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

通过fail数组找循环节

错位部分为 i - fail(i) ， 那么当 k * ( i - fail(i) ) == i 时， 找到循环

但是要注意判断要从1开始， 否则面临整数被0除！！

并且一直要循环到 lens 处 ， 因为 get_fail 时是推到了 i+1 项的！！！ 一定要注意！！！！ 理解算法细节！！！

另外每组之间一行 ‘\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 ;
}