Examples of Recursive functions [closed]

This illustration is in English, rather than an actual programming language, but is useful for explaining the process in a non-technical way:

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

In order to understand recursion, one must first understand recursion.

The rule of thumb for recursion is, "Use recursion, if and only if on each iteration your task splits into two or more similar tasks".

So Fibonacci is not a good example of recursion application, while Hanoi is a good one.

So most of the good examples of recursion are tree traversal in different disquises.

For example: graph traversal - the requirement that visited node will never be visited again effectively makes graph a tree (a tree is a connected graph without simple cycles)

divide and conquer algorithms (quick sort, merge sort) - parts after "divide" constitute children nodes, "conquer" constitues edges from parent node to child nodes.

How about testing a string for being a palindrome?

bool isPalindrome(char* s, int len)
{
  if(len < 2)
    return TRUE;
  else
    return s[0] == s[len-1] && isPalindrome(&s[1], len-2);
}

Of course, you could do that with a loop more efficiently.