HDU 5363 Key Set（快速幂取模）

 

 

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

 

 

题意：给你一个元素为1到n的集合S，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。

  

题解：我们知道偶数＋偶数＝偶数，奇数＋奇数＝偶数，假设现在有ａ个偶数，ｂ个奇数。则

 

 

根据二项式展开公式可得2^n-1。最后的结果还需减去

即空集的情况，因为题目要求非空子集，所以最终结果为2^n-1-1。

 

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
const int mod = 1e9 + 7;
long long power(long long n, long long m, long long mod)
{
    long long sum = 1;
    n %= mod;
    while (m){
       if (m % 2)
        sum = sum * n % mod;
       n = n * n % mod;
       m /= 2;
    }
    return sum;
}
int main()
{
    int t;
    scanf("%d",&t);
    while (t--){
        long long n;
        scanf("%I64d", &n);
        long long sum = power(2, n-1, mod) - 1;
        printf("%I64d\n",sum);
    }
    return 0;
}