【hihocoder】三十九周：二分.归并排序之逆序对

就是用归并排序求数组中得逆序对。假设数组为a:[2 4 5],和b:[1 3]，那么在这一次归并的时候逆序对这样求,belement表示当前result数组中b数组对应的元素个数,total表示逆序对的个数：

a:[2 4 5]  b:[1 3]   result{}

a:[2 4 5]  b[3]       result{1}              belement = 1;

a:[4 5]  b[3]          result{1 2}           belement = 1;        total = total + belement = 1;

a:[4 5]  b[]       　  result{1 2 3}        belement = 2;        total = 1;

a:[5]  b[]               result{1 2 3 4}     belement = 2;        total = total + belement = 3

a:[]  b[]                 result{1 2 3 4 5}  belement = 2;        total = total + belement = 5

所以数组2 4 5 1 3的逆序数总共有5个。

JAVA版本代码如下：注意total要设置成long型防止溢出。

import java.util.Scanner;
public class Main {

    public static void main(String[] args) {
        // TODO Auto-generated method stub
        
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int[] arr = new int[n];
        for(int i = 0;i < n;i++)
            arr[i] = in.nextInt();
        MergeSort(arr,0,arr.length-1);
        /*
        for(int i = 0;i < arr.length;i++)
            System.out.print(arr[i]);
            */
        System.out.print(total);
    }
    private static void MergeSort(int[] arr,int begin,int end){
        if(begin >= end)
            return;
        int mid = (begin+end)/2;
        MergeSort(arr, begin, mid);
        MergeSort(arr, mid+1, end);
        merge(arr, begin, end);
    }
    public static long total = 0;
    private static void merge(int[] arr,int begin,int end){
        int belement = 0;
        int mid = (begin+end)/2;
        int p1 = begin;
        int p2 = mid+1;
        int count = 0;
        int[] sorted = new int[end-begin+1];
        
        while(p1 <= mid && p2 <= end){
            if(arr[p1] > arr[p2]){
                sorted[count] = arr[p2];
                p2++;
                count++;
                belement++;        
                //System.out.println(belement);
            }else{
                total += belement;
                sorted[count] = arr[p1];
                p1++;
                count++;
            }
        }
        
        while(p1 <= mid){
            sorted[count] = arr[p1];
            count++;
            p1 ++;
            total += belement;
        }
        
        while(p2 <= end){
            sorted[count] = arr[p2];
            count ++;
            p2++;
        }
        
        for(int i = begin;i <= end;i++)
            arr[i] = sorted[i-begin];
    }
    
}