Phase 4: Computational Thinking & Algorithms · ~35 minutes · Python · uv

Recursion

A function calling itself isn't a special kind of loop. It's an ordinary function call — which means it can genuinely run out of room, and does.

Hiring signal: Can name the base case and recursive case of any recursive function on sight, and knows exactly why missing one crashes

What you will learn

Explain recursion as base case + recursive case, not as magic
Trace a recursive function's execution by hand for a small input
Reproduce and explain a real RecursionError from a missing base case
Use recursion on genuinely nested data, where it's the natural tool

Introduction

Type: Learn Languages: Python Prerequisites: Lesson 03 (Sorting) Time: ~35 minutes

Objective

Learning objectives

Explain recursion as base case + recursive case, not as magic
Trace a recursive function's execution by hand for a small input
Reproduce and explain a real RecursionError from a missing base case
Use recursion on genuinely nested data, where it's the natural tool

What you're building

A script (recursive_tools.py) that:

Implements a recursive function that sums all numbers in an arbitrarily nested list (structured like nested above), using the same base-case/recursive-case pattern as count_items
Contains a comment tracing your function by hand for a small input (3-4 numbers, at least one level of nesting), showing each call and what it returns
Reproduces this lesson's missing-base-case RecursionError in a separate, clearly-commented-out or guarded block (don't leave it as code that actually runs and crashes the script), and explains in a comment exactly which line is missing
Writes the corrected version alongside it, with a real base case

A recursive function computes the sum of a list using def sum_list(data): return data[0] + sum_list(data[1:]). What's wrong with it?

This function has a real recursive case (data[0] + sum_list(data[1:]), which does shrink data by one element each call, moving toward an eventually-empty list) but genuinely no base case at all — nothing checks whether data is empty and stops. Once data becomes [], data[0] raises an IndexError (list index out of range, from Phase 02) rather than a clean, deliberate stopping point. The fix needs an explicit base case: if not data: return 0, checked before touching data[0] at all.

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