while(i<=mid && j<=r)
    {
        if(q[i]<=q[j]) tmp[k++]=q[i++];
        else {
            res+=mid-i+1;
            tmp[k++]=q[j++];
        }
    }

mid-i+1个逆序对

当q[i]<=q[j] , (q[i], q[j]) 则不是逆序对。

else if(q[i]>q[j]) (q[i], q[j])是逆序对，并且q[i]....q[mid] 与q[j] 形成 mid-i+1个逆序对。

答案范围

当我们的输入样例是一个降序数组5 4 3 2 1

逆序对的数量res

$= n-1+ n-2+n-3+…+1$

$=n*(n-1)/2$

$n=1e5$

res=5e9 > INT_MAX=1e9

所以

res 为long long类型

#include<iostream>
using namespace std;
const int N=1e5+10;
int q[N], tmp[N];
int n;
typedef long long LL;

LL merge_sort(int l, int r){
    if(l>=r) return 0;
    LL s=0;

    int mid=l+r>>1;
    s=merge_sort(l, mid)+merge_sort(mid+1, r);

    int i=l, j=mid+1, k=0;
    while(i<=mid && j<=r){
        if(q[i]<=q[j]) tmp[k++]=q[i++];
        else {
            s+= mid-i+1;
            tmp[k++]=q[j++];
        }
    }
    while(i<=mid) tmp[k++]=q[i++];
    while(j<=r) tmp[k++]=q[j++];

    for(int i=l, k=0;i<=r;i++, k++) q[i]=tmp[k];
    return s;
}

int main(){
    cin>>n;
    for(int i=0;i<n;i++) scanf("%d", &q[i]);
    cout<<merge_sort(0, n-1) ;
    return 0;

}