归并排序-逆序对的数量

原理

略

代码

#include<iostream>
using namespace std;
const int N = 1e5 + 10;
typedef unsigned long long ULL;
int s[N], tmp[N];

ULL mergeSort(int l, int r){
    if(l >= r) return 0;
    
    int mid = (l + r) >> 1;
    ULL res = mergeSort(l, mid) + mergeSort(mid + 1, r);
    int i = l, j = mid + 1, k = 0;
    while(i <= mid && j <= r){
        if(s[i] <= s[j]) tmp[k++] = s[i++];
        else {
            res += mid - i + 1;
            tmp[k++] = s[j++];
        }
    }
    while(i <= mid) tmp[k++] = s[i++];
    while(j <= r) tmp[k++] = s[j++];
    for(k = 0; l <= r;) s[l++] = tmp[k++];
    return res;
}

int main(){
    int n;
    cin >> n;
    for(int i = 0; i < n; i++) cin >> s[i];
    cout << mergeSort(0, n - 1);
    return 0;
}

Q&A

以4 3 2 1为例，手动模拟即可明白这个代码