Quick Review of KMP Algorithm

Sat, 02 May 2020 23:40:40 -0700

Published in 1977, the Knuth-Morris-Pratt algorithm can search substring pattern in time linear to the total string length. Recently I encountered 2 Leetcode questions (1367, 1392) that can be effectively solved by KMP, and therefore want to use this post as a quick refresher and go through the basic mechanism and some concrete examples of this algorithm. (A nice video explanation of KMP can be found here

Intuition

In a naive substring search approach, when we find a mismatch between the pattern and the string, we shift the pattern by 1 character to start a new round of comparison (in the example below, we shift the starting B to index 1 after we detect the mismatch at index 4). But we already know the portion before C in the pattern, and we know that we’re gonna compare BAAAA against AAACB.... This means we are doing some kind of “backup” after a mismatch. KMP avoids this backup by using deterministic finite state machine, which will be shown in detail in next section.

Algorithm on Kailun's Blog

Quick Review of KMP Algorithm

Intuition