poj1961 kmp失效函数的运用

Period

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 AK ,that is A concatenated K times, for some string A. Of course, we also want to know the period K.
Input

The input 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

思路：根据失效函数的定义，对于前i个字符来说，如果这i个字符组成一个周期串，那么i-f[i]必定是一个循环节而且是最大的循环节。

#include <iostream>#include <algorithm>#include <cstring>#include <cstdio>using namespace std;char ch[1001000];int f[1001000];void getfail(char* p,int* f){    int m = strlen(p);    f[0] = 0;f[1] = 0;    for (int i = 1; i<m; i++) {        int j = f[i];        while (j&&p[i]!=p[j]) {            j = f[j];        }        f[i+1] = p[i] == p[j]?j+1:0;    }}int main(){    int n;    int kase = 1;    while (scanf("%d",&n)&&n) {        printf("Test case #%d\n",kase++);        scanf("%s",ch);        getfail(ch, f);        int len = strlen(ch);        for (int i = 2; i<=len; i++) {            if (f[i]&&i%(i-f[i]) == 0) {                printf("%d %d\n",i,i/(i-f[i]));            }        }        cout<<endl;    }}