Memoizationbased

Memoizationbased refers to a programming technique where the results of expensive function calls are cached and returned when the same inputs occur again. This is a form of caching and is closely related to dynamic programming. The primary goal of memoization is to speed up computer programs by avoiding redundant computations.

A function is memoized by associating it with a cache. Before executing the function, the system checks if the input arguments are already present in the cache. If they are, the cached result is returned directly, bypassing the actual function execution. If the input arguments are not in the cache, the function is executed, its result is stored in the cache with the corresponding input arguments, and then the result is returned.

Memoization is particularly effective for recursive functions that have overlapping subproblems. For example, calculating Fibonacci numbers recursively without memoization leads to repeated calculations of the same Fibonacci numbers many times, resulting in exponential time complexity. With memoization, each Fibonacci number is calculated only once, significantly improving performance to linear time complexity.

The implementation of memoization typically involves using a data structure, such as a hash map or an array, to store the computed results. The key for this data structure is usually the function's input arguments, and the value is the computed result. Memoization can be applied to various programming languages and is a common optimization strategy in software development. It's important to note that memoization is only beneficial for functions that are pure, meaning they always produce the same output for the same input and have no side effects.