[bzoj4766]文艺计算姬——完全二分图生成树个数

Brief Description

求\(K_{n,m}\)

Algorithm Design

首先我们有(Matrix Tree)定理，可以暴力生成几组答案，发现一些规律：

\[K_{n,m} = n^{m-1} * m^{n-1}
\]

然而直接乘法会爆longlong，所以使用快速乘

Code

#include <cstdio>
#define ll long long
ll n, m, p;
inline ll mul(ll a, ll b) {
  ll x = 0;
  while (b) {
    if (b & 1)
      x = (x + a) % p;
    a = (a << 1) % p;
    b >>= 1;
  }
  return x;
}
inline ll pow(ll a, ll b, ll p) {
  ll x = 1;
  while (b) {
    if (b & 1)
      x = mul(x, a);
    a = mul(a, a);
    b >>= 1;
  }
  return x;
}
int main() {
  scanf("%lld %lld %lld", &n, &m, &p);
  if (n == 0 || m == 0) {
    printf("0\n");
    return 0;
  }
  printf("%lld\n", mul(pow(n, m - 1, p), pow(m, n - 1, p)));
  return 0;
}