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AiTechWorlds
AiTechWorlds
Watch DP tables fill cell by cell for Fibonacci, LIS, Coin Change, 0/1 Knapsack, and LCS with synced multi-language code.
| F(0) | F(1) | F(2) | F(3) | F(4) | F(5) | F(6) | F(7) | F(8) | F(9) | F(10) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| dp | 0 | 1 | · | · | · | · | · | · | · | · | · |
def fib(n):
dp = [0] * (n + 1)
dp[1] = 1
for i in range(2, n + 1):
dp[i] = dp[i - 1] + dp[i - 2]
return dp[n]The Fibonacci sequence is the classic introduction to dynamic programming: each value is the sum of the previous two, computed bottom-up to avoid the exponential recomputation of naive recursion.
| Time | O(n) |
| Space | O(n) |
The Dynamic Programming Visualizer on AiTechWorlds animates how DP tables fill in cell by cell so you can finally see the subproblem structure behind dynamic programming. DP is one of the most feared interview topics because the recurrence relations are abstract — but watching a table populate makes the overlapping subproblems and optimal substructure obvious. This tool animates classic problems including Fibonacci, longest increasing subsequence (LIS), coin change, 0/1 knapsack, and longest common subsequence (LCS), highlighting the current cell, the cells it depends on, and the final answer path. Synced multi-language code maps each cell update to a line. Everything runs in your browser — AiTechWorlds built this for CS students and interview candidates.
Pick a problem
Choose Fibonacci, LIS, coin change, 0/1 knapsack, or LCS.
Set the inputs
Enter the sequence, amount, or items relevant to the chosen problem.
Run the fill
Press Run to animate the table filling, or step one cell at a time.
Watch dependencies
Each cell highlights the previous cells it is computed from.
Trace the answer
Follow the highlighted path that reconstructs the optimal solution.
100% Private — No Server Required
All processing happens directly in your browser. No data is uploaded, stored, or transmitted to any server.
Last reviewed on June 18, 2026 by the AiTechWorlds Tools Team. All processing runs locally in your browser.
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