An algorithm is said to be constant time (also written as $${\textstyle O(1)}$$ time) if the value of $${\textstyle T(n)}$$ (the complexity of the algorithm) is bounded by a value that does not … See more

An algorithm is said to take logarithmic time when $${\displaystyle T(n)=O(\log n)}$$. Since $${\displaystyle \log _{a}n}$$ and $${\displaystyle \log _{b}n}$$ are related by a See more

An algorithm is said to run in sub-linear time (often spelled sublinear time) if $${\displaystyle T(n)=o(n)}$$. In particular this includes … See more

An algorithm is said to take linear time, or $${\displaystyle O(n)}$$ time, if its time complexity is $${\displaystyle O(n)}$$. Informally, this means that the running time increases at most linearly with the size of the input. More precisely, this means that there is … See more

An algorithm is said to be subquadratic time if $${\displaystyle T(n)=o(n^{2})}$$.
For example, simple, comparison-based sorting algorithms are … See more

An algorithm is said to run in polylogarithmic time if its time $${\displaystyle T(n)}$$ is $${\displaystyle O{\bigl (}(\log n)^{k}{\bigr )}}$$ for some constant k. Another way to write this is $${\displaystyle O(\log ^{k}n)}$$.
For example, See more

An algorithm is said to run in quasilinear time (also referred to as log-linear time) if $${\displaystyle T(n)=O(n\log ^{k}n)}$$ for some positive constant k; linearithmic time is the case $${\displaystyle k=1}$$. Using soft O notation these algorithms are
Algorithms which … See more