Longest Increasing Subsequence

Craige Schensted (tableaux) / classical LIS, 1961

The longest increasing subsequence problem has classical roots including Schensted’s work on Young tableaux (1961) and the standard patience-sorting viewpoint. This visualization runs the textbook double loop: for each ending index, it looks back at smaller values, maintains a bar chart of the input for intuition, and fills a dp row where dp[k] is the best length ending at k. Gold marks the active cell, teal shows settled values, and coral highlights entries that reach the optimal length.