What is recursion and when should I use it?

Answer 1

Well, that's a pretty decent definition you have. And wikipedia has a good definition too. So I'll add another (probably worse) definition for you.

When people refer to "recursion", they're usually talking about a function they've written which calls itself repeatedly until it is done with its work. Recursion can be helpful when traversing hierarchies in data structures.

Answer 2

1. A function that calls itself
2. When a function can be (easily) decomposed into a simple operation plus the same function on some smaller portion of the problem. I should say, rather, that this makes it a good candidate for recursion.
3. They do!

The canonical example is the factorial which looks like:

int fact(int a) 
{
  if(a==1)
    return 1;

  return a*fact(a-1);
}

In general, recursion isn't necessarily fast (function call overhead tends to be high because recursive functions tend to be small, see above) and can suffer from some problems (stack overflow anyone?). Some say they tend to be hard to get 'right' in non-trivial cases but I don't really buy into that. In some situations, recursion makes the most sense and is the most elegant and clear way to write a particular function. It should be noted that some languages favor recursive solutions and optimize them much more (LISP comes to mind).

Answer 3

A recursive function is a function that contains a call to itself. A recursive struct is a struct that contains an instance of itself. You can combine the two as a recursive class. The key part of a recursive item is that it contains an instance/call of itself.

Consider two mirrors facing each other. We've seen the neat infinity effect they make. Each reflection is an instance of a mirror, which is contained within another instance of a mirror, etc. The mirror containing a reflection of itself is recursion.

A binary search tree is a good programming example of recursion. The structure is recursive with each Node containing 2 instances of a Node. Functions to work on a binary search tree are also recursive.

Answer 4

hey, sorry if my opinion agrees with someone, I'm just trying to explain recursion in plain english.

suppose you have three managers - Jack, John and Morgan. Jack manages 2 programmers, John - 3, and Morgan - 5. you are going to give every manager 300$ and want to know what would it cost. The answer is obvious - but what if 2 of Morgan-s employees are also managers?

HERE comes the recursion. you start from the top of the hierarchy. the summery cost is 0$. you start with Jack, Then check if he has any managers as employees. if you find any of them are, check if they have any managers as employees and so on. Add 300$ to the summery cost every time you find a manager. when you are finished with Jack, go to John, his employees and then to Morgan.

You'll never know, how much cycles will you go before getting an answer, though you know how many managers you have and how many Budget can you spend.

Recursion is a tree, with branches and leaves, called parents and children respectively. When you use a recursion algorithm, you more or less consciously are building a tree from the data.

Answer 5

Whenever a function calls itself, creating a loop, then that's recursion. As with anything there are good uses and bad uses for recursion.

The most simple example is tail recursion where the very last line of the function is a call to itself:

int FloorByTen(int num)
{
    if (num % 10 == 0)
        return num;
    else
        return FloorByTen(num-1);
}

However, this is a lame, almost pointless example because it can easily be replaced by more efficient iteration. After all, recursion suffers from function call overhead, which in the example above could be substantial compared to the operation inside the function itself.

So the whole reason to do recursion rather than iteration should be to take advantage of the call stack to do some clever stuff. For example, if you call a function multiple times with different parameters inside the same loop then that's a way to accomplish branching. A classic example is the Sierpinski triangle.

You can draw one of those very simply with recursion, where the call stack branches in 3 directions:

private void BuildVertices(double x, double y, double len)
{
    if (len > 0.002)
    {
        mesh.Positions.Add(new Point3D(x, y + len, -len));
        mesh.Positions.Add(new Point3D(x - len, y - len, -len));
        mesh.Positions.Add(new Point3D(x + len, y - len, -len));
        len *= 0.5;
        BuildVertices(x, y + len, len);
        BuildVertices(x - len, y - len, len);
        BuildVertices(x + len, y - len, len);
    }
}

If you attempt to do the same thing with iteration I think you'll find it takes a lot more code to accomplish.

Other common use cases might include traversing hierarchies, e.g. website crawlers, directory comparisons, etc.

Conclusion

In practical terms, recursion makes the most sense whenever you need iterative branching.

Answer 6

This is an old question, but I want to add an answer from logistical point of view (i.e not from algorithm correctness point of view or performance point of view).

I use Java for work, and Java doesn't support nested function. As such, if I want to do recursion, I might have to define an external function (which exists only because my code bumps against Java's bureaucratic rule), or I might have to refactor the code altogether (which I really hate to do).

Thus, I often avoid recursion, and use stack operation instead, because recursion itself is essentially a stack operation.