Farey Sequence（poj2478）

最新推荐文章于 2020-07-17 07:59:37 发布

csu__zhouyi

最新推荐文章于 2020-07-17 07:59:37 发布

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分类专栏：数论文章标签： ACM c++ 数论欧拉函数

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本文详细介绍了如何利用欧拉函数计算费尔数列中项数的方法，并通过AC代码展示了解题过程。欧拉函数在解决费尔数列问题中扮演关键角色，代码实现简洁高效。

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题目：

Description

The Farey Sequence Fn for any integer n with n >= 2 is the set of irreducible rational numbers a/b with 0 < a < b <= n and gcd(a,b) = 1 arranged in increasing order. The first few are
F2 = {1/2}
F3 = {1/3, 1/2, 2/3}
F4 = {1/4, 1/3, 1/2, 2/3, 3/4}
F5 = {1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5}

You task is to calculate the number of terms in the Farey sequence Fn.

Input

There are several test cases. Each test case has only one line, which contains a positive integer n (2 <= n <= 10⁶). There are no blank lines between cases. A line with a single 0 terminates the input.

Output

For each test case, you should output one line, which contains N(n) ---- the number of terms in the Farey sequence Fn.

Sample Input

Sample Output

一道直接运用欧拉公式就可以做出来的水题：

以下是ac代码：

#include<iostream>
using namespace std;
#define LL long long
LL sum[1000000+50]={0};LL ol[1000000+50]={0};
int main()
{
    int k,n;
    //欧拉函数打表

        ol[1]=1;
        for(int i=2;i<1000000+50;i++)
            if(!ol[i])
                for(int j=i;j<1000000+50;j+=i)
                {
                    if(!ol[j]) ol[j]=j;
                    ol[j]=ol[j]/i*(i-1);
                }
    sum[2]=ol[2];
    for(int i=3;i<1000000+50;i++)
    {
        sum[i]=sum[i-1]+ol[i];
    }

    while(cin>>n)
    {
        if(!n) break;
        cout<<sum[n]<<endl;
    }

    return 0;
}