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  • Happy 2006 欧几里得定理

    Happy 2006
    Time Limit: 3000MS   Memory Limit: 65536K
    Total Submissions: 11956   Accepted: 4224

    Description

    Two positive integers are said to be relatively prime to each other if the Great Common Divisor (GCD) is 1. For instance, 1, 3, 5, 7, 9...are all relatively prime to 2006. 

    Now your job is easy: for the given integer m, find the K-th element which is relatively prime to m when these elements are sorted in ascending order. 

    Input

    The input contains multiple test cases. For each test case, it contains two integers m (1 <= m <= 1000000), K (1 <= K <= 100000000).

    Output

    Output the K-th element in a single line.

    Sample Input

    2006 1
    2006 2
    2006 3
    

    Sample Output

    1
    3
    5
    

    Source

     

     

    周期性!

    #include<iostream>
    #include<cstdio>
    #include<algorithm>
    #include<cstring>
    using namespace std;
    typedef long long LL;
    #define MAXN 1000002
    /*
    要求找到与m互质的第k大的数字
    gcd(a,b) = gcd(b*t+a,b)
    */
    LL a[MAXN];
    LL gcd(LL a,LL b)
    {
        if(b==0)
            return a;
        return gcd(b,a%b);
    }
    int main()
    {
        LL m,k;
        while(scanf("%lld%lld",&m,&k)!=EOF)
        {
            LL p=0;
            for(int i=1;i<=m;i++)
            {
                if(gcd(i,m)==1)
                    a[++p] = i;
            }
            if(k%p==0)
                printf("%lld
    ",(k/p-1)*m+a[p]);
            else
                printf("%lld
    ",(k/p)*m+a[k%p]);
        }
    }
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  • 原文地址:https://www.cnblogs.com/joeylee97/p/6661844.html
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