diff --git a/codes/typescript/chapter_heap/my_heap.ts b/codes/typescript/chapter_heap/my_heap.ts new file mode 100644 index 00000000..c80abdcc --- /dev/null +++ b/codes/typescript/chapter_heap/my_heap.ts @@ -0,0 +1,160 @@ +/** + * File: my_heap.js + * Created Time: 2023-02-07 + * Author: Justin (xiefahit@gmail.com) + */ + +import { printHeap } from "../module/PrintUtil"; + +/* 最大堆类 */ +class MaxHeap { + private maxHeap: number[]; + /* 构造函数,建立空堆或根据输入列表建堆 */ + constructor(nums?: number[]) { + // 将列表元素原封不动添加进堆 + this.maxHeap = nums === undefined ? [] : [...nums]; + // 堆化除叶结点以外的其他所有结点 + for (let i = this.parent(this.size() - 1); i >= 0; i--) { + this.siftDown(i); + } + } + + /* 获取左子结点索引 */ + private left(i: number): number { + return 2 * i + 1; + } + + /* 获取右子结点索引 */ + private right(i: number): number { + return 2 * i + 2; + } + + /* 获取父结点索引 */ + private parent(i: number): number { + return Math.floor((i - 1) / 2); // 向下整除 + } + + /* 交换元素 */ + private swap(i: number, j: number): void { + const a = this.maxHeap[i], + b = this.maxHeap[j], + tmp = a; + this.maxHeap[i] = b; + this.maxHeap[j] = tmp; + } + + /* 获取堆大小 */ + public size(): number { + return this.maxHeap.length; + } + + /* 判断堆是否为空 */ + public isEmpty(): boolean { + return this.size() === 0; + } + + /* 访问堆顶元素 */ + public peek(): number { + return this.maxHeap[0]; + } + + /* 元素入堆 */ + public push(val: number): void { + // 添加结点 + this.maxHeap.push(val); + // 从底至顶堆化 + this.siftUp(this.size() - 1); + } + + /* 从结点 i 开始,从底至顶堆化 */ + private siftUp(i: number): void { + while (true) { + // 获取结点 i 的父结点 + const p = this.parent(i); + // 当“越过根结点”或“结点无需修复”时,结束堆化 + if (p < 0 || this.maxHeap[i] <= this.maxHeap[p]) break; + // 交换两结点 + this.swap(i, p); + // 循环向上堆化 + i = p; + } + } + + /* 元素出堆 */ + public poll(): number { + // 判空处理 + if (this.isEmpty()) throw new RangeError("Heap is empty."); + // 交换根结点与最右叶结点(即交换首元素与尾元素) + this.swap(0, this.size() - 1); + // 删除结点 + const val = this.maxHeap.pop(); + // 从顶至底堆化 + this.siftDown(0); + // 返回堆顶元素 + return val; + } + + /* 从结点 i 开始,从顶至底堆化 */ + private siftDown(i: number): void { + while (true) { + // 判断结点 i, l, r 中值最大的结点,记为 ma + const l = this.left(i), r = this.right(i); + let ma = i; + if (l < this.size() && this.maxHeap[l] > this.maxHeap[ma]) ma = l; + if (r < this.size() && this.maxHeap[r] > this.maxHeap[ma]) ma = r; + // 若结点 i 最大或索引 l, r 越界,则无需继续堆化,跳出 + if (ma == i) break; + // 交换两结点 + this.swap(i, ma); + // 循环向下堆化 + i = ma; + } + } + + /* 打印堆(二叉树) */ + public print(): void { + printHeap(this.maxHeap); + } +} + + +function testPush(maxHeap: MaxHeap, val: number): void { + maxHeap.push(val); // 元素入堆 + console.log(`\n添加元素 ${val} 后`); + maxHeap.print(); +} + +function testPoll(maxHeap: MaxHeap): void { + const val = maxHeap.poll(); // 堆顶元素出堆 + console.log(`\n出堆元素为 ${val}`); + maxHeap.print(); +} + +/* Driver Code */ +/* 初始化大顶堆 */ +const maxHeap = new MaxHeap([9, 8, 6, 6, 7, 5, 2, 1, 4, 3, 6, 2]); +console.log("\n输入列表并建堆后"); +maxHeap.print(); + +/* 获取堆顶元素 */ +let peek = maxHeap.peek(); +console.log(`\n堆顶元素为 ${peek}`); + +/* 元素入堆 */ +const val = 7; +maxHeap.push(val); +console.log(`\n元素 ${val} 入堆后`); +maxHeap.print(); + +/* 堆顶元素出堆 */ +peek = maxHeap.poll(); +console.log(`\n堆顶元素 ${peek} 出堆后`); +maxHeap.print(); + +/* 获取堆大小 */ +const size = maxHeap.size(); +console.log(`\n堆元素数量为 ${size}`); + +/* 判断堆是否为空 */ +const isEmpty = maxHeap.isEmpty(); +console.log(`\n堆是否为空 ${isEmpty}`); diff --git a/codes/typescript/module/PrintUtil.ts b/codes/typescript/module/PrintUtil.ts