hdu 5363 Key Set

最新推荐文章于 2021-10-19 18:21:32 发布

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最新推荐文章于 2021-10-19 18:21:32 发布

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分类专栏：快速幂

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Key Set

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

Total Submission(s): 1857 Accepted Submission(s): 973

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

(1≤T≤105), indicating the number of test cases. For each test case:

The first line contains an integer

(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

Sample Output

Author

zimpha@zju

题意and题解：给出一个数n，集合S中的元素就有n个（1~n)，找出S的所有非空子集中子集元素和为偶数的子集个数！（不理解的多读几遍）。子集个数为2^(n-1)-1个，

怎么求呢？如果直接求肯定超时啊，这就用到了快速幂的方法了，见代码：

<span style="font-family:SimSun;font-size:18px;"><span style="font-family:SimSun;font-size:18px;">#include<cstdio>
#define M 1000000007
int main()
{
    __int64 t,n;
    scanf("%I64d",&t);
    while(t--)
    {
        scanf("%I64d",&n);
        __int64 ans=1,base=2;
        n--;
        while(n)
        {
            if(n&1)
            {
                ans=(ans*base)%M;  //同余定理 
            }
            base=(base*base)%M;
            n=n/2;
        }
        printf("%I64d\n",ans-1);
    }
}</span></span>