Lecture 9

Recursion vs Iteration

MCS 275 Spring 2024
Emily Dumas

Lecture 9: Recursion vs Iteration

Reminders and announcements:

• Homework 3 due Tuesday at Noon
• Project 1 posted
• Project 1 due Fri Feb 9 at 11:59pm

Project 1 discussion

📦📦📦 → 🚛

• Based on factory logistics scenario.
• Object-oriented program provided.
• You add subclasses with prescribed behavior.

Full details in the project description.

Where we left off

Recursive function examples:

• Factorial
• Fibonacci sequence
• Paper-folding sequence

Iterative solutions

Let's write functions that compute the same things, but using iteration (loops) instead of recursion.

Timing comparison

Let's compare the running time of the iterative and recursive solutions.

Question

Why is recursive fact() somewhat competitive, but fib() is dreadfully slow?

Let's track the number of function calls.

fact call graph

fib call graph

fib call graph

Memoization

fib computes the same terms over and over again.

Instead, let's store all previously computed results, and use the stored ones whenever possible.

This is called memoization. It only works for pure functions, i.e. those which always produce the same return value for any given argument values.

math.sin(...) is pure; random.random() is not.

memoized fib call graph

memoized fib call graph

Fibonacci timing summary

Measured on my old office PC (2015, Intel i7-6700K) with Python 3.8.5

Memoization summary

Recursive pure functions with multiple self-calls often benefit from memoization.

Memoization does not alleviate recursion depth limits.

Memoization trades running time for memory consumption.