hdu5894hannnnah_j’s Biological Test

链接：http://acm.hdu.edu.cn/showproblem.php?pid=5894

题意：有n个座位（环），求m个人坐上去且两个人相隔至少k个空座位的方案数。

分析：先确定1个人的位置，那么剩下的就是C(n-m*k-1,m-1)，那么有n*C(n-m*k-1,m-1)种方案然后/m去掉重复的。

代码：

#include<map>#include<set>#include<cmath>#include<queue>#include<bitset>#include<math.h>#include<vector>#include<string>#include<stdio.h>#include<cstring>#include<iostream>#include<algorithm>#pragma comment(linker, "/STACK:102400000,102400000")using namespace std;const int N=1000010;const int M=50010;const int mod=1000000007;const int MOD1=1000000007;const int MOD2=1000000009;const double EPS=0.00000001;typedef long long ll;const ll MOD=1000000007;const int INF=1000000010;const ll MAX=1ll<<55;const double eps=1e-5;const double inf=~0u>>1;const double pi=acos(-1.0);typedef double db;typedef unsigned int uint;typedef unsigned long long ull;ll inv[N];ll C(ll n,ll m) {    if (m>n) return 0;    ll ret=1;    m=min(m,n-m);    for (int i=1;i<=m;i++) (ret*=(n-i+1)*inv[i]%MOD)%=MOD;    return ret;}int main(){    int t;    ll n,m,k;    inv[1]=1ll;    for (int i=2;i<N;i++)    inv[i]=(MOD-MOD/i)*inv[MOD%i]%MOD;    scanf("%d", &t);    while (t--) {        scanf("%lld%lld%lld", &n, &m, &k);        if (m==1) printf("%lld\n", n);        else printf("%lld\n", (C(n-m*k-1,m-1)*n%MOD)*inv[m]%MOD);    }    return 0;}