Find the smallest period of input string in O(n)?

Question

Given the following problem :

Definition :

Let S be a string over alphabet Σ .S\' is the smallest period of S

Answer 1

This problem can easily be solved by KMP

• Concatenate the string to itself and run KMP on it.
• Let n be the length of the original string.
• Search for the first value >= n in the KMP array. That value must be at a position k >= n (0-based).
• Then k - n + 1 is the length of the shortest period of the string.

Example:

Original string = abaaba
n = 6
New string = abaabaabaaba
KMP values for this new string: 0 0 1 1 2 3 4 5 6 7 8 9

The first value >= n is 6 which is at position 8. 8 - 6 + 1 = 3 is the length of the shortest period of the string (aba).