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;
}