HeapSort快速排序

1.概念：

堆：(二叉)堆数据结构是一种数组对象。它可以被视为一棵完全二叉树，树中每个结点与数组中存放该结点值的那个元素对应。

二叉堆有两种：最大堆和最小堆(小根堆)。

最大堆：所有节点的子节点比其自身小的堆。
最小堆：所有节点的子节点比其自身大的堆。

堆排序：堆排序利用了大根堆(或小根堆)堆顶记录的关键字最大(或最小)这一特征，使得在当前无序区中选取最大(或最小)关键字的记录变得简单

2.代码

package Sort;



import java.util.Scanner;



public class HeapSort {

    

    /**

     * build a max heap 

     * @param a 

     * @param size

     */

    public static void buildMaxHeap(int a[], int size) {

        for(int i = size/2; i > 0; i--) {

            maxHeapify(a, i, size);

        }

    }

    

    public static void maxHeapify(int a[], int i, int size) {

        int leftNode = 2 * i;

        int rightNode = 2 * i + 1;

        int largestNode = i;

        if(leftNode <= size && a[leftNode] > a[i]) {

            largestNode = leftNode;

        }

        if(rightNode <= size && a[rightNode] > a[largestNode]) {

            largestNode = rightNode;

        }

        if(largestNode != i) {

            int temp = a[i];

            a[i] = a[largestNode];

            a[largestNode] = temp;

            maxHeapify(a, largestNode, size);

        }

    }

    

    /**

     * print the current array

     * @param a

     * @param size

     */

    public static void printArray(int a[], int size) {

        for(int i = 1; i <= size; i++) {

            System.out.print(a[i] + " ");

        }

        System.out.println("");

    }

    



    public static void heapSort(int a[], int size) {

        buildMaxHeap(a, size);

        printArray(a, size);

        

        int len = size;

        for(int i = size; i >= 2; i--) {

            int temp = a[i];

            a[i] = a[1];

            a[1] = temp;

            len--;

            maxHeapify(a, 1, len);

            System.out.println("The intermediate result: ");

            printArray(a, size);

        }

    }

    

    public static void main(String args[]) {

        @SuppressWarnings("resource")

        Scanner scan = new Scanner(System.in);

        System.out.println("The size: ");

        int size = scan.nextInt();

        int a[] = new int[size+1];

        System.out.println("Input the elements: ");

        for(int i = 1 ; i <= size; i++) {

            a[i] = scan.nextInt();

        }

        heapSort(a, size);

        System.out.println("The final result: ");

        printArray(a, size);

    }

}