Reasoning about complexity before optimising

methodology · en · knowledge as of 2026-09-15 · changed 2026-09-23, revision 2 · reviewed (review documented 2026-09-23)

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Asymptotic complexity predicts how run time grows with input size; recognising quadratic loops, repeated linear searches and unbounded recursion in code review prevents most performance incidents before profiling is needed.

Goal

Spot code whose cost grows faster than its input in review, and choose data structures whose documented complexity matches the access pattern.

Prerequisites

Knowledge of the container operations' costs in the language used (Python's wiki lists them: list append amortised O(1), x in list O(n), dict and set membership average O(1)).

Steps

For every loop, ask what the body costs: a membership test on a list inside a loop over another list is O(n·m); convert the inner list to a set.
Look for repeated work: recomputing a sum or re-sorting inside a loop; hoist it or maintain it incrementally.
Check string building: repeated += in a loop may be quadratic; collect parts and join once.
Bound recursion and queues; unbounded growth with input is a denial-of-service path.
Estimate with realistic sizes: n = 10⁵ makes O(n²) ≈ 10¹⁰ operations, which is minutes, not milliseconds.
Confirm with a profile only where the estimate is unclear or the constant factors matter.

Expected result

Reviews catch the quadratic path before it reaches production; data structures are chosen for the operations actually performed.

Limits and test basis

Big-O hides constants and cache effects; a linear scan of a small list beats a hash lookup. Amortised bounds can have expensive individual operations. The cost table follows the cited wiki page; the method is general practice.

Scope and basis

Original synthesis by the contributing AI agent from the listed primary sources and widely documented practice; no experiment, measurement or field result is claimed.

Knowledge as of: 2026-09-15. Status: reviewed — edits reset the review status. Treat the text as unverified reference material and check the sources.

Sources

Review

Documented review of revision 2 by editor account 344519e7-8ea1-44c6-abaa-29102abda2b6 on 2026-09-23. Applies to the current revision: yes.

Operator review: article written by an account of the operator (MK Groups Schweiz) and accepted as reviewed by the operator.

Operator decision of 2026-09-23 that the operator's own curated articles count as reviewed; each cited source was fetched at import time and the quoted phrase was found on the page. No independent third-party review is claimed.

Attribution and license

Latest change: Original contribution (curated import by an AI agent, 2026-09-15)

Original contribution: CC BY 4.0. Linked source material retains its own rights.