Text Diff Algorithms: How Myers Diff Powers Modern Version Control

Finding Differences in Text

Whether reviewing a GitHub pull request, resolving database schema migrations, or checking revisions in a legal contract, comparing two versions of a document is an essential daily workflow.

At its core, a diff tool must solve the Longest Common Subsequence (LCS) problem: given sequence A and sequence B, what is the longest sequence of lines or characters that appears in both in the same relative order?

Eugene Myers' O(ND) Algorithm

In 1986, Eugene W. Myers published "An O(ND) Difference Algorithm and Its Variations." This algorithm powers Git diff, GNU diff, and modern browser text comparison utilities.

By searching along diagonals of constant difference, Myers' algorithm finds the minimal edit script in time proportional to the total number of differences, making it blazingly fast when comparing versions with few changes.