二叉堆和堆排序

二叉堆是一种特殊的二叉树。

• 它是一颗完全二叉树，表示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，这叫结构特性。
• 二叉堆不是最小堆就是最大堆。最小堆允许快速导出树的最小值，最大堆允许快速导出输的最大值。所有的节点都大于等于（最大堆）或小于等于（最小堆）每个它的子节点。这叫堆特性。 

// 创建最小堆
class MinHeap {
    constructor(compareFn = defaultCompare){
        this.compareFn = compareFn
        this.heap = []
    }
}
MinHeap.prototype.getLeftIndex = function(index){
    return 2 * index + 1
}
MinHeap.prototype.getRightIndex = function(index){
    return 2 * index + 2
}
MinHeap.prototype.getParentIndex = function(index){
    if(index === 0){
        return undefined
    }
    return Math.floor((index - 1) / 2)
}
MinHeap.prototype.insert = function(value){
    if(value != null){
        this.heap.push(value)
        this.shiftUp(this.heap.length - 1)
    }
}
MinHeap.prototype.shiftUp = function(index){
    let parentIndex = this.getParentIndex(index)
    while(index > 0 && this.heap[parentIndex] > this.heap[index]){
        swap(this.heap,parentIndex,index)
        index = parentIndex
        parentIndex = this.getParentIndex(index)
    }
}
MinHeap.prototype.size = function(){
    return this.heap.length
}
MinHeap.prototype.isEmpty = function(){
    return this.size() == 0
}
MinHeap.prototype.findMinimum = function(){
    return this.isEmpty() ? undefined : this.heap[0]
}
MinHeap.prototype.extract = function(){
    if(this.isEmpty()){
        return undefined
    }
    if(this.size() == 1){
        return this.heap.shift()
    }
    const removedValue = this.heap.shift()
    this.shiftDown(0)
    return removedValue
}
MinHeap.prototype.shiftDown = function(index){
    let element = index
    const left = this.getLeftIndex(index)
    const right = this.getRightIndex(index)
    const size = this.size()
    if(left < size && this.heap[element] - this.heap[left] > 0){
        element = left
    }else if(right < size && this.heap[element] - this.heap[right] > 0){
        element = right
    }
    if(index !== element){
        swap(this.heap,index,element)
        this.shiftDown(element)
    }
}