Space complexity

The space complexity of an algorithm or a data structure is the amount of memory space required to solve an instance of the computational problem as a function of characteristics of the input. It is the memory required by an algorithm until it executes completely.^[1] This includes the memory space used by its inputs, called input space, and any other (auxiliary) memory it uses during execution, which is called auxiliary space.

Similar to time complexity, space complexity is often expressed asymptotically in big O notation, such as ${\displaystyle O(n),}$ ${\displaystyle O(n\log n),}$ ${\displaystyle O(n^{\alpha }),}$ ${\displaystyle O(2^{n}),}$ etc., where n is a characteristic of the input influencing space complexity.