🪟 Sliding Window — Max Subarray Sum

Approach — tap to compare

Work to solve (k = 3)

approach	n=1K	n=1M
Brute Force	2,994	2,999,994
Sliding Window	1,000	1,000,000

Live: 0 ops · best sum 0

Sliding Window Pseudocode

1s ← sum(a[0 .. k−1])
2best ← s
3for i in k .. n−1:
4  s ← s + a[i] − a[i−k]
5  best ← max(best, s)
6return best

Speed: 50%Window size k: 3Array size: 10

Sliding Window Visualizer: Max Subarray Sum, Brute Force vs O(n)

This sliding window simulator animates the maximum-sum-subarray-of-size-k problem two ways so you learn why the optimization works, not just the trick. Brute force re-adds all k elements for every window position (O(n·k)); the sliding window reuses the k−1 overlapping elements between consecutive windows, adding the element that enters and subtracting the one that leaves (O(n)). A translucent window glides across numbered cells, the entering cell glows green and the leaving cell red, a gold outline marks the best window found so far, and a work-to-solve card projects the operation count at n = 1,000 and n = 1,000,000 so the gap between quadratic-ish and linear scaling is concrete. A synced pseudocode panel highlights the line running each step.

What you can do in this simulation

Tap between Brute Force (O(n·k)) and Sliding Window (O(n)) and watch the complexity badges and live operation counter change instantly
Watch the window glide one step at a time — the entering element flashes green (+ in) and the leaving element red (− out) with a running sum readout
Adjust the window size k and array size, and use the Work-to-solve card to compare operations at n = 1,000 versus n = 1,000,000
Press Play, Pause, or Step to run at any speed or advance one operation at a time, with a pseudocode panel highlighting the current line
See the best-sum window outlined in gold as it updates, and complete missions that ask you to solve the same array with both approaches

Concepts covered

sliding window technique · maximum subarray sum · fixed-size window · time complexity comparison · brute force vs optimized · O(n) vs O(n times k) · reuse overlapping work

Related simulations

Browse all Technology simulations →

Free to use in your browser — no signup required. Found a bug or have an idea to make it better? Tell us.

Please wait

Loading technology simulations

The requested content is still loading.

Finished experimenting?

Save one completion to this browser's signed guest ledger, or directly to your account when signed in.

approach

n=1K

n=1M

Brute Force

2,994

2,999,994

Sliding Window

1,000

1,000,000

Sliding Window Visualizer: Max Subarray Sum, Brute Force vs O(n)

What you can do in this simulation

Tap between Brute Force (O(n·k)) and Sliding Window (O(n)) and watch the complexity badges and live operation counter change instantly

Watch the window glide one step at a time — the entering element flashes green (+ in) and the leaving element red (− out) with a running sum readout

Adjust the window size k and array size, and use the Work-to-solve card to compare operations at n = 1,000 versus n = 1,000,000

Press Play, Pause, or Step to run at any speed or advance one operation at a time, with a pseudocode panel highlighting the current line

See the best-sum window outlined in gold as it updates, and complete missions that ask you to solve the same array with both approaches