（1）基本思想：歸併（Merge）排序法是將兩個（或兩個以上）有序表合併成一個新的有序表，即把待排序序列分爲若干個子序列，每個子序列是有序的。然後再把有序子序列合併爲整體有序序列。歸併排序（MERGE-SORT）是建立在歸併操作上的一種有效的排序算法,該算法是採用分治法（Divide and Conquer）的一個非常典型的應用。將已有序的子序列合併，得到完全有序的序列；即先使每個子序列有序，再使子序列段間有序。若將兩個有序表合併成一個有序表，稱爲二路歸併。
歸併過程爲：比較a[i]和a[j]的大小，若a[i]≤a[j]，則將第一個有序表中的元素a[i]複製到r[k]中，並令i和k分別加上1；否則將第二個有序表中的元素a[j]複製到r[k]中，並令j和k分別加上1，如此循環下去，直到其中一個有序表取完，然後再將另一個有序表中剩餘的元素複製到r中從下標k到下標t的單元。歸併排序的算法我們通常用遞歸實現，先把待排序區間[s,t]以中點二分，接着把左邊子區間排序，再把右邊子區間排序，最後把左區間和右區間用一次歸併操作合併成有序的區間[s,t]。
（2）算法描述
歸併操作的工作原理如下：
第一步：申請空間，使其大小爲兩個已經排序序列之和，該空間用來存放合併後的序列；
第二步：設定兩個指針，最初位置分別爲兩個已經排序序列的起始位置；
第三步：比較兩個指針所指向的元素，選擇相對小的元素放入到合併空間，並移動指針到下一位置；
重複步驟3直到某一指針超出序列尾，將另一序列剩下的所有元素直接複製到合併序列尾。
（3）代碼如下：
package structsmethod;
import java.util.Arrays;
public class mergingSort {
/*
* 歸併排序
*/
int a[]={49,38,65,97,76,13,27,49,78,34,12,64,5,4,62,99,98,54,56,17,18,23,34,15,35,25,53,51};
public mergingSort(){
sort(a,0,a.length-1);
for(int i=0;i<a.length;i++)
System.out.println(a[i]);
}
public void sort(int[] data, int left, int right) {
if(left<right){
//找出中間索引
int center=(left+right)/2;
//對左邊數組進行遞歸
sort(data,left,center);
//對右邊數組進行遞歸
sort(data,center+1,right);
//合併
merge(data,left,center,right);
}
}
public void merge(int[] data, int left, int center, int right) {
int [] tmpArr=new int[data.length];
int mid=center+1;
//third記錄中間數組的索引
int third=left;
int tmp=left;
while(left<=center&&mid<=right){
//從兩個數組中取出最小的放入中間數組
if(data[left]<=data[mid]){
tmpArr[third++]=data[left++];
}else{
tmpArr[third++]=data[mid++];
}
}
//剩餘部分依次放入中間數組
while(mid<=right){
tmpArr[third++]=data[mid++];
}
while(left<=center){
tmpArr[third++]=data[left++];
}
//將中間數組中的內容複製回原數組
while(tmp<=right){
data[tmp]=tmpArr[tmp++];
}
System.out.println(Arrays.toString(data));
}
public static void main(String[] args) {
mergingSort ms=new mergingSort();
ms.sort(ms.a, 0, ms.a.length-1);
}
}排序結果如下：
[38, 49, 65, 97, 76, 13, 27, 49, 78, 34, 12, 64, 5, 4, 62, 99, 98, 54, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]
[38, 49, 65, 97, 76, 13, 27, 49, 78, 34, 12, 64, 5, 4, 62, 99, 98, 54, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]
[38, 49, 65, 97, 76, 13, 27, 49, 78, 34, 12, 64, 5, 4, 62, 99, 98, 54, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]
[38, 49, 65, 97, 13, 76, 27, 49, 78, 34, 12, 64, 5, 4, 62, 99, 98, 54, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]
[38, 49, 65, 97, 13, 27, 76, 49, 78, 34, 12, 64, 5, 4, 62, 99, 98, 54, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]
[13, 27, 38, 49, 65, 76, 97, 49, 78, 34, 12, 64, 5, 4, 62, 99, 98, 54, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]
