【KMP】Period

KMP算法

Next[]函数深入理解，Next[]当前字符前匹配字符数，串长n-Next[i]=串内循环子串的长度p。

本题求子循环串内循环节数。

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

 

#include<iostream>
#include<stdio.h>
using namespace std;

char s[1000001];
int Next[1000001];

void getNext(int n){
    int i=0,j=-1;
    Next[0]=-1;
    while(i<n){
        if(j==-1||s[i]==s[j]){
            i++;j++;
            Next[i]=j;
        }
        else j=Next[j];
    }
}

int main()
{
    int n,k,t=1,p;
    //freopen("pe.txt","r",stdin);
    while(cin>>n&&n>1&&n<1000001){
        cin>>s;
        getNext(n);
        cout<<"Test case #"<<t++<<endl;
        for(k=2;k<=n;k++){
            p=k-Next[k];        //循环节的长度
            if(k%p==0&&k/p>1)
                cout<<k<<' '<<k/p<<endl;    //若字符串由循环节构成，第k个字母前完整循环节数
        }
        cout<<endl;
    }
    return 0;
}