Knapsack Problem Solver
Overview
The Knapsack Problem Solver demonstrates both the 0/1 knapsack and fractional knapsack problems. Watch as dynamic programming builds the optimal solution table for 0/1 knapsack, or see the greedy approach solve fractional knapsack. Visualize the solution table and see which items are selected. Essential for understanding dynamic programming, greedy algorithms, and resource allocation under constraints.
Tips
- 0/1 Knapsack: each item is either included or excluded (can’t take fractions)
- Fractional Knapsack: can take fractions of items (greedy by value/weight ratio)
- Dynamic programming for 0/1: builds table of optimal solutions for subproblems
- Time complexity: O(nW) for DP where n = items, W = capacity
- Greedy works for fractional but not 0/1 knapsack
- The DP table shows maximum value achievable for each weight limit
- Backtrack through table to find which items are in optimal solution
- Applications: resource allocation, cargo loading, portfolio selection, cutting stock