0/1 Knapsack DP Calculator & Visualizer
Interactive 0/1 Knapsack dynamic programming matrix solver showing DP cell updates, take/skip decisions, and item selection.
0/1 Knapsack Problem
Enter your custom input data → Run the real algorithm engine → Observe step transitions.
⚙️ Customize Algorithm Input Data
Initialized DP table of size (4 x 6) with zeros.
Algorithm state rule requirement
State pointers updated
Mathematical Formula
Overview & Explanation
The 0/1 Knapsack problem determines the maximum value of items that can be packed into a knapsack without exceeding its weight capacity.
How It Works
- Construct a 2D DP matrix of size (n+1) x (W+1).
- For each item i and capacity w, decide to either TAKE or SKIP the item.
- Backtrack through the DP matrix to identify selected items.
Practical Applications
- Resource allocation
- Portfolio investment selection
- Cargo loading
0/1 Knapsack Derivation
Items: (A, W:2, V:3), (B, W:3, V:4), Capacity: 5
Item A
Cap 2..5
Item B
Cap 5: Take 4+dp[1][2]=7 > Skip 3
Result
Max Value
Frequently Asked Questions
What is the time complexity of 0/1 Knapsack DP?
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