归并排序 Java

一、利用分治算法的思想，假设下标为0~7，分治过程如下：

[0~7]			全部无序
       /    \
    [0~3]    [4~7]		子序列内无序   
    /  \      /   \
[0~1] [2~3]  [4~5] [6~7]	子序列内无序
 / \  /  \   /   \  /  \
0   1 2  3   4   5  6   7	子序列内有序
 \ /  \  /   \  /   \  /
[0~1] [2~3]  [4~5]  [6~7]	子序列内有序
  \   /        \    /
    [0~3]      [4~7]		子序列内有序
         \     /
          [0~7]			全部有序

二、归并排序算法如下，其中数组r保存排序后的结果，s为待排序源数据数组：

public static void mergeSort(int [] r, int [] s, int begin, int end){
		if(begin == end){
			return;
		}
		int middle = (begin + end)/2;
		mergeSort(r, s, begin, middle);
		mergeSort(r,s, middle + 1, end);
		merge(r, s, begin, middle, end);
	}

其中搜集排序结果的函数merge如下：

public static void merge(int [] r, int [] s, int begin, int middle, int end){
		int i = begin;
		int j = middle + 1;
		int k = begin;
		while(i <= middle && j <= end){
			if(s[i] <= s[j]){
				r[k++] = s[i++];
			}else{
				r[k++] = s[j++];
			}
		}
		
		if(i <= middle){
			for(; i <= middle; i++){
				r[k++] = s[i];
			}
		}
		
		if(j <= end){
			for(; j <= end; j++){
				r[k++] = s[j];
			}
		}
		
		//把有序序列r[begin]~r[end],回写到s[begin]~s[end],这一步很重要
		for(int l = begin; l <= end; l++){
			s[l] = r[l];
		}
	}

三、完整的测试程序如下：

package mergeSort;

public class MergeSort {
	
	public static int [] s = new int[]{5,11,6,4,1,10,9,8,7};
	public static int [] r = new int[s.length];
	
	public static void main(String[] args) {
		printArr(s, "排序前:	");
		mergeSort(r,s,0,s.length - 1);//调用归并排序
		printArr(r, "排序后:	");//打印排序结果
	}
	
	//执行归并排序
	public static void mergeSort(int [] r, int [] s, int begin, int end){
		if(begin == end){
			return;
		}
		int middle = (begin + end)/2;
		mergeSort(r, s, begin, middle);
		mergeSort(r,s, middle + 1, end);
		merge(r, s, begin, middle, end);
	}
	
	//把两个无序的子序列s[begin]~s[middle]和子序列s[middle + 1]~s[end]合并为一个有序序列r[begin]~r[end],然后回写到s[begin]~s[end]
	public static void merge(int [] r, int [] s, int begin, int middle, int end){
		int i = begin;
		int j = middle + 1;
		int k = begin;
		while(i <= middle && j <= end){
			if(s[i] <= s[j]){
				r[k++] = s[i++];
			}else{
				r[k++] = s[j++];
			}
		}
		
		if(i <= middle){
			for(; i <= middle; i++){
				r[k++] = s[i];
			}
		}
		
		if(j <= end){
			for(; j <= end; j++){
				r[k++] = s[j];
			}
		}
		
		//把有序序列r[begin]~r[end],回写到s[begin]~s[end],这一步很重要
		for(int l = begin; l <= end; l++){
			s[l] = r[l];
		}
	}
	
	public static void printArr(int [] arr, String flag){
		System.out.print(flag);
		for(int i = 0; i < arr.length; i++){
			System.out.print(arr[i] + "	");
		}
		System.out.println();
	}
}

四、测试程序运行结果如下：

排序前:	5	11	6	4	1	10	9	8	7	
排序后:	1	4	5	6	7	8	9	10	11