codeforces 1156F Card Bag 概率dp

Posted 2022-12-09 cjlhy

Card Bag

状态只会从a小转移到a大，随便dp就好了。

#include<bits/stdc++.h>
using namespace std;

const int N = 5000 + 7;
const int mod = 998244353;

int n, a[N], sum[N], dp[N][N], sum_dp[N];
int inv[N];

int main() 
    inv[1] = 1;
    for(int i = 2; i < N; i++) 
        inv[i] = 1LL * (mod - mod / i) * inv[mod % i] % mod;
    
    scanf("%d", &n);
    for(int i = 1; i <= n; i++) 
        int x; scanf("%d", &x);
        a[x]++;
    
    for(int i = 1; i < N; i++) 
        sum[i] = sum[i - 1] + a[i];
    
    dp[0][0] = 1;
    for(int j = 1; j <= n; j++) 
        sum_dp[0] = dp[0][j - 1];
        for(int i = 1; i < N; i++) 
            sum_dp[i] = (sum_dp[i - 1] + dp[i][j - 1]) % mod;
        
        for(int i = 1; i < N; i++) 
            dp[i][j] = 1LL * sum_dp[i - 1] * inv[n - j + 1] % mod * a[i] % mod;
        
    
    int ans = 0;
    for(int i = 1; i < N; i++) 
        if(a[i] < 2) continue;
        for(int j = 1; j < n; j++) 
            ans += 1LL * (a[i] - 1) * inv[n - j] % mod * dp[i][j] % mod;
            if(ans >= mod) ans -= mod;
        
    
    printf("%d\n", ans);
    return 0;


/*
*/