Problem Solving: Order of complexity

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PAPER 1 - ⇑ Theory of computation ⇑

← Maths for big-O notation Order of complexity Limits of computation →



Order of Complexity[edit]

Notation Name Example
constant Determining if a number is even or odd; using a constant-size lookup table
logarithmic Finding an item in a sorted array with a binary search or a balanced search tree as well as all operations in a Binomial heap.
linear Finding an item in an unsorted list or a malformed tree (worst case) or in an unsorted array; Adding two n-bit integers by ripple carry.
linearithmic, loglinear, or quasilinear Performing a Fast Fourier transform; heapsort, quicksort (best and average case), or merge sort
quadratic Multiplying two n-digit numbers by a simple algorithm; bubble sort (worst case or naive implementation), Shell sort, quicksort (worst case), selection sort or insertion sort
polynomial or algebraic Tree-adjoining grammar parsing; maximum matching for bipartite graphs
exponential Finding the (exact) solution to the travelling salesman problem using dynamic programming; determining if two logical statements are equivalent using brute-force search
factorial Solving the travelling salesman problem via brute-force search; generating all unrestricted permutations of a poset; finding the determinant with expansion by minors.