hdu 1358 Period ( kmp )

最新推荐文章于 2020-05-06 00:06:21 发布

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#C++ #kmp #字符串

本文介绍了一种算法，用于检测字符串的前缀是否可以被表示为某个基本字符串的重复。通过分析KMP算法中的next数组特性，该算法能够高效地找出所有可能的周期。

Period

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 3497 Accepted Submission(s): 1762

Problem 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.

Input

The input file 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

题目大意:求取一个串的前缀能分解成的最多的循环节的数目

利用kmp中next的性质,next[i]记录的是str[0->i-1]中的前缀和后缀相同的最大值,也就是说如果串是由一个串重复多次生成的话,那么prefix和suffix一定会有重叠部分,只要next[i]!=0,由后缀和前缀相等,而且他们中间只差一个循环节,所以可以根据是否能够整除直接判断是否为循环串

也就是i%(i-next[i]) == 0 ,证明是一个循环串.