How to Write Optimal Nested Recursion Functions in Python

Discover efficient methods to write optimal nested recursion functions in Python using techniques like memoization with `lru_cache`.
---

Visit these links for original content and any more details, such as alternate solutions, latest updates/developments on topic, comments, revision history etc. For example, the original title of the Question was: how to write optimal nested recursion functions

If anything seems off to you, please feel free to write me at vlogize [AT] gmail [DOT] com.
---
How to Write Optimal Nested Recursion Functions in Python

Recursion is a fundamental programming technique, especially in Python. However, when it comes to nested recursion functions, things can get tricky, particularly in terms of performance. In this post, we'll explore a practical problem from a complicated Excel spreadsheet and learn how to write optimal nested recursion functions that are both efficient and easy to understand.

The Problem

Imagine you're trying to translate a complex Excel spreadsheet into Python where some functions depend on one another recursively. Here’s a simplified version of what the spreadsheet looks like:

[[See Video to Reveal this Text or Code Snippet]]

Translating this into Python might lead you to write separate functions like so:

[[See Video to Reveal this Text or Code Snippet]]

The challenge arises when you call d(100), which results in calling function a multiple times, leading to an exponential increase in the total function calls (specifically, 3^100 calls). This situation makes the program inefficient and nearly impossible to execute in a reasonable time.

The Solution: Using Memoization

To enhance the efficiency of our recursion, we can use memoization, a technique where you cache the results of expensive function calls and return the cached result when the same inputs occur again. In Python, the functools module provides a decorator called lru_cache that makes this process simple.

Here’s how you can modify your previous code by adding lru_cache to the function a:

[[See Video to Reveal this Text or Code Snippet]]

How it Works

Caching Results: By applying @ lru_cache to the function a, we ensure that any previous results of a(r) are stored. When a(r) is called with the same r again, it will retrieve the result from cache instead of recalculating it.

Efficiency Improvement: This change significantly improves performance for large values of r. Instead of recalculating the values multiple times, the function retrieves them from memory, which speeds up the execution dramatically. In fact, calls to d(100) can go from taking an impractical amount of time to finishing in less than a second!

Conclusion

Working with nested recursion in Python can be daunting due to its potential inefficiency. By utilizing memoization techniques such as lru_cache, we can significantly enhance the performance of our recursive functions. This method not only saves computational resources but also allows us to focus on the logic of our program without being bogged down by performance issues.

Now, with your newfound understanding of optimal nested recursion functions, you can tackle even the most complex of spreadsheets without concern. Happy coding!