UVAlive 3026 Period [KMP]

Period

Time Limit: 3000MS

64bit IO Format: %lld & %llu

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 AK, 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 ≤ 1000000) 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

Sample Output

Test case #1

2 2

3 3

Test case #2

2 2

6 2

9 3

12 4

通過fail數組找循環節

錯位部分為 i - fail(i) ， 那麼當 k * ( i - fail(i) ) == i 時， 找到循環

但是要注意判斷要從1開始， 否則面臨整數被0除！！

并且一直要循環到 lens 處 ， 因為 get_fail 時是推到了 i+1 項的！！！ 一定要注意！！！！ 了解算法細節！！！

另外每組之間一行 ‘\n’

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<cmath>
#include<vector>
#include<queue>
#include<stack>
#include<map>
#include<set>
#include<string>
#include<iomanip>
#include<ctime>
#include<climits>
#include<cctype>
#include<algorithm>
#ifdef WIN32
#define AUTO "%I64d"
#else
#define AUTO "%lld"
#endif
using namespace std;
#define smax(x,tmp) x=max((x),(tmp))
#define smin(x,tmp) x=min((x),(tmp))
#define maxx(x1,x2,x3) max(max(x1,x2),x3)
#define minn(x1,x2,x3) min(min(x1,x2),x3)
const int INF=;
const int maxn = ;
char s[maxn];
int lens;
int fail[maxn];
void get_fail(char s[],int lens)
{
    memset(fail,,sizeof(fail));
    fail[] = ; fail[] = ;
    for(int i=;i<lens;i++)
    {
        int root = fail[i];
        while(root && s[root]!=s[i]) root = fail[root];
        fail[i+] = s[root]==s[i]? root+ : ;
    }
}
int main()
{
    freopen("period.in","r",stdin);
    freopen("period.out","w",stdout);
    int cas = ;
    while(~scanf("%d",&lens) && lens)
    {
        scanf("%s",s);
        get_fail(s,lens);
        printf("Test case #%d\n",++cas);
        for(int i=;i<=lens;i++) // from 1 or divided by 0
            if(i%(i-fail[i])==)
            {
                int k = i / (i-fail[i]);
                if(k<=) continue;
                printf("%d %d\n",i,k);
            }
        printf("\n");
    }
    return ;
}