In the context of algorithms, what is memoization?

Memoization is a technique used to optimize the performance of algorithms by caching results of expensive function calls and reusing them when the same inputs occur again. This approach significantly reduces the computational cost, particularly for recursive functions that involve repeated calculations for the same inputs, such as in dynamic programming. By storing the output of a function for a given input, memoization avoids redundant calculations, which can lead to exponential time complexities in certain algorithms.

For example, in the case of Fibonacci number calculation, a naive recursive approach would repeatedly compute Fibonacci numbers for the same indices, leading to many repeated calls. By applying memoization, the results of previously computed Fibonacci numbers are stored, so that when those numbers are required again, the algorithm can simply retrieve them from memory instead of recalculating them.

This method is particularly effective in scenarios where multiple function calls are expected with overlapping subproblems, making it a key optimization strategy in many algorithms.