What is recursion and when should I use it?

Answer 1

1.) A method is recursive if it can call itself; either directly:

void f() {
   ... f() ... 
}

or indirectly:

void f() {
    ... g() ...
}

void g() {
   ... f() ...
}

2.) When to use recursion

Q: Does using recursion usually make your code faster? 
A: No.
Q: Does using recursion usually use less memory? 
A: No.
Q: Then why use recursion? 
A: It sometimes makes your code much simpler!

3.) People use recursion only when it is very complex to write iterative code. For example, tree traversal techniques like preorder, postorder can be made both iterative and recursive. But usually we use recursive because of its simplicity.

Answer 2

Recursion is a method of solving problems based on the divide and conquer mentality. The basic idea is that you take the original problem and divide it into smaller (more easily solved) instances of itself, solve those smaller instances (usually by using the same algorithm again) and then reassemble them into the final solution.

The canonical example is a routine to generate the Factorial of n. The Factorial of n is calculated by multiplying all of the numbers between 1 and n. An iterative solution in C# looks like this:

public int Fact(int n)
{
  int fact = 1;

  for( int i = 2; i <= n; i++)
  {
    fact = fact * i;
  }

  return fact;
}

There's nothing surprising about the iterative solution and it should make sense to anyone familiar with C#.

The recursive solution is found by recognising that the nth Factorial is n * Fact(n-1). Or to put it another way, if you know what a particular Factorial number is you can calculate the next one. Here is the recursive solution in C#:

public int FactRec(int n)
{
  if( n < 2 )
  {
    return 1;
  }

  return n * FactRec( n - 1 );
}

The first part of this function is known as a Base Case (or sometimes Guard Clause) and is what prevents the algorithm from running forever. It just returns the value 1 whenever the function is called with a value of 1 or less. The second part is more interesting and is known as the Recursive Step. Here we call the same method with a slightly modified parameter (we decrement it by 1) and then multiply the result with our copy of n.

When first encountered this can be kind of confusing so it's instructive to examine how it works when run. Imagine that we call FactRec(5). We enter the routine, are not picked up by the base case and so we end up like this:

// In FactRec(5)
return 5 * FactRec( 5 - 1 );

// which is
return 5 * FactRec(4);

If we re-enter the method with the parameter 4 we are again not stopped by the guard clause and so we end up at:

// In FactRec(4)
return 4 * FactRec(3);

If we substitute this return value into the return value above we get

// In FactRec(5)
return 5 * (4 * FactRec(3));

This should give you a clue as to how the final solution is arrived at so we'll fast track and show each step on the way down:

return 5 * (4 * FactRec(3));
return 5 * (4 * (3 * FactRec(2)));
return 5 * (4 * (3 * (2 * FactRec(1))));
return 5 * (4 * (3 * (2 * (1))));

That final substitution happens when the base case is triggered. At this point we have a simple algrebraic formula to solve which equates directly to the definition of Factorials in the first place.

It's instructive to note that every call into the method results in either a base case being triggered or a call to the same method where the parameters are closer to a base case (often called a recursive call). If this is not the case then the method will run forever.

Answer 3

Recursion refers to a method which solves a problem by solving a smaller version of the problem and then using that result plus some other computation to formulate the answer to the original problem. Often times, in the process of solving the smaller version, the method will solve a yet smaller version of the problem, and so on, until it reaches a "base case" which is trivial to solve.

For instance, to calculate a factorial for the number X, one can represent it as X times the factorial of X-1. Thus, the method "recurses" to find the factorial of X-1, and then multiplies whatever it got by X to give a final answer. Of course, to find the factorial of X-1, it'll first calculate the factorial of X-2, and so on. The base case would be when X is 0 or 1, in which case it knows to return 1 since 0! = 1! = 1.

Answer 4

In the most basic computer science sense, recursion is a function that calls itself. Say you have a linked list structure:

struct Node {
    Node* next;
};

And you want to find out how long a linked list is you can do this with recursion:

int length(const Node* list) {
    if (!list->next) {
        return 1;
    } else {
        return 1 + length(list->next);
    }
}

(This could of course be done with a for loop as well, but is useful as an illustration of the concept)

Answer 5

Recursion is solving a problem with a function that calls itself. A good example of this is a factorial function. Factorial is a math problem where factorial of 5, for example, is 5 * 4 * 3 * 2 * 1. This function solves this in C# for positive integers (not tested - there may be a bug).

public int Factorial(int n)
{
    if (n <= 1)
        return 1;

    return n * Factorial(n - 1);
}

Answer 6

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.