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.……………………
题意：
给定一个长度为n的字符串s，求他每个前缀的最短循环节。换句话说，对于每个i（2<=i<=n），求一个最大的整数k（如果k存在），使得s的前i个字符可以组成的前缀是某个字符串重复k次得到的。输出所有存在K的i和对应的k。
这是刘汝佳《算法竞赛入门经典训练指南》上的原题（p213），用KMP构造状态转移表。
解题代码（完全参照白书）：
//poj 1961 #include <stdio.h> const int maxn = 1000000 + 10; char p[maxn]; int f[maxn]; int main() { int n, t = 1; while (scanf("%d",&n) && n) { scanf("%s",p); f[0] = 0; f[1] = 0; for (int i = 1; i < n; i++) { int j = f[i]; while (p[i] != p[j] && j) j = f[j]; f[i+1] = (p[i] == p[j] ? j+1 : 0); }/*这段代码就是KMP里面核心的代码,这里没有文本串， 我们只需要处理模板即可*/ printf("Test case #%d\n",t++); for (int i = 2; i <= n; i++) { if (f[i] > 0 && i % (i-f[i]) == 0) printf("%d %d\n",i, i / (i-f[i])); } puts(""); } return 0; }
