ES6的JavaScript数据结构实现之二叉堆和堆排序

目的：ES6标准下的JS数据结构的一些实现代码。（作为记录和启发）

内容：二叉堆和堆排序。（未完成，待继续）

所有源码在我的Github上（如果觉得不错记得给星鼓励我哦）：ES6的JavaScript数据结构实现之二叉堆和堆排序

一、基础数据结构

1、二叉堆（最小堆和最大堆；插入值（保持最小堆或最大堆结构）；找到最大值或者最小值；移除最小堆的最小值（堆的根节点））

基本概念：二叉堆是一种特殊的二叉树，其有两个特性：结构特性和堆特性。结构特性是指它是一颗完全的二叉树（树的每一层都有左侧和右侧子节点（除了最后一层的叶节点），并且最后一层的叶节点尽可能都是左侧子节点）。堆特性是指二叉堆不是最小堆就是最大堆（最小堆可以快速导出树的最小值，最大堆可以快速导出树的最大值），所有的节点都大于等于（最大堆）或者小于等于（最小堆）每个它的子节点。

1.1 最小堆

const Compare = {
  LESS_THAN: -1,
  BIGGER_THAN: 1,
  EQUALS: 0
};

function defaultCompare(a, b) {
  if (a === b) {
    return Compare.EQUALS;
  }
  return a < b ? Compare.LESS_THAN : Compare.BIGGER_THAN;
}

function swap(array, a, b) {
  /* const temp = array[a];
  array[a] = array[b];
  array[b] = temp; */
  [array[a], array[b]] = [array[b], array[a]];
}
function reverseCompare(compareFn) {
  return (a, b) => compareFn(b, a);
}
class MinHeap {
  constructor(compareFn = defaultCompare) {
    this.compareFn = compareFn;
    this.heap = [];
  }
  getLeftIndex(index) {
    return 2 * index + 1;
  }
  getRightIndex(index) {
    return 2 * index + 2;
  }
  getParentIndex(index) {
    if (index === 0) {
      return undefined;
    }
    return Math.floor((index - 1) / 2);
  }

  size() {
    return this.heap.length;
  }

  isEmpty() {
    return this.size() <= 0;
  }

  clear() {
    this.heap = [];
  }
  findMinimum() {
    return this.isEmpty() ? undefined : this.heap[0];
  }
  insert(value) {
    if(value != null) {
      this.heap.push(value);
      const index = this.heap.length - 1;
      this.siftUp(index);
      return true; 
    }
    return false;
  }
  siftUp(index) {
    let parent = this.getParentIndex(index);
    while (
      index > 0 
      && this.compareFn(this.heap[parent], this.heap[index]) === Compare.BIGGER_THAN 
      ) {
      swap (this.heap, parent, index );
      index = parent;
      parent = this.getParentIndex(index);
    }
  }
  extract() {
    if (this.isEmpty()) {
      return undefined;
    }
    if (this.size() == 1) {
      return this.heap.shift();
    }
    const removedValue = this.heap[0];
    this.heap[0] = this.heap.pop();
    this.siftDown(0);
    return removedValue;
  }
  siftDown(index) {
    let element = index;
    const left = this.getLeftIndex(index);
    const right = this.getRightIndex(index);
    const size = this.size();
    if (
      left < size 
      && this.compareFn(this.heap[element], this.heap[left]) === Compare.BIGGER_THAN
      ) {
      element = left;
    } else if (
      right < size
      && this.compareFn(this.heap[element], this.heap[right] === Compare.BIGGER_THAN)
      ) {
      element = right;
    }
    if(index !== element) {
      swap(this.heap, index, element);
      this.siftDown(element); 
    }
  }
  heapify(array) {
    if (array) {
      this.heap = array;
    }
    const maxIndex = Math.floor(this.size() / 2) - 1;
    for (let i = 0; i <= maxIndex; i++) {
      this.siftDown(i);
    }
    return this.heap;
  }

  getAsArray() {
    return this.heap;
  }


}

const heap = new MinHeap();
heap.insert(2);
heap.insert(3);
heap.insert(4);
heap.insert(5);
console.log(heap);
heap.insert(1);
console.log(heap);
console.log(heap.findMinimum());
heap.clear();
const heap1 = new MinHeap();
for (let i = 1; i < 10; i++) {
  heap.insert(i);
}
console.log(heap);
console.log(heap.extract());
console.log(heap);

 

1.2 最大堆

把最小堆中的比较函数修改为相反的就行了，即把最小堆中的所有大于的比较换成小于的比较。

class MaxHeap extends MinHeap {
  constructor(compareFn = defaultCompare) {
    super(compareFn);
    this.compareFn = compareFn;
    this.compareFn = reverseCompare(compareFn);
  }

 

二、简单应用

1、堆排序

思路：用数组创建一个最大堆；最大的值放置堆的最后一个位置；将堆的大小减一，每次执行第二个步骤直至堆的大小为1。（这样就得到升序（从最小到最大）的数组，若要数组的降序排列，则我们用最小堆。） 

function heapify(array, index, heapSize, compareFn) {
  let largest = index;
  const left = (2 * index) + 1;
  const right = (2 * index) + 2;
  if (left < heapSize && compareFn(array[left], array[index]) > 0) {
    largest = left;
  }
  if (right < heapSize && compareFn(array[right], array[largest]) > 0) {
    largest = right;
  }
  if (largest !== index) {
    swap(array, index, largest);
    heapify(array, largest, heapSize, compareFn);
  }
}

function buildMaxHeap(array, compareFn) {
  for (let i = Math.floor(array.length / 2); i >= 0; i -= 1) {
    heapify(array, i, array.length, compareFn);
  }
  return array;
}

function heapSort(array = [], compareFn = defaultCompare) {
  let heapSize = array.length;
  buildMaxHeap(array, compareFn);
  while (heapSize > 1) {
    swap(array, 0, --heapSize);
    heapify(array, 0, heapSize, compareFn);
  }
  return array;
}

const heapSort1 = new heapSort();
const array = [7, 6, 3, 5, 4, 1, 2];

console.log('Before sorting: ', array);
console.log('After sorting: ', heapSort(array));