memóizálás

Memóizálás, often abbreviated as memoization, is an optimization technique used primarily to speed up computer programs by storing the results of expensive function calls and reusing them when the same inputs occur again. This technique is particularly useful in recursive algorithms where the same computations are repeated multiple times.

In memoization, a cache (or memo) is used to store the results of function calls. When the function is called again with the same inputs, the memoized result is returned, instead of recomputing the result. This can significantly reduce the time complexity of the function, especially for functions with overlapping subproblems, such as those found in dynamic programming.

There are two main approaches to implementing memoization:

1. Top-down memoization: This approach involves modifying the recursive function to first check if the result is already in the cache before computing it. If the result is in the cache, it is returned immediately. Otherwise, the result is computed, stored in the cache, and then returned.

2. Bottom-up memoization: This approach involves building up the solution iteratively, typically using a loop or a table, and storing the results of subproblems in the cache as they are computed. This approach is often more efficient in terms of space and time complexity.

Memoization is widely used in various fields, including computer science, mathematics, and economics. It is a fundamental concept in the design of efficient algorithms and is often used in conjunction with other optimization techniques, such as dynamic programming and caching.