求逆序对模板

方法一：离散化+树状数组

模板如下：

#include<iostream>
#include<cstdio>
#include <algorithm>
using namespace std;
const int MAXN=40001;
int n, a[MAXN], tree[MAXN], tot;

int lowbit(int x) { return x&-x; }


int query(int x) {
    int ans=0;
    while (x>0) {
        ans+=tree[x];
        x-=lowbit(x);
    }
    return ans;
}

void addz(int x) {
    while (x<=n) {
        tree[x]+=1;
        x+=lowbit(x);
    }
    return;
}

struct Node {
    int v, ord;
    bool operator < (const Node x) const { return v<x.v; }
}node[MAXN];

int main() {
    scanf("%d", &n);
    for (int i=1; i<=n; i++) {
        scanf("%d", &node[i].v);
        node[i].ord=i;
    }
    sort(node+1, node+n+1 );
    for (int i=1; i<=n; i++) a[node[i].ord]=i;
    for (int i=1; i<=n; i++) {
        addz(a[i]);
        tot+=i-query(a[i]); 
    }
    printf("%d", tot);
  return 0;
}

方法二：归并排序

模板如下：

#include<iostream>
#include<cstdio>
using namespace std;
int n,A[40010],T[40010],num;

void merge_sort(int x,int y){
    if(y-x>1){
        int mid=x+(y-x)/2;
        int p=x,q=mid,i=x;
        merge_sort(x,mid);
        merge_sort(mid,y);
        while(p<mid||q<y){
            if(q>=y||(p<mid&&A[p]<=A[q]))
                  T[i++]=A[p++];
            else {T[i++]=A[q++];num+=mid-p;}
        }
        for(i=x;i<y;i++) A[i]=T[i];
    }
}

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