排序算法二：归并排序(Merge sort)

归并排序(Merge sort)用到了分治思想，即分-治-合三步，算法平均时间复杂度是O(nlgn).

（一）算法实现

 private void merge_sort(int[] array, int first, int last) {
         if (first + 1 < last) {
             int mid = (first + last) / 2;
             merge_sort(array, first, mid);
             merge_sort(array, mid, last);

             // merge
             int i = first;
             int j = mid;
             int[] tempArray = new int[last - first];
             for (int k = 0; k < tempArray.length; k++) {
                 if (j == last) {
                     tempArray[k] = array[i++];
                 } else if (i == mid) {
                     tempArray[k] = array[j++];
                 } else if (array[i] <= array[j]) {
                     tempArray[k] = array[i++];
                 } else if (array[i] > array[j]) {
                     tempArray[k] = array[j++];
                 } else {
                     throw new RuntimeException("Merge sort error.");
                 }
             }
             System.arraycopy(tempArray, 0, array, first, last - first);
         }
     }

Merge sort

1）算法不是原地排序，合并时需要额外空间

2）算法平均时间复杂度是O(nlgn)

3）归并排序属于比较排序

4）归并排序属于稳定排序算法

（二）仿真结果

**************************************************
Number to Sort is:2500
Array to sort is:{633649,71377,977368,56277,635475,755791,746668,373470,820128,669757...}
Cost time of 【MergSort】 is(milliseconds):1
Sort result of 【MergSort】:{695,711,935,1074,1571,1681,2434,3967,4104,4452...}
**************************************************
Number to Sort is:25000
Array to sort is:{62806,677129,876202,279782,662046,978299,979879,374196,303999,484652...}
Cost time of 【MergSort】 is(milliseconds):5
Sort result of 【MergSort】:{15,34,74,94,131,141,316,372,375,417...}
**************************************************
Number to Sort is:250000

Array to sort is:{617507,750026,202102,267444,690991,638097,868240,413838,774218,463780...}

Cost time of 【MergSort】 is(milliseconds):67
Sort result of 【MergSort】:{6,9,19,28,31,39,44,45,56,59...}

相关代码：

 package com.cnblogs.riyueshiwang.sort;

 import java.util.Arrays;

 public class MergeSort extends abstractSort {

     @Override
     protected void sort(int[] toSort) {
         merge_sort(toSort, 0, toSort.length);
     }

     private void merge_sort(int[] array, int first, int last) {
         if (first + 1 < last) {
             int mid = (first + last) / 2;
             merge_sort(array, first, mid);
             merge_sort(array, mid, last);

             // merge
             int i = first;
             int j = mid;
             int[] tempArray = new int[last - first];
             for (int k = 0; k < tempArray.length; k++) {
                 if (j == last) {
                     tempArray[k] = array[i++];
                 } else if (i == mid) {
                     tempArray[k] = array[j++];
                 } else if (array[i] <= array[j]) {
                     tempArray[k] = array[i++];
                 } else if (array[i] > array[j]) {
                     tempArray[k] = array[j++];
                 } else {
                     throw new RuntimeException("Merge sort error.");
                 }
             }
             System.arraycopy(tempArray, 0, array, first, last - first);
         }
     }

     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 MergeSort().sortAndprint(array1);
         }
     }
 }

MergeSort.java