排序 堆排序-基础篇

堆是一棵特殊的树，具有如下特点：

1. 完全二叉树。除了最后一层，每一层从左到右是满员的。

2. 每个节点都是大于或者等于它的子节点。

3. 通常由数组实现。

数组表示堆的时候，具有如下特性：

数组中的任意索引x

1. 父节点为(x - 1)/ 2

2. 左子节点为2*x+1

3. 右子节点为2*x+2

 

基础代码部分

/**这里我们将介绍插入堆尾时的向上shuai选。移除堆顶时的向下shuai选**/

public void insert(int node) {
    heapArray[currentSize] = node;
    trickleUp(currentSize++);
}
public void trickleUp(int index) {
    int parent = (index - 1) / 2;
    int bottom = heapArray[index];
    while(index > 0 && heapArray[parent] < bottom) {
        heapArray[index] = heapArray[parent];
        index = parent;
        parent = (parent - 1) / 2;
    }
    heapArray[index] = bottom;
}


public int remove() {
    int root = heapArray[0];
    heapArray[0] = heapArray[--currentSize];
    trickleDown(0);
    return root;
}
public void trickleDown(int index) {
    int largerChild;
    int top = heapArray[index];
    
    while(index < currentSize / 2) {
        int leftChild = 2*index + 1;
        int rightChild = leftChild + 1;
        if(rightChild < currentSize && heapArray[rightChild] > heapArray[leftChild]) {
            largerChild = rightChild;
        } else {
            largerChild = leftChild;
        }

        if(top >= heapArray[largerChild]) {
            break;
        }
        heapArray[index] = heapArray[largerChild];
        index = largerChild;
    }
    heapArray[index] = top;
}