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

41234

 

Sample Output

0137

 

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 __int64const 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;}