# poj 1961 Period(kmp最短循环节)

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.……………………

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。

```//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;
f = 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;
}
```

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