A-level Computing/AQA/Paper 1/Theory of computation/Order of complexity

Maths for big-O notation Limits of computation Order of Complexity 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.