[HDOJ6114] Chess（组合数）

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=6114

其实就是n*m的格子里放棋子，当前层的棋子必须在上一层的右边，问多少种放法。

其实就是求组合数，注意n m大小。

#include <bits/stdc++.h>
using namespace std;

typedef long long LL;
const LL mod = 1e9+7;
const int maxn = 110000;
int n, m;
LL f[maxn];

void init() {
  f[0] = f[1] = 1;
  for(int i = 2; i < maxn; i++) f[i] = (f[i-1] * i) % mod;
}

LL mul(LL x, LL n) {
  LL ret = 1;
  while(n) {
    if(n & 1) ret = (ret * x) % mod;
    n >>= 1;
    x = (x * x) % mod;
  }
  return ret;
}
LL exgcd(LL a, LL b, LL &x, LL &y) {
  if(b == 0) {
    x = 1;
    y = 0;
    return a;
  }
  else {
    LL ret = exgcd(b, a%b, x, y);
    LL tmp = x;
    x = y;
    y = tmp - a / b * y;
    return ret;
  }
}
LL inv(LL a) {
  LL x, y;
  exgcd(a, mod, x, y);
  return (x % mod + mod) % mod;
}
LL C(LL x, LL y) {
  return f[x] * inv(f[x-y]) % mod * inv(f[y]) % mod;
}

signed main() {
    // freopen("in", "r", stdin);
    init();
    int T;
    scanf("%d", &T);
    while(T--) {
        scanf("%d%d",&n,&m);
        if(n == m) {
            printf("1
");
            continue;
        }
        if(n > m) swap(n, m);
        printf("%I64d
", C(m,n));
    }
    return 0;
}