[13, 27, 38, 49, 65, 76, 97, 49, 78, 34, 12, 64, 5, 4, 62, 99, 98, 54, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]
[13, 27, 38, 49, 65, 76, 97, 49, 78, 12, 34, 64, 5, 4, 62, 99, 98, 54, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]
[13, 27, 38, 49, 65, 76, 97, 12, 34, 49, 78, 64, 5, 4, 62, 99, 98, 54, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]
[13, 27, 38, 49, 65, 76, 97, 12, 34, 49, 78, 5, 64, 4, 62, 99, 98, 54, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]
[13, 27, 38, 49, 65, 76, 97, 12, 34, 49, 78, 4, 5, 64, 62, 99, 98, 54, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]
[13, 27, 38, 49, 65, 76, 97, 4, 5, 12, 34, 49, 64, 78, 62, 99, 98, 54, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]
[4, 5, 12, 13, 27, 34, 38, 49, 49, 64, 65, 76, 78, 97, 62, 99, 98, 54, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]
[4, 5, 12, 13, 27, 34, 38, 49, 49, 64, 65, 76, 78, 97, 62, 99, 98, 54, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]
[4, 5, 12, 13, 27, 34, 38, 49, 49, 64, 65, 76, 78, 97, 62, 99, 54, 98, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]
[4, 5, 12, 13, 27, 34, 38, 49, 49, 64, 65, 76, 78, 97, 54, 62, 98, 99, 56, 17, 18, 23, 34, 15, 35, 25, 53, 51]
[4, 5, 12, 13, 27, 34, 38, 49, 49, 64, 65, 76, 78, 97, 54, 62, 98, 99, 17, 56, 18, 23, 34, 15, 35, 25, 53, 51]
[4, 5, 12, 13, 27, 34, 38, 49, 49, 64, 65, 76, 78, 97, 54, 62, 98, 99, 17, 18, 56, 23, 34, 15, 35, 25, 53, 51]
[4, 5, 12, 13, 27, 34, 38, 49, 49, 64, 65, 76, 78, 97, 17, 18, 54, 56, 62, 98, 99, 23, 34, 15, 35, 25, 53, 51]
[4, 5, 12, 13, 27, 34, 38, 49, 49, 64, 65, 76, 78, 97, 17, 18, 54, 56, 62, 98, 99, 23, 34, 15, 35, 25, 53, 51]
[4, 5, 12, 13, 27, 34, 38, 49, 49, 64, 65, 76, 78, 97, 17, 18, 54, 56, 62, 98, 99, 23, 34, 15, 35, 25, 53, 51]
[4, 5, 12, 13, 27, 34, 38, 49, 49, 64, 65, 76, 78, 97, 17, 18, 54, 56, 62, 98, 99, 15, 23, 34, 35, 25, 53, 51]
[4, 5, 12, 13, 27, 34, 38, 49, 49, 64, 65, 76, 78, 97, 17, 18, 54, 56, 62, 98, 99, 15, 23, 34, 35, 25, 53, 51]
[4, 5, 12, 13, 27, 34, 38, 49, 49, 64, 65, 76, 78, 97, 17, 18, 54, 56, 62, 98, 99, 15, 23, 34, 35, 25, 51, 53]
[4, 5, 12, 13, 27, 34, 38, 49, 49, 64, 65, 76, 78, 97, 17, 18, 54, 56, 62, 98, 99, 15, 23, 25, 34, 35, 51, 53]
[4, 5, 12, 13, 27, 34, 38, 49, 49, 64, 65, 76, 78, 97, 15, 17, 18, 23, 25, 34, 35, 51, 53, 54, 56, 62, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
4
5
12
13
15
17
18
23
25
27
34
34
35
38
49
49
51
53
54
56
62
64
65
76
78
97
98
99
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]
[4, 5, 12, 13, 15, 17, 18, 23, 25, 27, 34, 34, 35, 38, 49, 49, 51, 53, 54, 56, 62, 64, 65, 76, 78, 97, 98, 99]