【算法导论】堆排序java实现

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最近开始做LeetCode的题目，发现自己仅仅能做简单的，中等题做起来就很吃力了。所以，恰有时间，就刷刷《算法导论》，并打算用java把算法导论中简单的算法实现下。加深java编程能力。

堆排序，时间复杂度O(nlogn),原址。原址：任何时刻都只需要常数个额外的元素空间存储临时数据。

最大堆中，除根节点外，所有节点i满足Heap[Parent(i)]>=Heap[i]。排序通常用最大堆，构造优先队列通常用最小堆。最大堆和最小堆实现基本一样，只要修改维护堆性质的函数即可。

废话不多说，直接代码：

public class MaxHeap {    int[] heap;//存放堆    int heapsize;//堆元素个数    //初始化，传入数组    public MaxHeap(int[] array) {        this.heap = array;        heapsize = heap.length;    }    //求节点i的父节点    public int heapParent(int i) {        return (i - 1) / 2;    }    //求节点i的左子节点    public int heapLeft(int i) {        return 2 * i + 1;    }    //求节点i的右子节点    public int heapRight(int i) {        return 2 * i + 2;    }    //维护堆的性质,此时间复杂度为O(log i)    public void heapMaximize(int i) {        int l = heapLeft(i);        int r = heapRight(i);        int maximum = i;        if (l < heapsize && heap[l] > heap[i])            maximum = l;        if (r < heapsize && heap[r] > heap[maximum])            maximum = r;        if (maximum == i || maximum >= heapsize)            return;        int tmp = heap[i];        heap[i] = heap[maximum];        heap[maximum] = tmp;        heapMaximize(maximum);    }    //构造最大堆,必须从下往上构造    public void buildMaxHeap() {        for (int i = heapsize / 2; i >= 0; i--)            heapMaximize(i);    }    //堆排序算法实现    public void heapSort() {        for (int i = heapsize - 1; i >= 0; i--) {            int tmp = heap[i];            heap[i] = heap[0];            heap[0] = tmp;            heapsize--;            heapMaximize(0);        }    }    public static void printHeapTree(int[] heap) {        for (int i = 1; i < heap.length; i = i * 2) {            for (int j = i - 1; j < 2 * i - 1 && j < heap.length; j++) {                System.out.print(heap[j] + " ");            }            System.out.println();        }    }    private static void printHeap(int[] heap) {        for (int i = 0; i < heap.length; i++) {            System.out.print(heap[i] + "  ");        }    }    public static void main(String[] args) {        int[] array = new int[]{10, 11, 12, 1, 2, 3, 4, 5, 13, 19, 6, 7, 8, 9, 5};        MaxHeap heap = new MaxHeap(array);        System.out.println("执行最大堆化前堆的结构：");        printHeapTree(heap.heap);        heap.buildMaxHeap();        System.out.println("执行最大堆化后堆的结构：");        printHeapTree(heap.heap);        heap.heapSort();        System.out.println("执行堆排序后数组的内容");        printHeap(heap.heap);    }}

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