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ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#774185 | #9782. NonZero PrefSuf Sums | ucup-team3510# | AC ✓ | 42ms | 12744kb | C++20 | 2.5kb | 2024-11-23 12:18:48 | 2024-11-23 12:18:54 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 105;
int mod;
int F[N][N * N], sum[N * N];
int G[N][N][N];
int C[N][N], fac[N], inv[N], Inv[N];
bool vis[N];
int ans[N];
int qpow(int x, int y)
{
int ans = 1;
while(y)
{
if(y & 1)
ans = (ll)ans * x % mod;
x = (ll)x * x % mod;
y >>= 1;
}
return ans;
}
void prep(int n)
{
int i, j;
fac[0] = 1;
for(i = 1; i <= n; i++)
fac[i] = (ll)fac[i - 1] * i % mod;
inv[n] = qpow(fac[n], mod - 2);
for(i = n; i >= 1; i--)
inv[i - 1] = (ll)inv[i] * i % mod;
for(i = 0; i <= n; i++)
{
C[i][0] = 1;
for(j = 1; j <= i; j++)
C[i][j] = (C[i - 1][j] + C[i - 1][j - 1]) % mod;
}
}
void calc(int n, int m, int l, int r)
{
int i, j;
for(i = 0; i <= m; i++)
F[0][i] = 0;
F[0][0] = 1;
for(i = 1; i <= n; i++)
{
for(j = 0; j <= m; j++)
F[i][j] = 0;
sum[0] = F[i - 1][0];
for(j = 1; j <= m; j++)
sum[j] = (sum[j - 1] + F[i - 1][j]) % mod;
for(j = 0; j <= m; j++)
{
if(j >= l)
F[i][j] = sum[j - l];
if(j > r)
F[i][j] = (F[i][j] + mod - sum[j - r - 1]) % mod;
}
}
}
int f(int n, int m)
{
if(vis[m])
return ans[m];
int i, j, k, tmp = 0;
for(k = 1; k <= m; k++)
{
for(i = 1; i <= n; i++)
for(j = 0; j < n - i; j++)
{
int awa = G[k][n - i - j][i - 1];
if(i >= 2 + k)
awa = (awa + mod - G[k][n - i - j][i - k - 2]) % mod;
tmp = (tmp + (ll)awa * fac[n] % mod * inv[i] % mod * inv[j] % mod * inv[n - i - j]) % mod;
// if(k == 3)
// printf("EE%d %d %d\n", i, j, (ll)awa * fac[n] % mod * inv[i] % mod * inv[j] % mod * inv[n - i - j] % mod);
}
}
tmp = 2ll * tmp % mod;
vis[m] = 1;
return ans[m] = tmp;
}
int main()
{
int n, m, i, j, k, ans = 0;
scanf("%d%d%d", &n, &m, &mod);
prep(100);
if(n == 1)
{
printf("%d\n", 2 * m % mod);
return 0;
}
for(i = 1; i <= m; i++)
{
calc(n, n, 1, i);
for(j = 1; j <= n; j++)
{
memcpy(G[i][j], F[j], sizeof(G[i][j]));
for(k = 1; k <= n; k++)
G[i][j][k] = (G[i][j][k - 1] + G[i][j][k]) % mod;
}
}
for(i = m; i >= 1; i--)
{
for(j = 1; j <= n; j++)
for(k = 0; k <= n; k++)
G[i][j][k] = (G[i][j][k] + mod - G[i - 1][j][k]) % mod;
}
for(i = 1; i <= m; i++)
ans = (ans + f(n, m / i)) % mod;
ans = (ans + 2ll * n * m) % mod;
calc(n, m * n, 0, 2 * m);
ans = (F[n][n * m] + ans) % mod;
ans = (qpow(2 * m + 1, n) + mod - ans) % mod;
printf("%d\n", ans);
return 0;
}
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Test #1:
score: 100
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time: 0ms
memory: 5888kb
input:
2 1 998244353
output:
2
result:
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Test #2:
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memory: 10936kb
input:
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output:
378553557
result:
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memory: 5924kb
input:
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output:
2
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Test #4:
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memory: 11132kb
input:
69 42 696969697
output:
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result:
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memory: 10700kb
input:
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output:
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memory: 7948kb
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Test #32:
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