What is recursion and when should I use it?

Answer 1

"If I have a hammer, make everything look like a nail."

Recursion is a problem-solving strategy for huge problems, where at every step just, "turn 2 small things into one bigger thing," each time with the same hammer.

Example

Suppose your desk is covered with a disorganized mess of 1024 papers. How do you make one neat, clean stack of papers from the mess, using recursion?

1. Divide: Spread all the sheets out, so you have just one sheet in each "stack".
2. Conquer:
   2. Go around, putting each sheet on top of one other sheet. You now have stacks of 2.
   3. Go around, putting each 2-stack on top of another 2-stack. You now have stacks of 4.
   4. Go around, putting each 4-stack on top of another 4-stack. You now have stacks of 8.
   5. ... on and on ...
   6. You now have one huge stack of 1024 sheets!

Notice that this is pretty intuitive, aside from counting everything (which isn't strictly necessary). You might not go all the way down to 1-sheet stacks, in reality, but you could and it would still work. The important part is the hammer: With your arms, you can always put one stack on top of the other to make a bigger stack, and it doesn't matter (within reason) how big either stack is.

Answer 2

function call itself or use its own definition.

Answer 3

A recursive statement is one in which you define the process of what to do next as a combination of the inputs and what you have already done.

For example, take factorial:

factorial(6) = 6*5*4*3*2*1

But it's easy to see factorial(6) also is:

6 * factorial(5) = 6*(5*4*3*2*1).

So generally:

factorial(n) = n*factorial(n-1)

Of course, the tricky thing about recursion is that if you want to define things in terms of what you have already done, there needs to be some place to start.

In this example, we just make a special case by defining factorial(1) = 1.

Now we see it from the bottom up:

factorial(6) = 6*factorial(5)
                   = 6*5*factorial(4)
                   = 6*5*4*factorial(3) = 6*5*4*3*factorial(2) = 6*5*4*3*2*factorial(1) = 6*5*4*3*2*1

Since we defined factorial(1) = 1, we reach the "bottom".

Generally speaking, recursive procedures have two parts:

1) The recursive part, which defines some procedure in terms of new inputs combined with what you've "already done" via the same procedure. (i.e. factorial(n) = n*factorial(n-1))

2) A base part, which makes sure that the process doesn't repeat forever by giving it some place to start (i.e. factorial(1) = 1)

It can be a bit confusing to get your head around at first, but just look at a bunch of examples and it should all come together. If you want a much deeper understanding of the concept, study mathematical induction. Also, be aware that some languages optimize for recursive calls while others do not. It's pretty easy to make insanely slow recursive functions if you're not careful, but there are also techniques to make them performant in most cases.

Hope this helps...

Answer 4

There are a number of good explanations of recursion in this thread, this answer is about why you shouldn't use it in most languages.* In the majority of major imperative language implementations (i.e. every major implementation of C, C++, Basic, Python, Ruby,Java, and C#) iteration is vastly preferable to recursion.

To see why, walk through the steps that the above languages use to call a function:

1. space is carved out on the stack for the function's arguments and local variables
2. the function's arguments are copied into this new space
3. control jumps to the function
4. the function's code runs
5. the function's result is copied into a return value
6. the stack is rewound to its previous position
7. control jumps back to where the function was called

Doing all of these steps takes time, usually a little bit more than it takes to iterate through a loop. However, the real problem is in step #1. When many programs start, they allocate a single chunk of memory for their stack, and when they run out of that memory (often, but not always due to recursion), the program crashes due to a stack overflow.

So in these languages recursion is slower and it makes you vulnerable to crashing. There are still some arguments for using it though. In general, code written recursively is shorter and a bit more elegant, once you know how to read it.

There is a technique that language implementers can use called tail call optimization which can eliminate some classes of stack overflow. Put succinctly: if a function's return expression is simply the result of a function call, then you don't need to add a new level onto the stack, you can reuse the current one for the function being called. Regrettably, few imperative language-implementations have tail-call optimization built in.

* I love recursion. My favorite static language doesn't use loops at all, recursion is the only way to do something repeatedly. I just don't think that recursion is generally a good idea in languages that aren't tuned for it.

** By the way Mario, the typical name for your ArrangeString function is "join", and I'd be surprised if your language of choice doesn't already have an implementation of it.

Answer 5

A recursive function is one which calls itself. The most common reason I've found to use it is traversing a tree structure. For example, if I have a TreeView with checkboxes (think installation of a new program, "choose features to install" page), I might want a "check all" button which would be something like this (pseudocode):

function cmdCheckAllClick {
    checkRecursively(TreeView1.RootNode);
}

function checkRecursively(Node n) {
    n.Checked = True;
    foreach ( n.Children as child ) {
        checkRecursively(child);
    }
}

So you can see that the checkRecursively first checks the node which it is passed, then calls itself for each of that node's children.

You do need to be a bit careful with recursion. If you get into an infinite recursive loop, you will get a Stack Overflow exception :)

I can't think of a reason why people shouldn't use it, when appropriate. It is useful in some circumstances, and not in others.

I think that because it's an interesting technique, some coders perhaps end up using it more often than they should, without real justification. This has given recursion a bad name in some circles.

Answer 6

Simple english example of recursion.

A child couldn't sleep, so her mother told her a story about a little frog,
    who couldn't sleep, so the frog's mother told her a story about a little bear,
         who couldn't sleep, so the bear's mother told her a story about a little weasel... 
            who fell asleep.
         ...and the little bear fell asleep;
    ...and the little frog fell asleep;
...and the child fell asleep.