JavaScript数据结构与算法十一二叉堆

二叉堆数据结构是一种特殊的二叉树，他能高效、快速的找出最大值和最小值，常应用于优先队列和著名的堆排序算法中。

二叉堆

二叉堆有以下两个特性：

1. 是一颗完全二叉树，表示数的每一层都有左侧和右侧子节点（除最后一层的叶节点），并且最后一层的叶节点尽可能是左侧子节点
2. 二叉堆不是最小堆就是最大堆，所有节点都大于等于（最大堆）或者小于等于（最小堆）每个他的子节点。

创建最小堆类

class MinHeap {constructor(compareFn = defaultCompare) {
    this.compareFn = compareFn;
    this.heap = [];}
}

二叉堆的数组表示

    static getLeftIndex(index) {return (2 * index) + 1;
  }

  static getRightIndex(index) {return (2 * index) + 2;
  }

  static 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 = [];
  }

查找二叉堆最小值或者最大值

 findMinimum() {return this.isEmpty() ? undefined : this.heap[0];
  }

交换函数实现

function swap(array, a, b) {/* const temp = array[a];
  array[a] = array[b];
  array[b] = temp; */
  [array[a], array[b]] = [array[b], array[a]];
}

向堆中插入新值

insert(value) {if (value != null) {
      const index = this.heap.length;
      this.heap.push(value);
      this.siftUp(index);
      return true;
    }
    return false;
  };
// 上移操作
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);
    }
  }

二叉堆中导出最大值或最小值

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;
  };
// 下移操作
 siftDown(index) {
    let element = index;
    const left = MinHeap.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;}
    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);
    }
  }

创建最大堆类

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

其他操作跟最小堆类一样，这里就不多加赘述。

堆排序算法

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;};
// 构建最大堆函数
function buildMaxHeap(array, compareFn) {for (let i = Math.floor(array.length / 2);i >= 0; i -= 1){heapify(array, i, array.length, compareFn);
      return array;
    }
  }
// 堆排序算法实现
function heapSort(array, compareFn = defaultCompare) {
  let heapSize = array.length;
  // 用数组创建一个最大堆用作源数据
  buildMaxHeap(array, compareFn);
  while(heapSize > 1){
    // 创建最大堆后，最大的值会被存储在堆的第一个位置，我们将它替换为堆的最后一个值，将堆的大小 -1
    swap(array, 0, --heapSize);
    // 将堆的根节点下移并重复步骤 2 直到堆的大小为 1
    heapify(array, 0, heapSize, compareFn);
  }
  return array;
}