memoizing

Memoizing, or memoization, is a programming optimization that stores the results of expensive function calls and returns the cached result when the same inputs occur again. It is a specialization of caching applied to a function's outputs within a program, often implemented with a data structure such as a dictionary or map that associates input arguments with their computed results. Memoization is commonly described as a form of dynamic programming, recording subproblem results to avoid recomputing them.

How it works: when a function is called, the implementation checks the cache for a key representing the input arguments. If a cached result exists, it is returned immediately; otherwise the function executes, the result is stored in the cache with the corresponding key, and the result is returned. Keys must capture all relevant inputs; for multiple arguments a composite key, a tuple, or serialized representation is often used. Some implementations limit memory with eviction policies like LRU.

Requirements and trade-offs: memoization requires that the function be deterministic and side-effect free so cached results remain valid. It can greatly speed up repeated calls, especially for expensive or recursive computations. The downsides include increased memory usage and the need to manage cache invalidation in response to changes in inputs or program state. In concurrent programs, synchronization may be needed to avoid race conditions.

Applications and variants: memoization is widely used in recursive algorithms, such as top-down dynamic programming, and as a language feature or library facility (for example, decorators or wrappers that add caching). It is related to, but distinct from, system-level caching and can be language-specific in how caches are implemented and purged.