1094: Round And Round We Go

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本文介绍了一种用于检测特定整数是否为循环数的算法。循环数是指当乘以1到其位数之间的任意整数时，其数字序列形成循环的整数。文章详细解释了循环数的概念，并提供了一个具体的实现案例。

1094: Round And Round We Go

Result	TIME Limit	MEMORY Limit	Run Times	AC Times	JUDGE
	3s	8192K	620	292	Standard

A cyclic number is an integer n digits in length which, when multiplied by any integer from 1 to n, yields a “cycle” of the digits of the original number. That is, if you consider the number after the last digit to “wrap around” back to the first digit, the sequence of digits in both numbers will be the same, though they may start at different positions.

For example, the number 142857 is cyclic, as illustrated by the following table:

Write a program which will determine whether or not numbers are cyclic. The input file is a list of integers from 2 to 60 digits in length. (Note that preceding zeros should not be removed, they are considered part of the number and count in determining n. Thus, “01” is a two-digit number, distinct from “1” which is a one-digit number.)

Output

For each input integer, write a line in the output indicating whether or not it is cyclic.

Sample Input

142857
142856
142858
01
0588235294117647

Sample Output

142857 is cyclic
142856 is not cyclic
142858 is not cyclic
01 is not cyclic
0588235294117647 is cyclic

This problem is used for contest: 35

#include<iostream>
#include<string>
#include<algorithm>
using namespace std;
const int maxn=1000;
int main()
{
    string str;
    int a[maxn+1];
    while(cin>>str)
    {
        memset(a,0,sizeof(a));
        int len=str.size();
        int l=maxn;
        for(int i=len-1;i>=0;i--)    a[l--]=str[i]-'0';
        for(int i=maxn;i>=0;i--) a[i]*=len+1;
        for(int i=maxn;i>=0;i--)
        {
            if(a[i]>=10)
            {
                a[i-1]+=a[i]/10;
                a[i]%=10;
            }
        }
        int flag=1,k;
        for(k=0;k<=maxn;k++) if(a[k]) break;
        //for(int i=k;i<=maxn;i++) cout<<a[i];cout<<".."<<endl;
        for(int i=k;i<=maxn;i++) if(a[i]!=9) {flag=0;break;}
        if(flag) cout<<str<<" is cyclic"<<endl;
        else cout<<str<<" is not cyclic"<<endl;
    }
    return 0;
}