Thread: Mmm...recursion~

You should go and learn some data structures(especially linked lists and binary trees) to practice a lot of recursion problems.

Some very good problems are in Stanford computer science library online. They are both introductory and challenging to some extent.

Then you can go further and learn about game theory and compression. Ask me if you can't have enough information and links.

recursion means calling the same function within the function:

Code:

bool function(int data)
{
  //whatever
  function(newData);//recursive call of function()
  //whatever
}

This can lead to an endless loop, so you should always be sure you use a terminating condition to prevent this:

Code:

bool function(int data)
{
   //terminating condition
   //do something different if terminating condition exists
   //otherwise continue blithely onward
   function(newData);
  //whatever
}

let's say you wanted to print all integers from 0 to 10 in order using recursion. You would pass 0 first; check to see if it equaled 10. If it does you would stop any further funciton calls. If it didn't you would increment it and pass it again.

Code:

bool function(int data)
{
   if(data == 10)
   {
     cout << data << endl;  //print out data
     return false; 
   } 

/*if data equals 10 this will stop this call and return false to the function that made this call.  The calling function ignores the return, but that doesn't matter, and it won't be ignored in all recursive functions.   IF data equals 10 none of the stuff below will be used.  If data != 10 then function() will proceed to stuff below
*/

   cout << data << endl;  //here we print out the desired info
   int newData = ++data; 
/*here we increment data and assign it to newData.  You could pass ++data itself but I think this is clearer
*/
    
   function(newData); //here's the recursive call
   
   return false;
/*this return won't happen untile the line immediately above it is completed if data isn't 10.  
*/
}

Here it is in a program:

Code:

#include <iostream.h>

bool function(int data);

int main()
{
  int  Data = 0;
  function(Data);
  return 0;
}
  
bool function(int data)
{
   if(data == 10)
   {
      cout << data << endl;
      return false;
    }

    cout << data << endl;
    int newData = ++data;
    function(newData);
    return false;
}

To see an interesting effect try this variant of function. Note the critical difference placement of the single line of code makes. You can use this effect to your advantage sometimes.

Code:

bool function(int data)
{
   if(data == 10)
   {
      cout << data << endl;
      return false;
    }

    //cout << data << endl;
    int newData = ++data;
    function(newData);

    cout << data << endl;

    return false;
}

Another famous example, the factorial function:

n! = n x (n-1) x (n-2) x .. x 3 x 2 x 1

This is a recursive definition. The is reached when 1 is reached, which is the end-step of the recursion. The recursion step is n x n-1)!. This can be easily seen as follows:

2! = 2 x 1
3! = 3 x 2 x 1 = 3 x 2!
4! = 4 x 3 x 2 x 1 = 4 x 3!
n! = n x (n-1) x .. x 2 x 1 = n x (n-1)!

This leads to this recursive function:

Code:

int fac (int n)
{
    if (n == 1) /* the end-step */
        return n;
    else
        return (n * fac (n - 1));

Hope this example helps a little in understanding recursion. To understand recursion, I used to study mathematical relations and then translate them to code. Another famous example is the Fibonacci numbers:

F[0] = 0
F[1] = 1
F[n] = F[n-1] + F[n-2]

Here the end-step is reached if n = 1. The recursion step is the recursive relation F[n] = F[n-1] + F[n-2]. This leads to the recursive function:

Code:

int fib (int n)
{
    if (n == 1)
        return (n);
    else
        return (fib (n-1) + fib (n-2));
}

More on Fibonacci can be found here:

http://mathworld.wolfram.com/FibonacciNumber.html