poj 2406 Power Strings（连续重复子串）

Power Strings

Time Limit: 3000MS		Memory Limit: 65536K
Total Submissions: 33469		Accepted: 13902

Description

Given two strings a and b we define a*b to be their concatenation. For example, if a = "abc" and b = "def" then a*b = "abcdef". If we think of concatenation as multiplication, exponentiation by a non-negative integer is defined in the normal way: a^0 = "" (the empty string) and a^(n+1) = a*(a^n).

Input

Each test case is a line of input representing s, a string of printable characters. The length of s will be at least 1 and will not exceed 1 million characters. A line containing a period follows the last test case.

Output

For each s you should print the largest n such that s = a^n for some string a.

Sample Input

abcd
aaaa
ababab
.

Sample Output

1
4
3

Hint

This problem has huge input, use scanf instead of cin to avoid time limit exceed.

题意：给定一个字符串L，已知这个字符串是由某个字符串S 重复R 次而得到的，
求R 的最大值。
思路：穷举字符串S 的长度k，然后判断是否满足。判断的时候，先看字符串L 的长度能否被k 整除，再看suffix(1)和suffix(k+1)的最长公共前缀是否等于n-k。在询问最长公共前缀的时候，suffix(1)是固定的，所以RMQ问题没有必要做所有的预处理， 只需求出height 数组中的每一个数到height[rank[1]]之间的最小值即可。整个做法的时间复杂度为O(n)。