排序算法三：堆排序（Heapsort）

堆排序（Heapsort）是一种利用数据结构中的堆进行排序的算法，分为构建初始堆，减小堆的元素个数，调整堆共3步。

（一）算法实现

     protected void sort(int[] toSort) {
         buildHeap(toSort);
         for (int i = toSort.length - 1; i > 0; i--) {
             CommonUtils.swap(toSort, 0, i);
             adjustHeap(toSort, 0, i);
         }
     }

     /**
      *
      * @param toSort
      *            array of heap, begins from 0
      * @param index
      *            index to adjust
      * @param size
      *            size of heap
      */
     private void adjustHeap(int[] toSort, int index, int size) {
         int leftNode = index * 2 + 1;
         int rightNode = leftNode + 1;

         int maxIndex = index;
         if (leftNode < size && toSort[leftNode] > toSort[maxIndex]) {
             maxIndex = leftNode;
         }
         if (rightNode < size && toSort[rightNode] > toSort[maxIndex]) {
             maxIndex = rightNode;
         }
         if (maxIndex != index) {
             CommonUtils.swap(toSort, index, maxIndex);
             adjustHeap(toSort, maxIndex, size);
         }

     }

     /**
      *
      * @param toSort
      *            array to sort
      */
     private void buildHeap(int[] toSort) {
         int lastNonLeaf = toSort.length / 2 - 1;
         for (int i = lastNonLeaf; i >= 0; i--) {
             adjustHeap(toSort, i, toSort.length);
         }
     }

Heap sort

1）堆排序是原地排序

2）堆排序的时间复杂度是O(nlgn)

3）堆排序属于比较排序

4）堆排序不是稳定排序算法

（二）仿真结果

**************************************************
Number to Sort is:2500
Array to sort is:{419836,72576,347420,355422,378503,65556,443634,137868,266344,918856...}
Cost time of 【HeapSort】 is(milliseconds):1
Sort result of 【HeapSort】:{185,874,996,1232,1448,2357,2728,2854,3137,3291...}
**************************************************
Number to Sort is:25000
Array to sort is:{169570,655593,54301,59080,890711,224726,720131,590749,600165,681962...}
Cost time of 【HeapSort】 is(milliseconds):7
Sort result of 【HeapSort】:{9,107,119,192,297,321,338,359,359,362...}
**************************************************
Number to Sort is:250000
Array to sort is:{233097,327821,972339,26697,803510,598167,178244,117664,904299,195258...}
Cost time of 【HeapSort】 is(milliseconds):59
Sort result of 【HeapSort】:{0,1,3,8,16,24,32,37,45,52...}

相关代码：

 package com.cnblogs.riyueshiwang.sort;

 import java.util.Arrays;

 public class HeapSort extends abstractSort {
     @Override
     protected void sort(int[] toSort) {
         buildHeap(toSort);
         for (int i = toSort.length - 1; i > 0; i--) {
             CommonUtils.swap(toSort, 0, i);
             adjustHeap(toSort, 0, i);
         }
     }

     /**
      *
      * @param toSort
      *            array of heap, begins from 0
      * @param index
      *            index to adjust
      * @param size
      *            size of heap
      */
     private void adjustHeap(int[] toSort, int index, int size) {
         int leftNode = index * 2 + 1;
         int rightNode = leftNode + 1;

         int maxIndex = index;
         if (leftNode < size && toSort[leftNode] > toSort[maxIndex]) {
             maxIndex = leftNode;
         }
         if (rightNode < size && toSort[rightNode] > toSort[maxIndex]) {
             maxIndex = rightNode;
         }
         if (maxIndex != index) {
             CommonUtils.swap(toSort, index, maxIndex);
             adjustHeap(toSort, maxIndex, size);
         }

     }

     /**
      *
      * @param toSort
      *            array to sort
      */
     private void buildHeap(int[] toSort) {
         int lastNonLeaf = toSort.length / 2 - 1;
         for (int i = lastNonLeaf; i >= 0; i--) {
             adjustHeap(toSort, i, toSort.length);
         }
     }

     public static void main(String[] args) {
         for (int j = 0, n = 2500; j < 3; j++, n = n * 10) {
             System.out
                     .println("**************************************************");
             System.out.println("Number to Sort is:" + n);
             int[] array = CommonUtils.getRandomIntArray(n, 1000000);
             System.out.print("Array to sort is:");
             CommonUtils.printIntArray(array);

             int[] array1 = Arrays.copyOf(array, n);
             new HeapSort().sortAndprint(array1);
         }
     }
 }

HeapSort.java