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Dynamic Programming: Coin Change

Interactive dynamic-programming simulation: watch the minimum-coin-change DP table fill cell by cell (unbounded knapsack recurrence), backtrack the optimal coin multiset, and compare it with the greedy heuristic.

Algorithms & AI3DAdvanced60 FPS

Details

CategoryAlgorithms & AI

RenderingThree.js · WebGL

DifficultyAdvanced

Target FPS60

ControlsCoin-denomination editor (add / remove / edit values, or randomize the set); target-amount slider (3-24); Solve DP button animates the table fill and backtrace; Reset; fill-speed slider; Show greedy toggle compares the greedy heuristic's coin count and multiset against the DP optimum; hover any DP-table bar to read its dp[i][a] value.

Three.jsdynamic programmingcoin changeunbounded knapsackInstancedMeshgreedy algorithm

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⚙ Under the hood

Interactive minimum-coin-change dynamic programming simulation: edit coin denominations, watch the unbounded-knapsack DP table fill cell by cell in 3D with the real dp[i][a] = min(dp[i-1][a], dp[i][a-coin]+1) recurrence, backtrack the optimal coin multiset, and compare it against the greedy heuristic on the classic counterexample where greedy fails.

Three.jsdynamic programmingcoin changeunbounded knapsackInstancedMeshgreedy algorithm

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install