16.分治排序

分阶段可以理解为就是递归拆分子序列的过程

治阶段，我们需要将两个已经有序的子序列合并成一个有序序列，比如上图中的最后一次合并，要将[4,5,7,8]和[1,2,3,6]两个已经有序的子序列，合并为最终序列[1,2,3,4,5,6,7,8]

 

import java.util.Arrays;

/**
 * 归并排序
 */
public class MergeSort {
    public static void mergeSort(int[] arr,int left,int right,int[] temp){
        if (left<right){
            int mid = (left+right)/2;
            //前一部分分解
            mergeSort(arr,left,mid,temp);
            //后一部分分解
            mergeSort(arr,mid+1,right,temp);
            //合并
            merge(arr,left,mid,right,temp);
        }
    }
    /**
     * 合并 如 4,5,7,8,  1,2,3,6
     * @param arr  原始数组 由两部分组成
     * @param left  数组的第一个索引
     * @param mid  数组前一部分最后一个元素的索引
     * @param right 数组的最后一个索引
     * @param temp 临时数组
     */
    public static void merge(int[] arr,int left,int mid,int right,int[] temp){
        System.out.println("从"+left+"到"+right+"中间为"+arr[mid]+"原始数组"+Arrays.toString(arr));
        int i = left;
        int j = mid+1;
        int t = 0;
        while (i<=mid&&j<=right){
            if (arr[i]<=arr[j]){
                temp[t] = arr[i];
                i++;
                t++;
            }else {
                temp[t] = arr[j];
                j++;
                t++;
            }
        }
        while (i<=mid){
            temp[t]=arr[i];
            i++;
            t++;
        }
        while (j<=right){
            temp[t]=arr[j];
            j++;
            t++;
        }
        //将temp数组的元素拷贝到arr
        t = 0;
        int tempLeft = left;
        while (tempLeft<=right){
            arr[tempLeft]=temp[t];
            t++;
            tempLeft++;
        }
        System.out.println("合并后"+Arrays.toString(arr));
    }
    public static void main(String[] args){
        //测试合并
        int[] arr = new int[]{4,5,7,8,1,2,3,6};
        int length = arr.length;
        merge(arr,0,(length-1)/2,length-1,new int[arr.length]);
        //从0到7中间为8原始数组[4, 5, 7, 8, 1, 2, 3, 6]
        //合并后[1, 2, 3, 4, 5, 6, 7, 8]
        int[] arr2 = new int[]{9,8,7,6,5,4,3,2,1};
        mergeSort(arr2,0,arr2.length-1,new int[arr2.length]);
        //从0到1中间为9原始数组[9, 8, 7, 6, 5, 4, 3, 2, 1]
        //合并后[8, 9, 7, 6, 5, 4, 3, 2, 1]
        //从0到2中间为9原始数组[8, 9, 7, 6, 5, 4, 3, 2, 1]
        //合并后[7, 8, 9, 6, 5, 4, 3, 2, 1]
        //从3到4中间为6原始数组[7, 8, 9, 6, 5, 4, 3, 2, 1]
        //合并后[7, 8, 9, 5, 6, 4, 3, 2, 1]
        //从0到4中间为9原始数组[7, 8, 9, 5, 6, 4, 3, 2, 1]
        //合并后[5, 6, 7, 8, 9, 4, 3, 2, 1]
        //从5到6中间为4原始数组[5, 6, 7, 8, 9, 4, 3, 2, 1]
        //合并后[5, 6, 7, 8, 9, 3, 4, 2, 1]
        //从7到8中间为2原始数组[5, 6, 7, 8, 9, 3, 4, 2, 1]
        //合并后[5, 6, 7, 8, 9, 3, 4, 1, 2]
        //从5到8中间为4原始数组[5, 6, 7, 8, 9, 3, 4, 1, 2]
        //合并后[5, 6, 7, 8, 9, 1, 2, 3, 4]
        //从0到8中间为9原始数组[5, 6, 7, 8, 9, 1, 2, 3, 4]
        //合并后[1, 2, 3, 4, 5, 6, 7, 8, 9]
    }
}