W - Period

Time Limit: 3000MS

Memory Limit: 30000KB

64bit IO Format: %I64d & %I64u

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Description

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.

Input

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

3
aaa
12
aabaabaabaab
0

Sample Output

Test case #1
2 2
3 3

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

#include<iostream>
#include<stdio.h>
#include<string.h>
#include<algorithm>

using namespace std;
#define MAXN 1000010
int next[MAXN];
char s[MAXN];
int len;

void get_next()
{
	int i=0;
	int j=-1;
	next[0]=-1;
	while(i<len)
	{
		if(j==-1||s[i]==s[j])
		{
			i++;j++;
			next[i]=j;		//这里如果改用另外一种形式写：if(s[i]!=s[j])
							//								next[i]=next[j];
							//							  else next[i]=j;
							//为什么就不行呢？这里理解不够深刻啊；
		}
		else j=next[j];
	}
}

int main()
{
	int n;
	int i;
	int count=0;
	while(scanf("%d",&n)!=EOF&&n)
	{
		count++;
		scanf("%s",s);
		len=strlen(s);
		get_next();
		printf("Test case #%d\n",count);
		for( i=2;i<=len;i++)
		if((i%(i-next[i]))==0)
         {
             int t=i/(i-next[i]);
             if(t>1)
             printf("%d %d\n",i,t);
         } 
         printf("\n");
     }
	return 0;
}