hdu 1358 Period(kmp)

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

aaa

aabaabaabaab

Sample Output

Test case #1

2 2 3 3

Test case #2

2 2 6 2 9 3 12 4

题意：找每个前缀的最小循环节，如果有就输出位置和循环次数

思路:kmp

#include <cstdio>
#include <map>
#include <iostream>
#include<cstring>
#include<bits/stdc++.h>
#define ll long long int
#define M 6
using namespace std;
inline ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
inline ll lcm(ll a,ll b){return a/gcd(a,b)*b;}
int moth[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};
int dir[4][2]={1,0 ,0,1 ,-1,0 ,0,-1};
int dirs[8][2]={1,0 ,0,1 ,-1,0 ,0,-1, -1,-1 ,-1,1 ,1,-1 ,1,1};
const int inf=0x3f3f3f3f;
const ll mod=1e9+7;
int nextt[1000007];
void getnext(string s){
    nextt[1]=0; int len=s.length();
    for(int i=2,j=0;i<=len;i++){
        while(j>0&&s[i-1]!=s[j]) j=nextt[j];
        if(s[i-1]==s[j]) j++;
        nextt[i]=j;
    }
}
int main(){
    ios::sync_with_stdio(false);
    int n;
    int cnt=0;
    while(cin>>n&&n){
        string s;
        cin>>s;
        getnext(s);
        int len=s.length();
        cout<<"Test case #"<<++cnt<<endl; 
        for(int i=2;i<=len;i++){
                if(nextt[i]==0) continue;
                int t=i-nextt[i];
                if(i%t==0){
                    cout<<i<<" "<<i/t<<endl;
                }
        }
        cout<<endl;
    }
    return 0;
}

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