Big O Notation Quiz
How the Scales are Structured
Who Usually Takes This Test?
See How You Compare
Below is a preview of how scores are typically distributed across each scale.
Example Questions From the Test
- O(n), because the original array contains n elements.
- O(1), because each individual stack frame has constant size.
- O(log n), because one frame is added at each level while the search range is repeatedly halved.
- O(n log n), because the array size is combined with the recursion depth.
- Quadratic time, because the n² term dominates as n grows.
- Linear time, because lower-order terms and constants are removed.
- Logarithmic time, because only the number of input-size digits matters.
- Cubic time, because the expression contains three separate terms.
- It becomes about four times as large.
- It becomes about twice as large.
- It becomes about eight times as large.
- It remains approximately unchanged.
Big O Notation Quiz - Description and methodology of the test
Students, self-learners, and developers can use this assessment to check whether they can reason about algorithmic growth rather than rely on memorized labels. The Big O Notation Quiz is useful when reviewing core analysis concepts before tackling more demanding problems. Because it is a Big O quiz, each item links formal notation with a concrete choice about loops, recursion, graphs, or data structures.
What This Assessment Explores
The questionnaire checks whether you can predict how algorithmic work changes as input grows. It covers upper, lower, and tight asymptotic bounds, dominant terms, time, and auxiliary space. Examples involve recursive search, nested loops, recurrences, graph traversal, hashing, and arrays. As an algorithm complexity test, it asks you to apply notation to procedures rather than repeat definitions.
The question themes are:
- Growth notation shows whether you distinguish O, Ω, and Θ.
- Loops and recurrences show whether you combine repeated work and recursion levels.
- Graphs and data structures show how representation affects cost.
- Scaling shows whether you predict the effect of changing n.
- Big O Notation Knowledge (0-16) reports correct answers: Foundations to Build (0-6) calls for review, Developing Knowledge (7-12) reflects partial command, and Strong Knowledge (13-16) reflects consistent application.
This result describes performance on the tested concepts and highlights topics to revisit.
Methodology and Scientific Basis
Each item presents an algorithm scenario or definition with four answer choices. You select the best answer, and one point is awarded for each correct response. As a time complexity quiz, the format tests applied recognition under fixed response conditions rather than written proofs or program construction.
The tested distinctions are conceptually consistent with Knuth’s asymptotic notation and the algorithm-analysis treatment in Cormen and colleagues; those sources support the concepts, not this questionnaire’s score bands or psychometric status. The items apply those ideas to growth comparisons, loop counts, recursive depth, recurrences, graph traversal, hashing, and auxiliary space.
Interpret the result as a snapshot of knowledge on these items. The bands are questionnaire-specific descriptors, not population norms: they show whether the tested foundations need review, are developing, or are consistently usable in familiar cases. Performance may also reflect prior instruction, wording familiarity, and careful reading, so a score does not measure every aspect of algorithmic skill. Use the result to choose review topics such as dominant terms, recurrences, graph traversal, and worst-case analysis.
- Knuth, Donald E. "Big Omicron and big Omega and big Theta." ACM SIGACT News, vol. 8, no. 2, 1976, pp. 18-24. 10.1145/1008328.1008329
- Cormen, Thomas H., Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. Introduction to Algorithms. 4th ed. Cambridge, MA: MIT Press, 2022.
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