Computational complexity

random access machine (RAM)

a model of computation where steps are executed sequentially, and each step is an operation that takes a constant amount of time (assignment, comparison, arithmetic operation, accessing object in memory)

tight bound

an upper and lower bound on a asymptotic running time

average-case running time

average running time over all possible inputs of a given size

exponential complexity

complexity grows at the power of some number to n, most expensive type of algorithm

linear complexity

complexity grows linearly with the size of inputs, generally seen with iterating over lists, can depend on recursive calls

logarithmic complexity

complexity grows with log of size of one of its inputs

polynomial complexity

complexity grows with n to some power grows, seen in nested loops or particular recursive calls, most common is quatratic

worst-case running time

maximum running time over all possible inputs of a given size, provides an upper bound on the running time

best-case running time

minimum running time over all possible inputs of a given size

step

operation that takes a fixed amount of time

constant complexity

upper bound is independent of input, can have loops or recursive calls that do not depend on the size of input

Big O notation

used to give the upper bound of the asymptotic growth, or the order of the function

asymptotic notation

describes the complexity of an algorithm as the size of its inputs approaches infinity, like linear, quadratic and polynomial equations