index 8da04063..f8bb6c12 100644 --- a/codes/typescript/module/PrintUtil.ts +++ b/codes/typescript/module/PrintUtil.ts @@ -4,8 +4,8 @@ * Author: Justin (xiefahit@gmail.com) */ -import { ListNode } from './ListNode'; -import { TreeNode } from './TreeNode'; +import { ListNode } from "./ListNode"; +import { TreeNode, arrToTree } from "./TreeNode"; /** * Print a linked list @@ -93,4 +93,20 @@ function showTrunks(p: Trunk | null) { // restart the vscode } -export { printLinkedList, printTree }; +/** + * Print a heap + * @param arr + */ +function printHeap(arr: number[]): void { + console.log("堆的数组表示:"); + console.log(arr); + console.log("堆的树状表示:"); + const root = arrToTree(arr); + printTree(root); +} + +export { + printLinkedList, + printTree, + printHeap +}; diff --git a/docs/chapter_heap/heap.md b/docs/chapter_heap/heap.md index 4fa839a1..86496156 100644 --- a/docs/chapter_heap/heap.md +++ b/docs/chapter_heap/heap.md @@ -214,7 +214,7 @@ comments: true === "TypeScript" ```typescript title="heap.ts" - + // TypeScript 未提供内置堆 Heap 类 ``` === "C" @@ -361,7 +361,31 @@ comments: true === "TypeScript" ```typescript title="my_heap.ts" + private maxHeap: number[]; + /* 构造函数,建立空堆或根据输入列表建堆 */ + constructor(nums?: number[]) { + // 将列表元素原封不动添加进堆 + this.maxHeap = nums === undefined ? [] : [...nums]; + // 堆化除叶结点以外的其他所有结点 + for (let i = this.parent(this.size() - 1); i >= 0; i--) { + this.siftDown(i); + } + } + /* 获取左子结点索引 */ + private left(i: number): number { + return 2 * i + 1; + } + + /* 获取右子结点索引 */ + private right(i: number): number { + return 2 * i + 2; + } + + /* 获取父结点索引 */ + private parent(i: number): number { + return Math.floor((i - 1) / 2); // 向下整除 + } ``` === "C" @@ -454,7 +478,10 @@ comments: true === "TypeScript" ```typescript title="my_heap.ts" - + /* 访问堆顶元素 */ + public peek(): number { + return this.maxHeap[0]; + } ``` === "C" @@ -608,7 +635,27 @@ comments: true === "TypeScript" ```typescript title="my_heap.ts" + /* 元素入堆 */ + public push(val: number): void { + // 添加结点 + this.maxHeap.push(val); + // 从底至顶堆化 + this.siftUp(this.size() - 1); + } + /* 从结点 i 开始,从底至顶堆化 */ + private siftUp(i: number): void { + while (true) { + // 获取结点 i 的父结点 + const p = this.parent(i); + // 当“越过根结点”或“结点无需修复”时,结束堆化 + if (p < 0 || this.maxHeap[i] <= this.maxHeap[p]) break; + // 交换两结点 + this.swap(i, p); + // 循环向上堆化 + i = p; + } + } ``` === "C" @@ -836,7 +883,36 @@ comments: true === "TypeScript" ```typescript title="my_heap.ts" + /* 元素出堆 */ + public poll(): number { + // 判空处理 + if (this.isEmpty()) throw new RangeError("Heap is empty."); + // 交换根结点与最右叶结点(即交换首元素与尾元素) + this.swap(0, this.size() - 1); + // 删除结点 + const val = this.maxHeap.pop(); + // 从顶至底堆化 + this.siftDown(0); + // 返回堆顶元素 + return val; + } + /* 从结点 i 开始,从顶至底堆化 */ + private siftDown(i: number): void { + while (true) { + // 判断结点 i, l, r 中值最大的结点,记为 ma + const l = this.left(i), r = this.right(i); + let ma = i; + if (l < this.size() && this.maxHeap[l] > this.maxHeap[ma]) ma = l; + if (r < this.size() && this.maxHeap[r] > this.maxHeap[ma]) ma = r; + // 若结点 i 最大或索引 l, r 越界,则无需继续堆化,跳出 + if (ma == i) break; + // 交换两结点 + this.swap(i, ma); + // 循环向下堆化 + i = ma; + } + } ``` === "C" @@ -966,7 +1042,15 @@ comments: true === "TypeScript" ```typescript title="my_heap.ts" - + /* 构造函数,建立空堆或根据输入列表建堆 */ + constructor(nums?: number[]) { + // 将列表元素原封不动添加进堆 + this.maxHeap = nums === undefined ? [] : [...nums]; + // 堆化除叶结点以外的其他所有结点 + for (let i = this.parent(this.size() - 1); i >= 0; i--) { + this.siftDown(i); + } + } ``` === "C"