**π‘ Problem Formulation:** You are given a list in Python and your task is to find the length of this list. However, instead of using the built-in `len()`

function, you will implement recursive functions to achieve this. Consider the input list `[3, 1, 4, 1, 5, 9]`

and the desired output is `6`

.

## Method 1: Basic Recursion

This method involves defining a recursive function which calls itself with a smaller part of the list until the list is empty. The function signature is `def recursive_len(lst):`

. It’s a straightforward method purely for educational purposes to grasp the concept of recursion.

Here’s an example:

def recursive_len(lst): if not lst: return 0 return 1 + recursive_len(lst[1:]) # Example usage print(recursive_len([3, 1, 4, 1, 5, 9]))

Output: `6`

This code checks if the list is empty; if it is, the function returns 0. Otherwise, it returns 1 plus the recursive call to itself with the list minus the first element, effectively reducing the problem size with each call.

## Method 2: Tail Recursion with Helper Function

Tail recursion optimizes the basic recursion by passing the accumulator through function arguments. This technique uses a helper function with an additional parameter to keep track of the count. Function signature is `def recursive_len_tail(lst, acc=0):`

.

Here’s an example:

def recursive_len_tail(lst, acc=0): if not lst: return acc return recursive_len_tail(lst[1:], acc + 1) # Example usage print(recursive_len_tail([3, 1, 4, 1, 5, 9]))

Output: `6`

This snippet introduces an accumulator as a second parameter to keep the current count which reduces the stack size used by the function calls. When the list is empty, it simply returns the accumulator’s value.

## Method 3: Recursion with Slice Copy

This approach uses slicing to create a copy of the list minus the head element and passes it to the recursive call. The function is more intuitive for those learning recursion but less efficient due to list copying. The function signature is `def recursive_len_slice(lst):`

.

Here’s an example:

def recursive_len_slice(lst): if not lst: return 0 return 1 + recursive_len_slice(lst[:1]) # Example usage print(recursive_len_slice([3, 1, 4, 1, 5, 9]))

Output: `6`

In this code, slicing is used to create a copy of the list without the first element each time the function is recursively called. The inefficiency comes from the fact that each recursive call creates a new list in memory.

## Method 4: Recursion with Index Tracking

Index tracking uses an index to keep track of the current position in the list instead of slicing the list. This method is more memory efficient. Function signature is `def recursive_len_index(lst, index=0):`

.

Here’s an example:

def recursive_len_index(lst, index=0): if index == len(lst): return 0 return 1 + recursive_len_index(lst, index + 1) # Example usage print(recursive_len_index([3, 1, 4, 1, 5, 9]))

Output: `6`

The function uses an index to track the recursion depth, and once the index matches the length of the list, a base value of 0 is returned. It’s a memory-efficient solution since it avoids making copies of the list.

## Bonus One-Liner Method 5: Lambda with Reduce

For those who love one-liners, Python’s `functools.reduce`

combined with a lambda function can be used to create a recursive-like behavior to count elements in a list. Although it’s not traditional recursion, it’s a neat trick. Function signature is `recursive_len = lambda lst: reduce(lambda x, _: x + 1, lst, 0)`

.

Here’s an example:

from functools import reduce recursive_len = lambda lst: reduce(lambda x, _: x + 1, lst, 0) # Example usage print(recursive_len([3, 1, 4, 1, 5, 9]))

Output: `6`

This one-liner defines `recursive_len`

as a lambda function that uses reduce to increment a counter every time an element is encountered in the list. It’s a slick way to effectively simulate recursion in a functional programming style.

## Summary/Discussion

**Method 1: Basic Recursion.**Easy to understand for beginners. Inefficient due to many list slicing operations that increase memory usage.**Method 2: Tail Recursion with Helper Function.**More efficient stack usage with accumulator. However, Python doesn’t optimize tail recursion, limiting its benefits.**Method 3: Recursion with Slice Copy.**Intuitive but still suffers from inefficiency caused by generating list copies with each recursion.**Method 4: Recursion with Index Tracking.**Memory efficient as it avoids list copying. It’s a practical approach when dealing with larger lists.**Bonus Method 5: Lambda with Reduce.**Not true recursion, but a clever functional approach. It shines in simplicity and conciseness, yet not the most readable for those unfamiliar with reduce.