Period

describe

For each prefix of a given string S with N characters (each character has an ASCII code between 97 and 126, inclusive), we want to know whether the prefix is a periodic string. That is, for each i (2 <= i <= N) we want to know the largest K > 1 (if there is one) such that the prefix of S with length i can be written as A^K ,that is A concatenated K times, for some string A. Of course, we also want to know the period K.

enter

The input consists of several test cases. Each test case consists of two lines. The first one contains N (2 <= N <= 1 000 000) : the size of the string S.The second line contains the string S. The input file ends with a line, having the number zero on it.

output

For each test case, output "Test case #" and the consecutive test case number on a single line; then, for each prefix with length i that has a period K > 1, output the prefix size i and the period K separated by a single space; the prefix sizes must be in increasing order. Print a blank line after each test case.

sample input

aaa
12
aabaabaabab
0

Sample output

Test case #1
2 2
3 3

Test case #2
2 2
6 2
9 3
12 4

Problem- solving idea: find the cyclic substring of the given string prefix (only output when the number of cyclic substrings is greater than 1)

#include <iostream>
#include <cstring>
#include <cstdio>
using namespace std;
#define N 1000005
#define N 1000005
int next[N];
char s[N];
int slen;
void getNext()
{
    int j=0,k=-1;
    next[0] = -1;
    while(j < slen)
       {
            if(k == -1 || s[j] == s[k])
            next[++j] = ++k;
            else
            k = next[k];
       }
} //KMP array processing
intmain ()
{
    int t=0;
    while(cin>>slen,slen!=0)
    {
        scanf("%s",s);
        cout<<"Test case #"<<++t<<endl;
        getNext();
        int l=1;
        for(int i=2;i<=slen;i++)
        {
            if (i%(i-next[i])== 0 ) //Only when the remainder is 0, it means that there is a cyclic substring
           {
                l =i/(i- next[i]); //The maximum number of loop substrings that can be divided into
                 if (l!= 1 )
                cout<<i<<" "<<l<<endl;
           }
        }
        cout<<"\n";
    }

}

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