Memóriakomplexitás

Memóriakomplexitás, in the context of computer science and algorithm analysis, refers to the amount of memory an algorithm requires to run. It is one of the two primary measures, along with time complexity, used to evaluate the efficiency of an algorithm. Memory complexity is typically expressed using Big O notation, which describes the upper bound of the memory usage as the input size grows.

The memory used by an algorithm can be broadly categorized into two types: auxiliary space and input space. Input space is the memory required to store the input data itself, and it is often considered separate from the algorithm's own memory requirements. Auxiliary space, on the other hand, is the extra memory an algorithm needs to perform its operations. This includes space for variables, data structures, and the call stack during recursive calls.

When analyzing the memory complexity, we focus on how the auxiliary space scales with the size of the input. For example, an algorithm with linear memory complexity, denoted as O(n), will require memory that grows proportionally to the input size n. An algorithm with constant memory complexity, O(1), will use a fixed amount of memory regardless of the input size. Quadratic memory complexity, O(n^2), indicates that the memory usage grows with the square of the input size. Understanding memory complexity is crucial for designing algorithms that are not only fast but also operate within reasonable memory constraints, especially when dealing with large datasets or limited hardware resources.