Period

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 7535    Accepted Submission(s): 3628

Problem 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 file 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

题意：

求字符串s每个前缀的最短循环节。求一个最大整数k，使得s的前i个字符组成的前缀是某个字符串重复k次得到的，输出i和k。

代码：

//白书213页例题。
#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
char P[1000006];
int n,f[1000006];
int main()
{
    int cas=0;
    while(scanf("%d",&n)&&n){
        scanf("%s",P);
        f[0]=f[1]=0;
        for(int i=1;i<n;i++){
            int j=f[i];
            while(j&&P[i]!=P[j]) j=f[j];
            f[i+1]=(P[i]==P[j]?j+1:0);
        }
        printf("Test case #%d\n",++cas);
        for(int i=2;i<=n;i++)
            if(f[i]!=0&&i%(i-f[i])==0) printf("%d %d\n",i,i/(i-f[i]));
        printf("\n");
    }
    return 0;
}