The Grid Fills In
Watching a 2-D table compute and then reveal its answer path.
This animation builds the LCS table for two strings laid along the top and left edges of a grid, cell by cell in reading order.
Watch three things at each cell. First, arrows flash back to its three feeder cells — top, left, and diagonal. Those arrows are the recurrence: top means "drop the last character of the left-edge string", left means "drop the last character of the top string", diagonal means "consume both". Second, the character comparison plays out: when the row and column characters match, the diagonal sparkles green and the cell takes diagonal + 1; on a mismatch, the cell simply picks the larger of top and left. Third, the number stamps in, and the heat coloring deepens as values grow toward the bottom-right corner — you can literally see the answer accumulating.
The finale is the part most people never draw by hand: starting from the corner, the backtrack path traces in reverse through the table, stepping diagonally at every match. As it does, the matched characters light up in both strings — the table did not just compute a length, it silently recorded the alignment itself.