LOJ#6342. 跳一跳(期望)

题意

$n \leqslant 10^5$

Sol

随便推一推就好了吧。。

$f[i] = \frac{f[i] + f[i +1] + \dots f[n]}{n - i + 1} + 1$

移一下项，然后化一化，就做完了。。

然而这题卡空间MMP

#include<cstdio>
#include<algorithm>
#include<iostream>
//#define int long long
#define Pair pair<int, int>
#define fi first
#define se second
#define MP(x, y) make_pair(x, y)
using namespace std;
const int MAXN = 1e7 + , INF = 1e9 + , mod = 1e9 + ;
inline int read() {
    char c = getchar(); int x = , f = ;
    while(c < '' || c > '') {if(c == '-') f = -; c = getchar();}
    while(c >= '' && c <= '') x = x *  + c - '', c = getchar();
    return x * f;
}
int N;
int inv[MAXN];
main() {
    N = read();
    int s = , now = ;
    inv[] = ;
    for(int i = ; i <= N; i++) inv[i] = 1ll * (mod - mod / i) * inv[mod % i] % mod;
    for(int i = N - ; i >= ; i--) {
        now = 1ll * (s + N - i + ) * inv[N - i] % mod;
        s = (s + now) % mod;
    }
    cout << (now + mod) % mod;
    return ;
}
/*
10000000
*/