Python 3.10: guide with Recursive Function and Memory Limit Exceeded scenarios
I'm maintaining legacy code that Can someone help me understand Quick question that's been bugging me - I'm working with a `MemoryError` when trying to run a recursive function that calculates the Fibonacci sequence for a large number, specifically above `n=1000`... My function looks like this: ```python def fibonacci(n): if n <= 0: return 0 elif n == 1: return 1 else: return fibonacci(n-1) + fibonacci(n-2) ``` I've tried optimizing the function using memoization by defining a cache dictionary, but I still run into memory issues when calling `fibonacci(1000)`. Here’s the modified version: ```python cache = {} def fibonacci(n): if n in cache: return cache[n] if n <= 0: return 0 elif n == 1: return 1 else: result = fibonacci(n-1) + fibonacci(n-2) cache[n] = result return result ``` However, when I call `fibonacci(1000)`, it still runs out of memory after a while, even though my cache is growing. I suspect it might be due to the depth of recursion or the size of the cache itself. I've also looked into Python's `sys.setrecursionlimit()`, but changing that doesn't seem to resolve the memory scenario. Is there a better way to implement this function to efficiently compute Fibonacci numbers without hitting memory limits? I've read about iterative methods and dynamic programming, but I'm unsure how to implement those effectively. Any advice would be greatly appreciated! Has anyone else encountered this? I've been using Python for about a year now. What am I doing wrong? Thanks for your help in advance! Any examples would be super helpful.