Pack the most valuable haul without overloading the bag. The knapsack problem looks simple but defeats greedy strategies — dynamic programming cracks it.
0/1 KnapsackLive
dynamic programming optimization
Camera
4 kg
$500
packed
Laptop
8 kg
$700
packed
Water
3 kg
$200
packed
Tent
10 kg
$400
left
Food
5 kg
$300
packed
Book
2 kg
$90
left
Radio
6 kg
$260
left
Rope
3 kg
$130
left
Controls
Presets
The knapsack problem: pick items to maximize value without exceeding a weight limit. Greedily grabbing the most valuable item fails; the optimal answer needs dynamic programming, which builds a table of best values for every capacity. It models budgeting, cargo loading, and resource allocation — and is a classic NP-hard problem solved efficiently by DP.
Reading this result: DP fills all 20 kg for $1700; notice the best pack is not simply the highest-value items — it trades value against weight, which is exactly why greedy selection fails here.
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How it works
Given items with weights and values and a capacity limit, the 0/1 knapsack problem chooses a subset of maximum value. Grabbing the highest-value or best-ratio item first can be badly suboptimal, so the solution builds a table of the best achievable value for every capacity. It models budgeting, cargo loading, and portfolio selection — a classic NP-hard problem tamed by DP.
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The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.
Is this knapsack problem solver tool really free?▾
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The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.