What is recursion and when should I use it?

Answer 1

Here's a simple example: how many elements in a set. (there are better ways to count things, but this is a nice simple recursive example.)

First, we need two rules:

1. if the set is empty, the count of items in the set is zero (duh!).
2. if the set is not empty, the count is one plus the number of items in the set after one item is removed.

Suppose you have a set like this: [x x x]. let's count how many items there are.

1. the set is [x x x] which is not empty, so we apply rule 2. the number of items is one plus the number of items in [x x] (i.e. we removed an item).
2. the set is [x x], so we apply rule 2 again: one + number of items in [x].
3. the set is [x], which still matches rule 2: one + number of items in [].
4. Now the set is [], which matches rule 1: the count is zero!
5. Now that we know the answer in step 4 (0), we can solve step 3 (1 + 0)
6. Likewise, now that we know the answer in step 3 (1), we can solve step 2 (1 + 1)
7. And finally now that we know the answer in step 2 (2), we can solve step 1 (1 + 2) and get the count of items in [x x x], which is 3. Hooray!

We can represent this as:

count of [x x x] = 1 + count of [x x]
                 = 1 + (1 + count of [x])
                 = 1 + (1 + (1 + count of []))
                 = 1 + (1 + (1 + 0)))
                 = 1 + (1 + (1))
                 = 1 + (2)
                 = 3

When applying a recursive solution, you usually have at least 2 rules:

• the basis, the simple case which states what happens when you have "used up" all of your data. This is usually some variation of "if you are out of data to process, your answer is X"
• the recursive rule, which states what happens if you still have data. This is usually some kind of rule that says "do something to make your data set smaller, and reapply your rules to the smaller data set."

If we translate the above to pseudocode, we get:

numberOfItems(set)
    if set is empty
        return 0
    else
        remove 1 item from set
        return 1 + numberOfItems(set)

There's a lot more useful examples (traversing a tree, for example) which I'm sure other people will cover.