Longest Common Subsequence
In plain terms
Finding the longest sequence common to two strings, preserving order.
Going deeper
LCS identifies the longest subsequence (not necessarily contiguous) appearing in both inputs in the same order. It's solved with dynamic programming.
Under the hood
O(m·n) DP; underlies diff tools and bioinformatics sequence alignment.
Examples
Diff/version control, DNA alignment, plagiarism detection, spell suggestion.
Think of it like...
Like finding the longest shared storyline between two slightly different movie cuts.