5. Recursion A recursive definition is one which uses the word or concept being defined in the definition itself Example: “A computer is a machine that computes data” Recursion is a programming technique in which a method calls itself to solve a problem

6. Recursive Definitions Mathematical formulas often are expressed recursively N!, for any positive integer N, is defined to be the product of all integers between 1 and N inclusive This definition can be expressed recursively as: 1! = 1 N! = N * (N-1)! The concept of the factorial is defined in terms of another factorial until the base case of 1! is reached

7. public int getSum (int num) { if (num == 1) // base case return 1; else return (num + getSum (num - 1)); } // climbing the mountain

8. Infinite Recursion All recursive definitions must have a non-recursive part If they don't, there is no way to terminate the recursive path The non-recursive part is called the base case, and is implemented using an if-statement Recursion without a base case causes infinite recursion This problem is similar to an infinite loop, and will cause a StackOverflow exception

9. Recursive Programming A method in Java can invoke (call) itself; if set up that way, it is called a recursive method The code of a recursive method must be structured to handle both the base case and the recursive case Each call to the method sets up a new execution environment, with new parameters and new local variables As always, when the method execution completes, control returns to the method that invoked it (which may be an earlier invocation of itself)

10. Demos: –RecursionClass –RecursionClient

11. Recursion vs. Iteration (looping) Just because we can use recursion to solve a problem, doesn't mean we should Sometimes a loop is easier to understand, and more efficient Nevertheless, recursive solutions often are more simple and efficient than iterative solutions You must be able to determine when recursion is the correct technique to use http://en.wikipedia.org/wiki/Tower_of_Hanoi

12. Video: http://www.youtube.com/watch?v=BnUTikyR1CU

13. Assignments In a class called Recursion2, write the following methods: –factorial( ) -- receives an int parameter, return the factorial –exponent( ) – receieves 2 int parameters, x and y, returns x to the y power Obviously, these must be recursive methods. Now, write a client, Recursion2Client, to test the methods. –Error check: other than the “x” in exponent, parameters must be positive.