Uva 11609 - Teams 解题报告（组合数学）

Problem E
Teams

Input: Standard Input

Output: Standard Output

 

In a galaxy far far away there is an ancient game played among the planets. The specialty of the game is that there is no limitation on the number of players in each team, as long as there is a captain in the team. (The game is totally strategic, so sometimes less player increases the chance to win). So the coaches who have a total of N players to play, selects K (1 ≤ K ≤ N) players and make one of them as the captain for each phase of the game. Your task is simple, just find in how many ways a coach can select a team from hisN players. Remember that, teams with same players but having different captain are considered as different team.

 

Input

 

The first line of input contains the number of test cases T ≤ 500. Then each of the next T lines contains the value ofN (1 ≤ N ≤ 10^9), the number of players the coach has.

 

Output

 

For each line of input output the case number, then the number of ways teams can be selected. You should output the result modulo 1000000007.

 

For exact formatting, see the sample input and output.

 

 

 

Sample Input                                                                               Output for Sample Input

3

1

2

3

Case #1: 1

Case #2: 4

Case #3: 12

 

 

Problem Setter: Towhidul Islam Talukdar

Special Thanks: Md. Arifuzzaman Arif

    解题报告：大水题。先从n个人中选出冠军，一共n种选法。其他人在或者不在，都是两种情况，一共2^(n-1)种情况。二分快速幂一下。代码如下：

#include <cstdio>#include <cstring>#include <algorithm>using namespace std;const int mod = 1000000007;typedef long long LL;LL powMod(LL a, LL b){    LL res=1;    while(b)    {        if(b&1)            res = res*a%mod;        a=a*a%mod;        b>>=1;    }    return res;}int cas=1;void work(){    int n;    scanf("%d",&n);    printf("Case #%d: %lld\n", cas++, powMod(2, n-1)*n%mod);}int main(){    int T;    scanf("%d",&T);    while(T--)        work();}