Finding shortest repeating cycle in word?

Question

I'm about to write a function which, would return me a shortest period of group of letters which would eventually create the given word.

For example word abkebabkebabkeb is created by repeated abkeb word. I would like to know, how efficiently analyze input word, to get the shortest period of characters creating input word.

Answer 1

Here is a correct O(n) algorithm. The first for loop is the table building portion of KMP. There are various proofs that it always runs in linear time.

Since this question has 4 previous answers, none of which are O(n) and correct, I heavily tested this solution for both correctness and runtime.

def pattern(inputv):
    if not inputv:
        return inputv

    nxt = [0]*len(inputv)
    for i in range(1, len(nxt)):
        k = nxt[i - 1]
        while True:
            if inputv[i] == inputv[k]:
                nxt[i] = k + 1
                break
            elif k == 0:
                nxt[i] = 0
                break
            else:
                k = nxt[k - 1]

    smallPieceLen = len(inputv) - nxt[-1]
    if len(inputv) % smallPieceLen != 0:
        return inputv

    return inputv[0:smallPieceLen]

Answer 2

This is an example for PHP:

<?php
function getrepeatedstring($string) {
    if (strlen($string)<2) return $string;
    for($i = 1; $i<strlen($string); $i++) {
        if (substr(str_repeat(substr($string, 0, $i),strlen($string)/$i+1), 0, strlen($string))==$string)
            return substr($string, 0, $i);
    }
    return $string;
}
?>