CZ
CalcyZone
computer-science Verified Precision Tool

0/1 Knapsack DP Calculator & Visualizer

Interactive 0/1 Knapsack dynamic programming matrix solver showing DP cell updates, take/skip decisions, and item selection.

Interactive Algorithm Visualizer

0/1 Knapsack Problem

Enter your custom input data → Run the real algorithm engine → Observe step transitions.

⚙️ Customize Algorithm Input Data

Weight
Value
Weight
Value
Weight
Value
Step 1 of 16⚡ Algorithm Running
WHAT HAPPENED?

Initialized DP table of size (4 x 6) with zeros.

WHY?

Algorithm state rule requirement

WHAT CHANGED?

State pointers updated

Mathematical Formula

dp[i][w] = max(dp[i-1][w], val[i-1] + dp[i-1][w - wt[i-1]])

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

1

Item A

Cap 2..5

= dp[1][5] = 3
2

Item B

Cap 5: Take 4+dp[1][2]=7 > Skip 3

= dp[2][5] = 7
3

Result

Max Value

= 7 (Items A + B)

Frequently Asked Questions

What is the time complexity of 0/1 Knapsack DP?
The time complexity is O(n × W) where n is item count and W is weight capacity.