Knapsack Problem Dynamic Programming Visualizer

Setup Problem

Knapsack Controls

Items

DP Table

Algorithm Steps

How to Use

Setup: Enter knapsack capacity and click "Setup" or use "Sample Problem"
Start: Click "Start" to begin the dynamic programming solution
Step Through: Click "Next" to see each step or "Run Through" for automatic execution
Observe: Watch the DP table fill and see optimal selections
Colors: Yellow shows current computation, Green shows selected items
Reset: Click "Reset" to start over

Knapsack Problem

0/1 Knapsack Problem finds the maximum value that can be obtained with given weight capacity, where each item can be taken at most once.

Dynamic Programming Approach:

Create DP table: dp[i][w] = max value with first i items and weight w
Base case: dp[0][w] = 0 (no items, no value)
For each item: choose max of including or excluding it
If weight ≤ w: dp[i][w] = max(dp[i-1][w], dp[i-1][w-weight] + value)
Else: dp[i][w] = dp[i-1][w]
Traceback to find selected items

Time Complexity: O(n×W) where n = items, W = capacity

Use Cases

Resource Allocation: Distribute limited budget or resources to maximize value or impact
Portfolio Optimization: Select investments with maximum return within capital constraints
Cargo Loading: Pack items into containers maximizing value while respecting weight limits
Project Selection: Choose projects to maximize profit within time or budget constraints
Memory Management: Allocate cache memory to maximize performance within size restrictions
Schedule Optimization: Select tasks to maximize productivity within time available
Supply Chain: Optimize inventory selection to maximize value with limited storage space
Equipment Loadout: Select gear for missions maximizing capability within weight limit

Real-World Example

Scenario: A shipping company needs to maximize cargo value for a truck with 50kg capacity.

Items:
Item 1: 10kg, $100
Item 2: 20kg, $250
Item 3: 30kg, $300
Optimal Solution: Select Items 1 & 2 = 30kg, $350 value

The knapsack algorithm finds the optimal combination of items maximizing value while respecting weight constraints. This is critical for logistics, finance, and resource management where decisions must balance multiple constraints.

Benefits: Optimal solution guaranteed, handles constraints efficiently, applicable to many real-world problems