HDU Problem - 5363 Key Set 【快速幂】

Key Set

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)

Total Submission(s): 1763    Accepted Submission(s): 928

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

 

对于一个有n的元素的集合，组成的非空子集有2^n - 1个，其中和为奇数的个数比和为偶数的个数多一个。注意利用快速幂函数，不要超过了long long。

#include <stdio.h>
__int64 pow(__int64 x, __int64 y) {
    __int64 res = 1;
    __int64 base = x;
    y -= 1;
    while (y) {
        if (y&1) res = base*res%1000000007;
        base = base*base%1000000007;
        y >>= 1;
    }
    return res;
}
int main() {
    int t;
    __int64 n;
    scanf("%d", &t);
    while (t--) {
        scanf("%I64d", &n);
        printf("%I64d\n", pow(2, n) - 1);
    }
    return 0;
}