進堆積< / span >
< a id = "__codelineno-13-6" name = "__codelineno-13-6" href = "#__codelineno-13-6" > < / a > < span class = "w" > < / span > < span class = "k" > try< / span > < span class = "w" > < / span > < span class = "n" > self< / span > < span class = "p" > .< / span > < span class = "n" > max_heap< / span > < span class = "p" > .< / span > < span class = "o" > ?< / span > < span class = "p" > .< / span > < span class = "n" > appendSlice< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > );< / span >
< a id = "__codelineno-13-7" name = "__codelineno-13-7" href = "#__codelineno-13-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 堆積化除葉節點以外的其他所有節點< / span >
< a id = "__codelineno-13-8" name = "__codelineno-13-8" href = "#__codelineno-13-8" > < / a > < span class = "w" > < / span > < span class = "kr" > var< / span > < span class = "w" > < / span > < span class = "n" > i< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > usize< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > parent< / span > < span class = "p" > (< / span > < span class = "n" > self< / span > < span class = "p" > .< / span > < span class = "n" > size< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-13-9" name = "__codelineno-13-9" href = "#__codelineno-13-9" > < / a > < span class = "w" > < / span > < span class = "k" > while< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > -=< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-13-10" name = "__codelineno-13-10" href = "#__codelineno-13-10" > < / a > < span class = "w" > < / span > < span class = "k" > try< / span > < span class = "w" > < / span > < span class = "n" > self< / span > < span class = "p" > .< / span > < span class = "n" > siftDown< / span > < span class = "p" > (< / span > < span class = "n" > i< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-13-11" name = "__codelineno-13-11" href = "#__codelineno-13-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-13-12" name = "__codelineno-13-12" href = "#__codelineno-13-12" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< details class = "pythontutor" >
< summary > 視覺化執行< / summary >
< p > < div style = "height: 549px; width: 100%;" > < iframe class = "pythontutor-iframe" src = "https://pythontutor.com/iframe-embed.html#code=class%20MaxHeap%3A%0A%20%20%20%20%22%22%22%E5%A4%A7%E9%A0%82%E5%A0%86%E7%A9%8D%22%22%22%0A%0A%20%20%20%20def%20__init__%28self%2C%20nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%BB%BA%E6%A7%8B%E5%AD%90%EF%BC%8C%E6%A0%B9%E6%93%9A%E8%BC%B8%E5%85%A5%E4%B8%B2%E5%88%97%E5%BB%BA%E5%A0%86%E7%A9%8D%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E5%B0%87%E4%B8%B2%E5%88%97%E5%85%83%E7%B4%A0%E5%8E%9F%E5%B0%81%E4%B8%8D%E5%8B%95%E6%96%B0%E5%A2%9E%E9%80%B2%E5%A0%86%E7%A9%8D%0A%20%20%20%20%20%20%20%20self.max_heap%20%3D%20nums%0A%20%20%20%20%20%20%20%20%23%20%E5%A0%86%E7%A9%8D%E5%8C%96%E9%99%A4%E8%91%89%E7%AF%80%E9%BB%9E%E4%BB%A5%E5%A4%96%E7%9A%84%E5%85%B6%E4%BB%96%E6%89%80%E6%9C%89%E7%AF%80%E9%BB%9E%0A%20%20%20%20%20%20%20%20for%20i%20in%20range%28self.parent%28self.size%28%29%20-%201%29%2C%20-1%2C%20-1%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20self.sift_down%28i%29%0A%0A%20%20%20%20def%20left%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E7%8D%B2%E5%8F%96%E5%B7%A6%E5%AD%90%E7%AF%80%E9%BB%9E%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20%2A%20i%20%2B%201%0A%0A%20%20%20%20def%20right%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E7%8D%B2%E5%8F%96%E5%8F%B3%E5%AD%90%E7%AF%80%E9%BB%9E%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20%2A%20i%20%2B%202%0A%0A%20%20%20%20def%20parent%28self%2C%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E7%8D%B2%E5%8F%96%E7%88%B6%E7%AF%80%E9%BB%9E%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%20%28i%20-%201%29%20//%202%20%20%23%20%E5%90%91%E4%B8%8B%E6%95%B4%E9%99%A4%0A%0A%20%20%20%20def%20swap%28self%2C%20i%3A%20int%2C%20j%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E4%BA%A4%E6%8F%9B%E5%85%83%E7%B4%A0%22%22%22%0A%20%20%20%20%20%20%20%20self.max_heap%5Bi%5D%2C%20self.max_heap%5Bj%5D%20%3D%20self.max_heap%5Bj%5D%2C%20self.max_heap%5Bi%5D%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E7%8D%B2%E5%8F%96%E5%A0%86%E7%A9%8D%E5%A4%A7%E5%B0%8F%22%22%22%0A%20%20%20%20%20%20%20%20return%20len%28self.max_heap%29%0A%0A%20%20%20%20def%20sift_down%28self%2C%20i%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%BE%9E%E7%AF%80%