Recursive Methods as a Problem Solving Techique

  1. Recursive Method:

    Example: direct recursive method 
          public class myClass
      {
         ....
	 public (static) ... recursiveMethod(...)
         {
	    ...
	    ...
	    recursiveMethod(new set of parameters)
	    ...
	    ...
	 }
      }

    Example: indirect recursive method 
          public class myClass
      {
         ....
	 public (static) ... recursiveMethod1(...)
         {
	    ...
	    ...
	    recursiveMethod2(.....)
	    ...
	    ...
	 }

	 public (static) ... recursiveMethod2(...)
         {
	    ...
	    ...
	    recursiveMethod1(.....)
	    ...
	    ...
	 }
      }

  2. Recursion is extremely suitable for solving problem that have the following characteristics:

  3. Recursive problem solving technique:

    General structure of a Recursive Solution 
          public ... recursiveSolve("problem N")
      {
	 if ( "problem N" is a base case )
	 {
	    return( (known) solution for base case );
	 }
	 else
	 {
	    Split "problem N" into k smaller "problems < N" 
		and a "problem X"

	    sol_1 = recursiveSolve("smaller problem 1");
	    sol_2 = recursiveSolve("smaller problem 2");
	    ....
	    sol_k = recursiveSolve("smaller problem k");

	    solution = solve "problem X" using the solutions
	               "sol_1", "sol_2", ..., "sol_k"

	    return(solution);
	 }
      }
    • The statements in this skeletal program must be customized for each problem
    • There is no "magic formula", use your wits...
      (study Mathematics will help you build wits)

  4. Example: factorial

    The recursive program:

    Recursive Method to find Factorial of integer N 
       public class Numeric
   {
      public static int factorial(int N)
      {
	 if ( N == 0 )
	 {
	    return( 1 );   // (known) solution for base case
	 }
	 else
	 {
	    int sol;
	    int solX;

	    sol = factorial(N-1);
	    solX = N * sol;

	    return(solX);
	 }
      }
   }

  5. NOTE: The recursive solution depends heavily on the temporal dimension of local & parameter scoping

  6. Demo programs: