Wannafly Camp 2020 Day 1A 期望逆序对 - 概率期望

分类讨论即可

#include <bits/stdc++.h>
using namespace std;
#define int long long
const int N = 5005;
const int mod = 998244353;
int i2;
int qpow(int p,int q) {
    int b=p,r=1;
    while(q>0) {
        if(q&1) r*=b;
        b*=b;
        r%=mod;
        b%=mod;
        q>>=1;
    }
    return r;
}
int inv(int x) {
    return qpow(x,mod-2);
}

struct seg {
    int l,r,inv;
    int len() {
        return r-l+1;
    }
    seg operator + (const seg &b) {
        seg c;
        c.l = min(l,b.l);
        c.r = max(r,b.r);
        return c;
    }
    seg operator * (const seg &b) {
        seg c;
        c.l = max(l,b.l);
        c.r = min(r,b.r);
        return c;
    }
    bool operator < (const seg &b) {
        return (l+r) < (b.l+b.r);
    }
} a[N];

struct num {
    int x;
    num() {
        x=0;
    }
    num(int t) {
        x=t;
    }
    num operator + (const num &b) {
        num c;
        c.x = x + b.x;
        c.x %= mod;
        return c;
    }
    num operator - (const num &b) {
        num c;
        c.x = x - b.x;
        c.x %= mod;
        c.x += mod;
        c.x %= mod;
        return c;
    }
    num operator * (const num &b) {
        num c;
        c.x = x * b.x;
        c.x %= mod;
        return c;
    }
    num operator / (const num &b) {
        num c;
        if(b.x==2)
            c.x = x * i2;
        else
            c.x = x * inv(b.x);
        c.x %= mod;
        return c;
    }
    num operator / (const seg &b) {
        num c;
        c.x = x * b.inv;
        c.x %= mod;
        return c;
    }
    void operator = (const int &b) {
        x = b;
    }
    void operator = (const num &b) {
        x = b.x;
    }
    num operator + (const int &b) {
        num c;
        c.x = x + b;
        c.x %= mod;
        return c;
    }
    num operator - (const int &b) {
        num c;
        c.x = x - b;
        c.x %= mod;
        return c;
    }
    num operator * (const int &b) {
        num c;
        c.x = x * b;
        c.x %= mod;
        return c;
    }
    num operator / (const int &b) {
        num c;
        c.x = x * inv(b);
        c.x %= mod;
        return c;
    }
    int get() {
        return x;
    }
};

int n;

num calc(seg a,seg b) {
    if(a.r<b.l) return num(0);
    if(b.r<a.l) return num(1);
    if(a.l>=b.l && a.r<=b.r) { //cout<<"A";
        return (num(a.l-b.l)+num(a.r-a.l)/num(2))/b;
    }
    if(b.l>=a.l && b.r<=a.r) { //cout<<"B";
        return (num(a.r-b.r)+num(b.r-b.l)/num(2))/a;
    }
    if(a.l>=b.l && b.r<=a.r) { //cout<<"C";
        return num(1)-num(b.r-a.l+1)*num(b.r-a.l+2)/num(2)/b/a;
    }
    if(b.l>=a.l && a.r<=b.r) { //cout<<"D";
        return num(a.r-b.l)*num(a.r-b.l+1)/num(2)/b/a;
    }
}

num check(seg a,seg b) {
    num x;
    for(int i=a.l;i<=a.r;i++) {
        for(int j=b.l;j<=b.r;j++) {
            if(j<i) x=x+1;
        }
    }
    x=x/((a.r-a.l+1)*(b.r-b.l+1));
    return x;
}

signed main() {
    i2=inv(2);
    scanf("%lld",&n);
    //for(int i=1;i<=n;i++) arrinv[i]=__inv(i);
    for(int i=1;i<=n;i++) {
        int t1,t2;
        scanf("%lld%lld",&t1,&t2);
        a[i].l=t1;
        a[i].r=t2;
        a[i].inv=inv(a[i].r-a[i].l+1);
    }
    sort(a+1,a+n+1);
    num ans = 0;
    /*for(int i=1;i<=n;i++) {
        for(int j=1;j<=n;j++) {
            cout<<(calc(a[i],a[j])).get()<<" ";
        }
        cout<<endl;
    }
    for(int i=1;i<=n;i++) {
        for(int j=1;j<=n;j++) {
            cout<<(check(a[i],a[j])).get()<<" ";
        }
        cout<<endl;
    }*/

    for(int i=2;i<=n;i++) {
        for(int j=1;j<i;j++) {
            ans = ans + calc(a[j],a[i]);
        }
    }
    cout<<ans.get()<<endl;
}