What is Big-O notation?

Big-O is the upper-bound on how an algorithm's runtime or memory usage grows as input size n grows. O(n) means linear growth; O(n²) means a 10× larger input costs 100× more time.

Why does complexity matter more than constant factors?

For non-trivial input sizes a single complexity-class jump always beats a constant-factor speedup. Switching bubble sort (O(n²)) to merge sort (O(n log n)) turns a 10-second job into a 50-ms one once n passes a few thousand.

How do I derive my code's Big-O class?

Walk through your code top-down. Identify the dominant operation in each loop or recursive call, then multiply nested loops together and drop lower-order terms. Reading the chart against reference curves on this page helps you sanity-check the derivation.

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Big-O Complexity Visualiser

Pick your algorithm's time and space classes. The chart plots them against the reference curves (constant, logarithmic, linear, quadratic) on the same axes so the growth rate is obvious at a glance.

Time complexitye.g. Merge sort, heap sortSpace complexitye.g. Single loop over input

TimeO(n log n)

SpaceO(n)

Complexity vs. reference curves

Reading the chart

Curves are plotted on a shared axis. Your time class is always included; the rest (O(1), O(log n), O(n), O(n²)) are reference lines so you can eyeball whether your algorithm scales gracefully (closer to the bottom curves) or painfully (closer to quadratic). For large inputs the gap between O(n) and O(n²) becomes the only thing that matters.

Why complexity matters more than the constant

A 100× constant-factor speedup loses to a single complexity-class jump for any non-trivial input. Going from O(n²) to O(n log n) (e.g. switching from bubble sort to merge sort) is the kind of change that turns a 10-second job into a 50-ms one once the input gets past a few thousand elements.

Want a per-line walkthrough?

The chat-version of this tool (@bigO inside EveChat) takes your actual code and walks through the dominant operation in each loop. Useful when you're not sure which class your implementation lands in. Open in EveChat

Reading the chart