HDU 5363 Key Set（2015 Multi-University Training Contest 6）

Key Set

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)
Total Submission(s): 1384    Accepted Submission(s): 761

Problem Description

soda has a set  S  with  n  integers  {1,2,…,n} . A set is called key set if the sum of integers in the set is an even number. He wants to know how many nonempty subsets of  S  are key set.

 

Input

There are multiple test cases. The first line of input contains an integer  T   (1≤T≤105) , indicating the number of test cases. For each test case:

The first line contains an integer  n   (1≤n≤109) , the number of integers in the set.

 

Output

For each test case, output the number of key sets modulo 1000000007.

 

Sample Input

   
   
   
   

    
    
    
    4
1
2
3
4
   
   
   
   

 

Sample Output

   
   
   
   

    
    
    
    0
1
3
7
   
   
   
   

 

Author

zimpha@zju

 

Source

2015 Multi-University Training Contest 6

 题意：给你一个具有n个元素的集合S{1,2,…,n}，问集合S的非空子集中元素和为偶数的非空子集有多少个。

解：答案是2^n-1,用快速幂，不然要超时

#include<stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;
#define LL __int64
const LL mod=1e9+7;
LL quick_mod(LL x,LL n)//快速幂
{
    LL ans=1;
    x=x%mod;
    while(n)
    {
        if(n&1)
            ans=(ans*x)%mod;
        n>>=1;
        x=(x*x)%mod;
    }
    return ans;

}
int main()
{
    LL t;
    scanf("%I64d",&t);
    while(t--)
    {
        LL n;
        scanf("%I64d",&n);
        printf("%I64d\n",quick_mod(2,n-1)-1);
    }
    return 0;
}