HDU-2017 多校训练赛8-1011-Killer Names

描述

题解

代码

#include <iostream>

using namespace std;

typedef long long ll;

const int MAXN = 2222;
const int MOD = 1e9 + 7;

int n, m;
int C[MAXN][MAXN];
ll p[MAXN];

ll QPow(ll x, ll n)
{
ll ret = 1;
ll tmp = x % MOD;

while (n)
{
if (n & 1)
{
ret = (ret * tmp) % MOD;
}
tmp = tmp * tmp % MOD;
n >>= 1;
}

return ret;
}

void init()
{
C[0][0] = 1;
for (int i = 1; i < MAXN; i++)
{
C[i][0] = 1;
for (int j = 1; j <= i; j++)
{
C[i][j] = (C[i - 1][j] + C[i - 1][j - 1]) % MOD;
}
}
}

int main(int argc, const char * argv[])
{
init();

int T;
scanf("%d", &T);

while (T--)
{
scanf("%d%d", &n, &m);
for (int i = 1; i <= m; i++)
{
p[i] = QPow(i, n);
}
for (int i = 2; i <= m; i++)
{
for (int j = 1; j < i; j++)
{
p[i] = (p[i] - p[j] * C[i][j] % MOD + MOD) % MOD;
}
}

ll ans = 0;
for (int i = 1; i < m; i++)
{
for (int j = 1, k = m - i; j <= k; j++)
{
ans = (ans + p[i] * p[j] % MOD * C[m][i] % MOD * C[k][j] % MOD) % MOD;
}
}

printf("%lld\n", ans);
}

return 0;
}