想不通之H - Rng HDU - 6574

最新推荐文章于 2020-11-11 23:26:17 发布

原创最新推荐文章于 2020-11-11 23:26:17 发布 · 396 阅读

1 ·

CC 4.0 BY-SA版权

文章标签：

#数学

本文探讨了通过随机生成两个区间并计算它们交集的概率问题。给出了一种算法，该算法利用数学公式和快速幂运算来高效求解。输入为一个整数n，输出为两区间交集概率的特定形式。

Rng

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 262144/262144 K (Java/Others)
Total Submission(s): 227 Accepted Submission(s): 144

Problem Description

Avin is studying how to synthesize data. Given an integer n, he constructs an interval using the following method: he first generates a integer r between 1 and n (both inclusive) uniform-randomly, and then generates another integer l between 1 and r (both inclusive) uniform-randomly. The interval [l, r] is then constructed. Avin has constructed two intervals using the method above. He asks you what the probability that two intervals intersect is. You should print p* q(−1)(MOD 1, 000, 000, 007), while pq denoting the probability.

Input

Just one line contains the number n (1 ≤ n ≤ 1, 000, 000).

Output

Print the answer.

Sample Input

1 2

Sample Output

1 750000006

#include <cstdio>
#include <cstring>
#include <iostream>
#define LL long long

using namespace std;

const LL mod=1e9+7;
int n;

LL ksm(LL a,LL b)
{
	LL ans=1;
	while(b)
	{
		if(b&1) ans=(ans*a)%mod;
		a=(a*a)%mod;
		b=b>>1;	
	}
	return ans;
}

int main(int argc, char const *argv[])
{
	while(scanf("%d",&n)!=EOF)
	{
		LL qwe=(n+1)*ksm(2*n,mod-2)%mod;
		printf("%lld\n",qwe );
	}
	return 0;
}