E9%BB%9E%20i%20%E9%96%8B%E5%A7%8B%EF%BC%8C%E5%BE%9E%E9%A0%82%E8%87%B3%E5%BA%95%E5%A0%86%E7%A9%8D%E5%8C%96%22%22%22%0A%20%20%20%20%20%20%20%20while%20True%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E5%88%A4%E6%96%B7%E7%AF%80%E9%BB%9E%20i%2C%20l%2C%20r%20%E4%B8%AD%E5%80%BC%E6%9C%80%E5%A4%A7%E7%9A%84%E7%AF%80%E9%BB%9E%EF%BC%8C%E8%A8%98%E7%82%BA%20ma%0A%20%20%20%20%20%20%20%20%20%20%20%20l%2C%20r%2C%20ma%20%3D%20self.left%28i%29%2C%20self.right%28i%29%2C%20i%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20l%20%3C%20self.size%28%29%20and%20self.max_heap%5Bl%5D%20%3E%20self.max_heap%5Bma%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20ma%20%3D%20l%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20r%20%3C%20self.size%28%29%20and%20self.max_heap%5Br%5D%20%3E%20self.max_heap%5Bma%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20ma%20%3D%20r%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E8%8B%A5%E7%AF%80%E9%BB%9E%20i%20%E6%9C%80%E5%A4%A7%E6%88%96%E7%B4%A2%E5%BC%95%20l%2C%20r%20%E8%B6%8A%E7%95%8C%EF%BC%8C%E5%89%87%E7%84%A1%E9%A0%88%E7%B9%BC%E7%BA%8C%E5%A0%86%E7%A9%8D%E5%8C%96%EF%BC%8C%E8%B7%B3%E5%87%BA%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20ma%20%3D%3D%20i%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E4%BA%A4%E6%8F%9B%E5%85%A9%E7%AF%80%E9%BB%9E%0A%20%20%20%20%20%20%20%20%20%20%20%20self.swap%28i%2C%20ma%29%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E8%BF%B4%E5%9C%88%E5%90%91%E4%B8%8B%E5%A0%86%E7%A9%8D%E5%8C%96%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%3D%20ma%0A%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
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< / details >
< h2 id = "823" > 8.2.3 複雜度分析< a class = "headerlink" href = "#823" title = "Permanent link" > ¶ < / a > < / h2 >
< p > 下面，我們來嘗試推算第二種建堆積方法的時間複雜度。< / p >
< ul >
< li > 假設完全二元樹的節點數量為 < span class = "arithmatex" > \(n\)< / span > ，則葉節點數量為 < span class = "arithmatex" > \((n + 1) / 2\)< / span > ，其中 < span class = "arithmatex" > \(/\)< / span > 為向下整除。因此需要堆積化的節點數量為 < span class = "arithmatex" > \((n - 1) / 2\)< / span > 。< / li >
< li > 在從頂至底堆積化的過程中，每個節點最多堆積化到葉節點，因此最大迭代次數為二元樹高度 < span class = "arithmatex" > \(\log n\)< / span > 。< / li >
< / ul >
< p > 將上述兩者相乘，可得到建堆積過程的時間複雜度為 < span class = "arithmatex" > \(O(n \log n)\)< / span > 。< strong > 但這個估算結果並不準確，因為我們沒有考慮到二元樹底層節點數量遠多於頂層節點的性質< / strong > 。< / p >
< p > 接下來我們來進行更為準確的計算。為了降低計算難度，假設給定一個節點數量為 < span class = "arithmatex" > \(n\)< / span > 、高度為 < span class = "arithmatex" > \(h\)< / span > 的“完美二元樹”，該假設不會影響計算結果的正確性。< / p >
< p > < a class = "glightbox" href = "../build_heap.assets/heapify_operations_count.png" data-type = "image" data-width = "100%" data-height = "auto" data-desc-position = "bottom" > < img alt = "完美二元樹的各層節點數量" class = "animation-figure" src = "../build_heap.assets/heapify_operations_count.png" / > < / a > < / p >
< p align = "center" > 圖 8-5 完美二元樹的各層節點數量 < / p >
< p > 如圖 8-5 所示，節點“從頂至底堆積化”的最大迭代次數等於該節點到葉節點的距離，而該距離正是“節點高度”。因此，我們可以對各層的“節點數量 < span class = "arithmatex" > \(\times\)< / span > 節點高度”求和，< strong > 得到所有節點的堆積化迭代次數的總和< / strong > 。< / p >
< div class = "arithmatex" > \[
T(h) = 2^0h + 2^1(h-1) + 2^2(h-2) + \dots + 2^{(h-1)}\times1
\]< / div >
< p > 化簡上式需要藉助中學的數列知識，先將 < span class = "arithmatex" > \(T(h)\)< / span > 乘以 < span class = "arithmatex" > \(2\)< / span > ，得到：< / p >
< div class = "arithmatex" > \[
\begin{aligned}
T(h) & = 2^0h + 2^1(h-1) + 2^2(h-2) + \dots + 2^{h-1}\times1 \newline
2 T(h) & = 2^1h + 2^2(h-1) + 2^3(h-2) + \dots + 2^{h}\times1 \newline
\end{aligned}
\]< / div >
< p > 使用錯位相減法，用下式 < span class = "arithmatex" > \(2 T(h)\)< / span > 減去上式 < span class = "arithmatex" > \(T(h)\)< / span > ，可得：< / p >
< div class = "arithmatex" > \[
2T(h) - T(h) = T(h) = -2^0h + 2^1 + 2^2 + \dots + 2^{h-1} + 2^h
\]< / div >
< p > 觀察上式，發現 < span class = "arithmatex" > \(T(h)\)< / span > 是一個等比數列，可直接使用求和公式，得到時間複雜度為：< / p >
< div class = "arithmatex" > \[
\begin{aligned}
T(h) & = 2 \frac{1 - 2^h}{1 - 2} - h \newline
& = 2^{h+1} - h - 2 \newline
& = O(2^h)
\end{aligned}
\]< / div >
< p > 進一步，高度為 < span class = "arithmatex" > \(h\)< / span > 的完美二元樹的節點數量為 < span class = "arithmatex" > \(n = 2^{h+1} - 1\)< / span > ，易得複雜度為 < span class = "arithmatex" > \(O(2^h) = O(n)\)< / span > 。以上推算表明，< strong > 輸入串列並建堆積的時間複雜度為 < span class = "arithmatex" > \(O(n)\)< / span > ，非常高效< / strong > 。< / p >
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