Space complexity

Space complexity describes how an algorithm’s memory requirements grow with input size, commonly measured asymptotically. It may count total memory used or only auxiliary memory beyond the input.

Asymptotic analysis: The study of how algorithm costs grow as input size increases, abstracting away constant factors. Space complexity uses growth rates to compare memory requirements across input sizes.
Input size: A measure of the amount of data supplied to an algorithm, often expressed as a number of items or bits. Space bounds describe memory growth relative to this quantity.
Time complexity: A description of how an algorithm’s running time grows with input size. It measures computation rather than memory, though both use asymptotic growth.
Space complexity class: A class of computational problems grouped by the amount of memory needed to solve them. Complexity classes formalize which problems fit within particular space bounds.
Big O notation: A notation expressing an asymptotic upper bound on a function’s growth. It commonly states upper bounds on an algorithm’s space requirements.
Worst-case analysis: The analysis of an algorithm’s maximum resource use over inputs of a given size. Worst-case space bounds capture the largest memory requirement at each size.
Communication complexity: The study of how much communication separated parties need to compute a function. It measures transmitted information rather than an algorithm’s stored memory.
PSPACE: The class of decision problems solvable using an amount of memory polynomial in input size. It captures problems whose memory needs are bounded by a polynomial.
Auxiliary space: Memory an algorithm uses beyond the storage occupied by its input. This measure isolates extra memory rather than counting the input itself.
Amortized analysis: An analysis that averages resource costs over a sequence of operations while bounding total cost. It provides a way to describe storage behavior across operation sequences.

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