HDU5363 Key Set【快速模幂】

Key Set

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)
Total Submission(s): 2757    Accepted Submission(s): 1380

 

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.

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Sample Input

4 1 2 3 4

 

Sample Output

0 1 3 7

问题链接：HDU5363 Key Set

问题描述：（略）

问题分析：

  可以根据组合计算推导出f(n)=2^(n-1)-1。使用快速模幂计算即可。

程序说明：（略）

参考链接：（略）

题记：（略）

AC的C++语言程序如下：

/* HDU5363 Key Set */

#include <iostream>

using namespace std;

typedef long long LL;

const LL MOD = 1000000007;

// 快速模幂
LL powmod(LL x, LL n, LL m)
{
    LL result = 1;
    for(; n; n>>=1) {
        if(n & 1) {
            result *= x;
            result %= m;
        }
        x *= x;
        x %= m;
    }

    return result;
}

int main()
{
    int t;
    scanf("%d", &t);
    while(t--) {
        LL n;

        scanf("%lld", &n);

        printf("%lld\n", powmod(2, n- 1, MOD) - 1);
    }

    return 0;
}