uva 11609 组合数学

#include <iostream>#include <cstdlib>#include <cstdio>const int MOD = 1000000007;typedef long long ll;using namespace std;ll N, T;ll spow(ll x, ll n ){    if ( n == 0LL ) return 1LL;    if ( n == 1LL ) return x % MOD;    ll v = spow( x, n / 2LL );    if ( n % 2LL == 1LL )        return ((v * v) % MOD * x) % MOD;    else return (v * v) % MOD;}int main(){    while ( cin >> T )        for ( int t = 1 ; t <= T ; ++ t )        {            cin >> N;            printf("Case #%d: %lld\n", t, spow(2LL, N - 1LL)*N % MOD);        }    return 0;}

题意: 给出n个人, 从中选出k个人作为player, 每种组合都会有一个队长(captain), 同样的player, 只要队长不同那就算是不同的组合.


解题思路:1. sum( C(n, k)*C(k, 1) ) = sum( C(n, 1)*C(n-1, k-1) ) = n*sum( C(n-1, k-1) ) = n*2^(n-1);