Logarithmic time complexity
An algorithmic running-time growth rate proportional to the logarithm of the input size, commonly expressed as O(log n).
Advanced Algorithms and Data Structures
Logarithmic time is a running-time bound that grows proportionally to the logarithm of the input size or another stated size parameter.
- How it is used
- Guides data-structure selection when partial ordering, heap operations, or balanced-tree access should scale beyond linear scans.
- How deep it goes
- Explains height and comparison bounds, worst-case versus amortized guarantees, logarithm bases, and practical constant-factor trade-offs.
- Examples
- Uses task-priority insertion, binary-heap comparisons, cache performance tables, and balanced k-d-tree construction.
- What you can do after
- Evaluate data structures by separating asymptotic growth, balance assumptions, worst-case guarantees, amortization, and implementation constants.
Read how Advanced Algorithms and Data Structures explains logarithmic time complexity →
Grokking Algorithms, Second Edition
Logarithmic time describes an algorithmic running time that grows in proportion to the logarithm of the input size.
- How it is used
- Compares algorithm growth rates and highlights why binary search scales better than simple search.
- How deep it goes
- Explains logarithmic growth through examples and comparisons, while simplifying operation counts and deferring fuller Big O treatment.
- Examples
- Uses binary-search guesses, folded grids, operation counts, and quicksort call stacks as concrete examples.
- What you can do after
- Evaluate whether an algorithm grows logarithmically and compare its scaling with linear and other common runtimes.
Read how Grokking Algorithms, Second Edition explains logarithmic time complexity →
Learn C++ by Example
Logarithmic complexity is an algorithmic growth rate proportional to the logarithm of the number of input elements, commonly expressed as O(log(n)).
- How it is used
- Explains why ordered associative containers keep searches, insertions, and removals efficient.
- How deep it goes
- Explains branch-by-branch search, doubling behavior, and tree balancing, but does not derive logarithms mathematically.
- Examples
- Uses a three-node search path and contrasts map lookup with worst-case vector scanning.
- What you can do after
- Evaluate data-structure choices by comparing logarithmic map operations with linear vector searches.
Read how Learn C++ by Example explains logarithmic time complexity →
Latency
Logarithmic time is an algorithmic growth class in which required operations increase proportionally to the logarithm of input size.
- How it is used
- Compares algorithmic growth to guide work elimination and low-latency optimization.
- How deep it goes
- Defines growth behavior and trade-offs, then shows data-structure cases without deriving logarithmic operations internally.
- Examples
- Uses a complexity-growth figure and binary search tree operation table to compare logarithmic, linear, quadratic, and constant growth.
- What you can do after
- Evaluate algorithm choices by comparing asymptotic growth with input size, execution frequency, and absolute latency.
Related concepts
- linear time complexitycontrasts with · Linear time complexity is an asymptotic running-time growth rate proportional to input size, or to the combined sizes of multiple inputs, up to a constant factor.
- binary searchmeasured by · Binary search is an algorithm that locates a target or boundary in an ordered collection by repeatedly comparing with a midpoint and halving the remaining search range.
- performancemeasured by · Performance is the measurable effectiveness or operational behavior of a system under specified conditions, assessed through relevant qualities such as task results, speed, responsiveness, throughput, or resource use.
- insertmeasures · An insertion is an operation that adds an element, record, or key-value association to a collection or data store, with placement and replacement behavior determined by the target.
- execution context stackmeasures · An execution context stack is a runtime last-in-first-out structure that records active function or method calls and their execution state and return information.
- AVL treemeasures · An AVL tree is a self-balancing binary search tree that maintains bounded differences between subtree heights through rotations.
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