by Kevin Ennis

I’m just gonna get this out of the way right up front, because people get really angry otherwise:

Consider this post as a series of learning exercises. These examples are designed to make you think — and, if I’m doing it right, maybe expand your understanding of functional programming a little bit.

Hey, dawg. I heard you like recursion, so I put a “Hey, dawg. I heard you like recursion, so I put a “Hey, dawg…

Loosely defined, recursion is the process of taking a big problem and sub-dividing it into multiple, smaller instances of the same problem.

Put into practice, that generally means writing a function that calls itself. Probably the most classic example of this concept is the factorial function.

You may remember from math class that the factorial of a number n is the product of all positive integers less than or equal to n. In other words, the factorial of 5 is 5 x 4 x 3 x 2 x 1. The mathematical notation for this is 5!.

Something interesting you might have noticed about that pattern: 5! is actually just 5 x 4!. And 4! is just 4 x 3!. So on and so forth until you get down to 1.

Here’s how we’d write that in JavaScript:

If this seems confusing, I’d encourage you to mentally walk through the code using the example of factorial( 3 ).

Here’s a bit of help, in case you need it:

  1. factorial( 3 ) is 3 x factorial( 2 ).
  2. factorial( 2 ) is 2 x factorial( 1 ).
  3. factorial( 1 ) meets our if condition, so it’s just 1.

So what’s really happening here is that you’re winding up the call stack, getting down to 1, and then unwinding the stack. As you unwind the call stack, you multiply each result. 1 x 2 x 3 is 6, and that’s your return value.

Reversing A String

One of my co-workers recently told me about a whiteboard question that he’d been asked in an interview, and I thought it was kind of a fun problem.

Write a function that accepts a string a reverses it. Recursively.

If you’re the ambitious type, I’d encourage you to take a few minutes and try to solve this one on your own. Keep in mind the core principle of recursion, which is to take a big problem and break it down into smaller instances of itself.

If you got stuck (or you’re the decidedly unambitious type), here’s my solution:

Again, I’ll give a quick walk-through example in case you got stuck. We’ll use reverse(‘bar’) as a starting point.

  1. reverse(‘bar’) is reverse(‘ar’) + ‘b’
  2. reverse(‘ar’) is reverse(‘r’) + ‘a’
  3. reverse(‘r’) meets our if condition, so it’s just ‘r’

When the call stack unwinds, we end up with ‘r’ + ‘a’ + ‘b’.

Writing a Recursive Map Function

For our final example, we’re going to write a map() function. We want to be able to use it like this:

Again, I’d strongly encourage you to take a few minutes and try this one on your own. Here are a few hints and reminders:

  1. map() should always return a new array.
  2. Break the problem down into smaller chunks.
  3. Remember the reverse() example.

Oh, good. You’re back. How did it go?

j/k, this is a blog and I can’t hear you. lol.

Anyway, here’s how I did it:

So let’s go through this using the example I gave earlier:

  1. Call map() using the array [ ‘a’, ‘b’, ‘c’ ]
  2. Create a new array that holds the result of calling fn(‘a’)
  3. Return [ ‘A’ ].concat( map([ ‘b’, ‘c’ ]) )
  4. Repeat steps 1 through 3 with [ ‘b’, ‘c’ ]
  5. Repeat steps 1 through 3 for [ ‘c’ ]
  6. Eventually, we call map() with an empty array, which ends the recursion.

You should never, ever, ever do this in a real application. You’ll blow out the stack on large arrays, and more importantly, you create a huge amount of garbage by instantiating so many new objects. Use Array#map in production code.

Wrap Up

Hopefully I did a decent job in explaining this stuff. If you’re still struggling a bit to wrap your head around recursion, the best advice I can give is to start with small examples and mentally trace the call stack. Try something like reverse(‘abc’) and walk through it, step-by-step. Eventually it’ll click.

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And if you’re in the Boston area and want to come work on crazy, interesting, hard problems with me at Starry, shoot me an email. I’m hiring.