Understanding recursion [closed]

Answer 1

Recursion

Method A, calls Method A calls Method A. Eventually one of these method A's won't call and exit, but it's recursion because something calls itself.

Example of recursion where I want to print out every folder name on the hard drive: (in c#)

public void PrintFolderNames(DirectoryInfo directory)
{
    Console.WriteLine(directory.Name);

    DirectoryInfo[] children = directory.GetDirectories();

    foreach(var child in children)
    {
        PrintFolderNames(child); // See we call ourself here...
    }
}

Answer 2

Simple recursive example in Common Lisp:

MYMAP applies a function to each element in a list.

1) an empty list has no element, so we return the empty list - () and NIL both are the empty list.

2) apply the function to the first list, call MYMAP for the rest of the list (the recursive call) and combine both results into a new list.

(DEFUN MYMAP (FUNCTION LIST)
  (IF (NULL LIST)
      ()
      (CONS (FUNCALL FUNCTION (FIRST LIST))
            (MYMAP FUNCTION (REST LIST)))))

Let's watch the traced execution. On ENTERing a function, the arguments are printed. On EXITing a function, the result is printed. For each recursive call, the output will be indented on level.

This example calls the SIN function on each number in a list (1 2 3 4).

Command: (mymap 'sin '(1 2 3 4))

1 Enter MYMAP SIN (1 2 3 4)
| 2 Enter MYMAP SIN (2 3 4)
|   3 Enter MYMAP SIN (3 4)
|   | 4 Enter MYMAP SIN (4)
|   |   5 Enter MYMAP SIN NIL
|   |   5 Exit MYMAP NIL
|   | 4 Exit MYMAP (-0.75680256)
|   3 Exit MYMAP (0.14112002 -0.75680256)
| 2 Exit MYMAP (0.9092975 0.14112002 -0.75680256)
1 Exit MYMAP (0.841471 0.9092975 0.14112002 -0.75680256)

This is our result:

(0.841471 0.9092975 0.14112002 -0.75680256)

Answer 3

To explain recursion to a six-year-old, first explain it to a five-year-old, and then wait a year.

Actually, this is a useful counter-example, because your recursive call should be simpler, not harder. It would be even harder to explain recursion to a five-year old, and though you could stop the recursion at 0, you have no simple solution for explaining recursion to a zero-year-old.

To solve a problem using recursion, first sub-divide it into one or more simpler problems that you can solve in the same way, and then when the problem is simple enough to solve without further recursion, you can return back up to higher levels.

In fact, that was a recursive definition of how to solve a problem with recursion.

Answer 4

If you want a book that does a good job of explaining recursion in simple terms, take a look at Gödel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter, specifically Chapter 5. In addition to recursion it does a nice job of explaining a number of complex concepts in computer science and math in an understandable way, with one explanation building on another. If you haven't had much exposure to these sorts of concepts before, it can be a pretty mindblowing book.

Answer 5

When working with recursive solutions, I always try to:

• Establish the base case first i.e. when n = 1 in a solution to factorial
• Try to come up with a general rule for every other case

Also there are different types of recursive solutions, there's the divide and conquer approach which is useful for fractals and many others.

It would also help if you could work on simpler problems first just to get the hang of it. Some examples are solving for the factorial and generating the nth fibonacci number.

For references, I highly recommend Algorithms by Robert Sedgewick.

Hope that helps. Good luck.

Answer 6

This is more of a complaint than a question. Do you have a more specific question on recursion? Like multiplication, it's not a thing people write a lot about.

Speaking of multiplication, think of this.

Question:

What's a*b?

Answer:

If b is 1, it's a. Otherwise, it's a+a*(b-1).

What's a*(b-1)? See the above question for a way to work it out.