Recur Table Build

Recur Table Build is a dynamic programming game that teaches the one algorithmic technique most computer science students understand during a lecture and cannot apply the next morning. Dynamic programming is hard to learn from a textbook because the insight it provides is computational rather than conceptual — you have to see the waste before you can appreciate the fix. The game shows you the waste first. A recursive call tree explodes onto the screen, its branches multiplying, the same function calls appearing over and over highlighted in red. For Fibonacci at n=8, the tree has 67 nodes. The same computation done with a DP table has 8. A counter shows the ratio. At n=50 the ratio is ten trillion to one. Then the table appears. A compact grid of cells, base cases pre-filled, the rest empty. For each cell, dependency arrows animate from the cells that contribute to it — from above and to the left for grid problems, from the diagonal and both sides for string problems, from the row above with two choices for the knapsack. The player selects the correct value from three options. The cell fills. The next cell is focused. The table builds. Eight levels introduce four structural types of DP problem. The one-dimensional sequence table, used for Fibonacci, stair climbing, and the coin change problem — which also demonstrates that the greedy algorithm gives the wrong answer for certain coin sets, and shows exactly where and why. The two-dimensional grid table, used for counting paths and maximising treasure — where the player learns to trace the optimal path backward through a completed table. The string alignment table for edit distance, with three arrows per cell representing the three possible operations. And the optimisation table for the knapsack problem, where each cell requires choosing between skipping an item and taking it. Three game modes cover the full workflow. Fill the table by selecting from options. Predict individual values without options, computing the recurrence from memory. Reconstruct the optimal solution by tracing backward through a completed table — the step most explanations skip. After eight levels, the player can identify the recurrence relation in a new DP problem, fill the table correctly, and extract the solution.