advanced patterns in Recursive Fibonacci Calculation for Large Inputs in JavaScript
I'm working with an scenario with a recursive function I've written to calculate Fibonacci numbers in JavaScript. The function works fine for small inputs, but when I try to compute Fibonacci(40), it takes an excessive amount of time and sometimes even leads to the browser freezing. Here's the code I've written: ```javascript function fibonacci(n) { if (n <= 1) return n; return fibonacci(n - 1) + fibonacci(n - 2); } console.log(fibonacci(40)); ``` I understand that this implementation has an exponential time complexity, but I didn't anticipate such severe performance optimization. I've tried memoizing the results to optimize it, but I am not sure where to start or how to implement it correctly without changing the recursion structure. Here’s what I attempted: ```javascript const memo = {}; function fibonacciMemoized(n) { if (n in memo) return memo[n]; if (n <= 1) return n; memo[n] = fibonacciMemoized(n - 1) + fibonacciMemoized(n - 2); return memo[n]; } console.log(fibonacciMemoized(40)); ``` With the memoized version, it seems to work fine for Fibonacci(40), but I'm still confused about how recursion and memoization interplay with each other. Are there any best practices for implementing memoization in recursive functions, or is there a better design pattern I should consider for this kind of question? I'm using Node.js v14.17.0, and any guidance on optimizing recursion in JavaScript would be greatly appreciated.