Balls 牛客 期望DP

Balls

solutio

$$dp[i]=\frac{dp[i-1]}{i+1}+dp[i-1]$$

code

/*Siberian Squirrel*/
/*Cute KiloFish*/
#include<bits/stdc++.h>

#define IO ios::sync_with_stdio(false);cin.tie(0);cout.tie(0)
#define ACM_LOCAL

using namespace std;
typedef long long ll;

const double PI = acos(-1);
const double eps = 1e-4;
const int INF = 0x3f3f3f3f;
/*const int MOD = 998244353, r = 119, k = 23, g = 3;
const int MOD = 1004535809, r = 479, k = 21, g = 3;*/
const int MOD = 1e9 + 7;
const int M = 1e7 + 10;
const int N = 3e6 + 10;
const int UP = 50;
//inline int rnd(){static int seed=2333;return seed=(((seed*666666ll+20050818)%998244353)^1000000007)%1004535809;}

int n;
double dp[N];

void solve(int res = 0) {
    
    
    dp[0] = 1;
    for(int i = 1; i <= n; ++ i) {
    
    
        dp[i] = dp[i - 1] / (i + 1) + dp[i - 1];
    }
    cout << fixed << setprecision(7) << dp[n] << endl;
}

int main() {
    
    
    IO;
#ifdef ACM_LOCAL
    freopen("input", "r", stdin);
    freopen("output", "w", stdout);
#endif
    int o = 1, cases = 0;
//    cin >> o;
    while(o --) {
    
    
        cin >> n;
        solve();
    }
    return 0;
}