Do I need to install anything?

No. It runs in any modern browser, free, with no account required.

For K-12 Students · 0/1 Knapsack

0/1 Knapsack for a seating chart

Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate a seating chart live below — adjust the inputs and watch it respond, right in your browser.

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

Backpack capacity (kg)

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.

▶ Run in Python

Data Inspector

Total value$1700

Weight used20 / 20 kg

Items packed4

Governing equation

V [i, w] = max (V [i - 1, w], v_{i} + V [i - 1, w - w_{i}]), max i \sum v_{i} x_{i} s.t. i \sum w_{i} x_{i} \leq 20

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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Frequently asked questions

Is this good for k-12 students?: Yes — this version of "0/1 Knapsack for a seating chart" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.