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How can I optimize recursive algorithms using memoization in TypeScript?

Memoization is an optimization technique where you store the results of expensive function calls. In TypeScript, you can apply memoization to avoid redundant calculations in recursive functions.

Memoization is a technique used to optimize recursive algorithms by storing the results of expensive function calls and reusing them when the same inputs occur again, instead of recalculating them. This is particularly useful in problems that involve overlapping subproblems, such as dynamic programming algorithms like Fibonacci sequence calculation, knapsack problem, or recursive tree traversals. In TypeScript, you can implement memoization by creating a cache (e.g., an object or map) where the results of function calls are stored based on their inputs. Before performing a calculation, you first check the cache to see if the result already exists. If it does, you return the cached result; otherwise, you compute it and store the result in the cache for future use. Memoization can significantly improve the performance of recursive algorithms, reducing their time complexity from exponential to linear in some cases. It’s commonly applied in problems like calculating Fibonacci numbers, solving the longest common subsequence, and pathfinding algorithms. Understanding and applying memoization can be a game-changer in improving the efficiency of algorithms, especially those that deal with recursive calls and large input sizes.

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