Big O Notation

aid: big-o-notation
name: Big O Notation
description: Big O Notation is a mathematical notation used in computer science to describe the performance or complexity
  of algorithms, providing a way to classify algorithms by how their runtime or space requirements grow as input size grows.
  It is foundational to algorithm design, API performance benchmarking, and software engineering education.
type: Index
deliveryModel:
  model: unknown
  open_source: false
  commercial: false
  callable_host: false
  label: Delivery model not determined — needs a product licence on record
  confidence: low
  source:
  - none
  generated: '2026-08-28'
  method: derived
accessModel:
  pricing: unknown
  onboarding: unknown
  trial: false
  try_now: false
  public: false
  label: Unknown
  confidence: low
  source: []
  generated: '2026-07-22'
  method: derived
image: https://kinlane-images.s3.amazonaws.com/shared/apis-json/icons/big-o-notation.png
tags:
- Algorithms
- Big O Notation
- Complexity
- Computer Science
- Performance
- Data Structures
url: https://raw.githubusercontent.com/api-evangelist/big-o-notation/refs/heads/main/apis.yml
created: '2025-01-01'
modified: '2026-04-21'
specificationVersion: '0.23'
apis: []
common:
- type: Reference
  url: https://en.wikipedia.org/wiki/Big_O_notation
- type: Reference
  url: https://www.bigocheatsheet.com
- type: Features
  data:
  - name: O(1) - Constant Time
    description: Algorithm runtime does not change with input size. Example - hash table lookups.
  - name: O(log n) - Logarithmic Time
    description: Runtime grows logarithmically with input. Example - binary search.
  - name: O(n) - Linear Time
    description: Runtime grows linearly with input size. Example - linear search.
  - name: O(n log n) - Linearithmic Time
    description: Runtime grows as n multiplied by log n. Example - merge sort, heap sort.
  - name: O(n²) - Quadratic Time
    description: Runtime grows quadratically with input size. Example - bubble sort, nested loops.
  - name: O(2^n) - Exponential Time
    description: Runtime doubles with each additional input element. Example - recursive Fibonacci.
  - name: O(n!) - Factorial Time
    description: Runtime grows factorially. Example - brute-force traveling salesman.
- type: UseCases
  data:
  - name: Algorithm Selection
    description: Choosing the most efficient algorithm for a given problem based on complexity class.
  - name: API Performance Benchmarking
    description: Analyzing API endpoint performance characteristics under varying data sizes.
  - name: Code Review
    description: Evaluating the time and space complexity of code changes during review.
  - name: Database Query Optimization
    description: Understanding complexity of database operations to optimize query performance.
  - name: Scalability Analysis
    description: Predicting how software will perform as data volumes grow at scale.
  - name: Interview Preparation
    description: Preparing for technical interviews requiring algorithm complexity analysis.
- type: Vocabulary
  data:
  - term: Time Complexity
    definition: Measure of computation time as a function of input size.
  - term: Space Complexity
    definition: Measure of memory usage as a function of input size.
  - term: Best Case
    definition: Minimum time required for algorithm execution (Omega notation).
  - term: Worst Case
    definition: Maximum time required for algorithm execution (Big O notation).
  - term: Average Case
    definition: Expected time required for algorithm execution (Theta notation).
  - term: Asymptotic Analysis
    definition: Behavior of algorithm as input size approaches infinity.
  - term: Amortized Analysis
    definition: Average performance of operations over time accounting for occasional expensive operations.
maintainers:
- FN: Kin Lane
  email: kin@apievangelist.com