堆排序（Heap-Sort）

（二叉）堆是一个数组，它可以被看成一颗近似的完全二叉树。树上的每个节点对应数组中一个元素。除了最底层外，该树是完全充满的，而且是从左向右填充的。堆排序是一种用堆来实现的排序算法，它的时间复杂度为O(nlgn)，下面是堆排序的Java实现：

import java.util.Arrays;/** * Created by CvShrimp on 2017/10/11. */public class HeapSort {    public static void maxHeap(int[] heap, int i, int endIndex) {        int selfIndex = i - 1;        int largest = selfIndex;        int leftChildIndex = 2 * i - 1;        int rightChildIndex = 2 * i;        if(leftChildIndex <= endIndex && heap[leftChildIndex] > heap[selfIndex]) {            largest = leftChildIndex;        }        if(rightChildIndex <= endIndex && heap[rightChildIndex] > heap[largest]) {            largest = rightChildIndex;        }        if(largest != selfIndex) {            swapHeapElement(heap, selfIndex, largest);            maxHeap(heap, largest + 1, endIndex);        }    }    public static void buildMaxHeap(int[] heap) {        int startIndex = heap.length/2 - 1;        for(int i = startIndex; i >= 0; i--) {            maxHeap(heap, i + 1, heap.length - 1);        }    }    public static void heapSort(int[] heap) {        //构建最大堆，最大的元素在树的根节点        buildMaxHeap(heap);        int maxIndex = heap.length - 1;        for(int i = maxIndex; i >= 0;) {            //最大的元素和最后一个元素互换位置            swapHeapElement(heap, 0, i);            i--;            //对剩下的前i+1个元素，再构建最大堆            maxHeap(heap, 1, i);        }    }    public static void swapHeapElement(int[] heap, int i, int j) {        int temp = heap[i];        heap[i] = heap[j];        heap[j] = temp;    }    public static void main(String[] args) {        int[] heap = {1,5,6,3,4,10,7,66,666,66};        HeapSort.heapSort(heap);        System.out.print("Sorted heap: ");        System.out.print(Arrays.toString(heap));    }}