Knapsack Visualizer — DP Table
Animated 0/1 knapsack dynamic programming — fills the DP table cell by cell, highlighting dependencies, with step controls. Runs in your browser.
Pseudocode
Press Run to animate the algorithm.
Time · Space
How to use
- 1 Press Run to fill the dynamic-programming table cell by cell.
- 2 Each row is an item; each column is a capacity from 0 to W.
- 3 A cell is the best of skipping the item (blue cell above) or taking it.
- 4 The bottom-right cell is the best achievable value. Shuffle for new items.
Why use this tool
- See 0/1 knapsack solved by dynamic programming, not brute force.
- Watch each cell built from the two cells it depends on.
- Understand the O(n·W) running time versus exponential brute force.
- Runs entirely in your browser. No signup, no uploads.
Frequently asked questions
What is the 0/1 knapsack problem?
Given items each with a weight and value and a capacity W, choose a subset (each item taken once or not at all) that maximizes total value without exceeding W.
How does the DP table work?
dp[i][w] is the best value using the first i items within capacity w. Each cell is max(skip the item = dp[i-1][w], take it = dp[i-1][w-wi] + vi).
What is the time complexity?
O(n·W) time and O(n·W) space (reducible to O(W)). This is pseudo-polynomial — efficient when W is small.
Why is it called 0/1 knapsack?
Each item is either fully taken (1) or left out (0) — you cannot take fractions, unlike the fractional knapsack which a greedy method solves.
What is 0/1 Knapsack Visualizer?
A 0/1 Knapsack Visualizer animates the dynamic-programming table where dp[i][w] is the best value using the first i items within capacity w, computed as max of skipping or taking each item. The bottom-right cell is the optimal value.
0/1 Knapsack Visualizer is a free algorithm utility by Zerethon Tools. Animated 0/1 knapsack dynamic programming — fills the DP table cell by cell, highlighting dependencies, with step controls. Runs in your browser. Runs entirely in the browser — no signup, no upload.
- Category
- Algorithm
- Pricing
- Free
- Privacy
- Browser-based
- Signup
- Not required
Privacy
Your data never leaves your browser unless explicitly stated. 0/1 Knapsack Visualizer runs entirely client-side — no server upload, no logging, no tracking of your input.
Related tools
Bubble Sort Visualizer
Animated bubble sort with step controls, speed, custom input, live comparison/swap counters and pseudocode. Runs entirely in your browser.
Open toolInsertion Sort Visualizer
Animated insertion sort with step controls, speed, custom input, live comparison/write counters and pseudocode. Runs in your browser.
Open toolSelection Sort Visualizer
Animated selection sort with step controls, speed, custom input, live comparison/swap counters and pseudocode. Runs in your browser.
Open toolMerge Sort Visualizer
Animated merge sort with step controls, speed, custom input, live comparison/write counters and pseudocode. Runs in your browser.
Open toolBuild, share, and grow on Zerethon Social
Free signup. Earn points, collect achievements, and connect with creators worldwide.