归并排序

1.问题划分
2.递归求解
3合并问题

import java.util.Arrays;
import java.util.Random;
public class Main{	

	public static void isSort(int[] arr){
		for(int i=0,j=1;j<arr.length;i++,j++){
			if(arr[i]>arr[j]){
				System.out.println("排序失败");
				System.out.print(Arrays.toString(arr));
				return;
			}
		}
		System.out.println("排序成功");
		System.out.print(Arrays.toString(arr));
	}
	private static void merge(int[] arr,int[] aux,int left,int mid,int right){
		for(int k=left;k<=right;k++){
			aux[k]=arr[k];
		}
		int i=left;
		int j=mid+1;
		for(int k=left;k<=right;k++){
			if(i>mid) arr[k]=aux[j++];
			else if(j>right) arr[k]=aux[i++];
			else if(aux[j]<aux[i]) arr[k]=aux[j++];
			else arr[k]=aux[i++];
			
		}
	}
	public static void sort(int[] arr,int [] aux,int left,int right){
		if(left>=right) return;
		int mid=left+(right-left)/2;
		sort(arr,aux,left,mid);
		sort(arr,aux,mid+1,right);
		merge(arr,aux,left,mid,right);
	}
	public static void main(String[] args){
		Random random=new Random();
		int[] arr=new int[10000000];
		int[] aux=new int[10000000];
		for(int i=0;i<10000;i++){
			arr[i]=random.nextInt(10000);
		}
		sort(arr,aux,0,arr.length-1);
		isSort(arr);
	}
}

　利用归并求逆序对

	public static int merge_and_count(int[] arr,int[] aux,int lo,int mid,int hi){
		int k=hi;
		int i=mid;
		int j=hi;
		int count=0;
		while(i>=lo&&j>mid){
			if(arr[i]>arr[j]){
				count+=j-mid;
				aux[k--]=arr[i--];
			}else{
				aux[k--]=arr[j--];
			}
		}
		while(i>=lo){
			aux[k--]=arr[i--];
		}
		while(j>mid){
			aux[k--]=arr[j--];
		}
		for(int r=lo;r<=hi;r++){
			arr[r]=aux[r];
		}
		return count;
	}
	public static int sort(int[] arr,int aux[],int lo,int hi){
		if(lo>=hi) return 0;
		int count=0;
		int mid=lo+(hi-lo)/2;
		count+=sort(arr,aux,lo,mid);
		count+=sort(arr,aux,mid+1,hi);
		count+=merge_and_count(arr,aux,lo,mid,hi);
		return count;
	}