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AiTechWorlds
AiTechWorlds
Animate the 0/1 Knapsack 2D DP table maximizing value within a weight capacity, with synced code.
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | |
|---|---|---|---|---|---|---|---|---|
| — | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| item1 (w1,v1) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| item2 (w3,v4) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| item3 (w4,v5) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| item4 (w5,v7) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
def knapsack(wt, val, W):
n = len(wt)
dp = [[0] * (W + 1) for _ in range(n + 1)]
for i in range(1, n + 1):
for w in range(W + 1):
dp[i][w] = dp[i-1][w]
if wt[i-1] <= w:
dp[i][w] = max(dp[i][w], dp[i-1][w-wt[i-1]] + val[i-1])
return dp[n][W]The 0/1 Knapsack problem maximizes total value within a weight capacity, choosing whole items. The 2D table dp[i][w] is the best value using the first i items within capacity w.
| Time | O(n × W) |
| Space | O(n × W) |
The 0/1 Knapsack Visualizer animates the 2D dynamic programming solution that maximizes total value within a weight capacity, choosing whole items. dp[i][w] is the best value using the first i items within capacity w, computed as max of skipping or taking item i. It runs in O(n × W) time and space.
Press Play
Watch the 2D table fill row by row as each item is considered.
Step through
Use Step Forward/Back or the timeline to see the take-vs-skip decision per cell.
Read the code
View the Knapsack DP in C++, Java, Python, or JavaScript and copy it.
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Last reviewed on June 14, 2026 by the AiTechWorlds Tools Team. All processing runs locally in your browser.