Weighted Edit Distance: Cost Landscape & Alignment Path

Every pair of strings has a dynamic-programming cost matrix hidden inside it: a grid where cell (i, j) holds the minimum cost to turn the first i characters of one string into the first j characters of the other. This simulator renders that matrix as a real 3D bar landscape, colours each bar by its accumulated cost, and traces the actual optimal alignment path — the exact sequence of insertions, deletions, substitutions and (optionally) adjacent-character transpositions — as a glowing line through the surface. Sliders let you set independent, asymmetric costs for each operation type, and the whole landscape and path recompute live, showing how the cheapest edit sequence bends when one kind of edit becomes more expensive than the others.