It's been a while since I last wrote up a specific lesson idea so when my friend Garth asked about recursion ideas I thought I'd write this one up. This is a unit I used to teach in my intro class at Stuy using Racket (nee Scheme) but I coded up a quick and dirty Python version.
Recursion is a polarizing topic. Some people love it, others hate it. I'm sure the usual suspects of intro recursion problems doesn't help. Factorial, Fibonacci, Hanoi, things you can do with loops 1 ancillary topics that come along with it.
If you're doing graphics you can do fractal trees and the like but that's not always an option and there could be a disconnect from doing that to using recursion to solve problems.
I decided to take it out of the mathy graphicy world and do some text processing. Let's write a sentence generator. The recursion is light but I think it's pretty cool.
What follows outlines the unit. The actual lessons should be embellished and more brought to life but writing that up would make this post even longer.
What's a sentence? Let's start really simple. In the simplest form a sentence is noun verb. Let's write a program to generate sentences of this form:
import random NOUNS = ['dog','cat','boy','hammer','ball'] VERBS = ['ate','ran','bludgeoned','stalked'] def verb(): return random.choice(VERBS) def noun(): return random.choice(NOUNS) def sentence(): return noun()+' '+verb()
Of course, this isn't an interesting sentence. A slightly better sentence would use the form noun_phrase verb where a noun_phrase could be something like "a boy" "the dog" or just "hammer." A noun_phrase would be zero or one article followed by a noun.
We can write a function called articleq() that will either return an article (the, a) or an empty string. This leads to these additional functions:
def articleq(): if random.randrange(100) > 50: return random.choice(['the','a']) else: return '' def noun_phrase(): """ article? noun """ return articleq() + ' ' + noun()
The above will generate a noun_phrase that has an article about 50% of the time.
Okay, here comes the recursion.
A noun_phrase also can have adjectives - specifically, zero or more adjectives. This leads to adding this code (and changing noun_phrase):
ADJECTIVES = ['scary','hairy','charming','loud','beautiful','cromulent'] def adjectivestar(): prob = random.randrange(100) if prob < 70: return random.choice(ADJECTIVES)+" " + adjectivestar() else: return '' def noun_phrase(): """ article? adjective* noun """ return articleq() + ' ' + adjectivestar() + ' ' + noun()
The recursion comes from the idea that an adjectivestar (star is for the regexp notion that * means 0 or more of something) is either an empty string or a single adjective + another adjectivestar(). That adjectivestar can the in turn call itself again and again until the random number hits the base case of returning.
With the noun side replaced, we can similarly replace verb with verb_phrase. A verb_phrase might be a verb followed by zero or one adverbs.
The full code of this sentence generator can be found here.
Once we're done, assuming we filled our word lists with enough variety we can generate a bunch of sentences and hilarity will ensue. Sure, the tenses won't match and the parts of speech will be messed up but still, you'll get a lot of cool fun sentences.
You can also extend things with or without more recursion. You can generate a paragraph made up of multiple sentences or how about a compound_sentence which could be defined as sentence or sentence conjunction compound_sentence <– more recursion.
Not only is this a fun project but it also alludes to recursive parsing which some of your students might study later on.
This project can be a lot of fun. It's recursion but it's not math and in addition to the creative coding parts students can also get creative with sentence structure and word list.
Give it a go.
The loop thing is an issue if the student learned loops prior to recursion. It seems that students that start with functional programming show the reverse - they find loop problems tedious when they can "more easily" just use a functional construct.