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ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#786195 | #9782. NonZero PrefSuf Sums | ucup-team2172 | AC ✓ | 1311ms | 57924kb | C++23 | 2.7kb | 2024-11-26 20:39:43 | 2024-11-26 20:39:47 |
Judging History
answer
#include <bits/stdc++.h>
#define inf (0x7f7f7f7f)
#define Max(a, b) ((a) > (b) ? (a) : (b))
#define Min(a, b) ((a) < (b) ? (a) : (b))
typedef long long ll;
using namespace std;
template <class T>
inline void read(T &x){
int ch = 0, f = 0; x = 0;
for(; !isdigit(ch); ch = getchar()) if(ch == '-') f = 1;
for(; isdigit(ch); ch = getchar()) x = x * 10 + ch - 48;
if(f) x = -x;
}
const int N = 105;
int dp[N][2*N*N], f[N][N][N*N], inv[N], js[N], n, m, mod;
inline int Pow(int a, int b){
int ans = 1;
for(; b; b >>= 1, a = 1ll * a * a % mod)
if(b & 1) ans = 1ll * ans * a % mod;
return ans;
}
int main(){
read(n), read(m), read(mod);
int all = 1; inv[0] = 1;
for(int i = 1; i <= n; i++){
all = 1ll * all * i % mod;
js[i] = all;
inv[i] = Pow(all, mod - 2);
}
int res1 = 0;
for(int i = 0; i <= m; i++) f[0][i][0] = 1;
for(int j = 1; j <= m; j++)
for(int i = 1; i <= n; i++)
for(int k = 0; k <= n; k++)
for(int p = 0; p <= i && k - p * j >= 0; p++){
(f[i][j][k] += 1ll * f[i-p][j-1][k-p*j] * inv[p] % mod) %= mod;
}
// cout << f[1][2][2] << " " << f[1][1][1] << endl;
for(int a = 1; a <= m; a++)
for(int i = 1; i < n; i++){
int sum = 0, tmp = 0;
for(int j = 1; j + i <= n; j++)
for(int k = 1; k < i; k++)
(tmp += 1ll * f[j][m/a][k] * inv[n-i-j] % mod) %= mod;
for(int b = 1; b <= m / a; b++)
for(int j = 1; j + i <= n; j++)
for(int k = 0; k + b + 2 <= i && k < i; k++)
(sum += 1ll * (f[j][b][k] - f[j][b-1][k] + mod) * inv[n-i-j] % mod) %= mod;
sum = 1ll * sum * js[n] % mod * inv[i] % mod;
tmp = 1ll * tmp * js[n] % mod * inv[i] % mod;
// cout << a << " " << i << " " << sum << " " << tmp << endl;
res1 = (res1 + tmp) % mod;
res1 = (res1 - sum + mod) % mod;
}
res1 = 2ll * res1 % mod;
// cout << res1 << endl;
dp[0][0] = 1;
for(int i = 1; i <= n; i++)
for(int s = 0; s <= 2 * i * m; s++)
for(int j = 0; j <= 2 * m && j <= s; j++)
(dp[i][s] += dp[i-1][s-j]) %= mod;
int res2 = dp[n][n*m];
//case 2: only positive or only negative
int res3 = 2ll * m * n % mod;
//case 3: all zero
int res = (res1 + res2 + res3) % mod;
int ans = 1;
// cout << res << endl;
for(int i = 1; i <= n; i++) ans = 1ll * (2 * m + 1) * ans % mod;
cout << ((ans - res) % mod + mod) % mod << endl;
return 0;
}
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Test #1:
score: 100
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memory: 5684kb
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memory: 21204kb
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Test #3:
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memory: 5556kb
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Test #4:
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time: 127ms
memory: 21144kb
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memory: 57924kb
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