1. Introduction to Recursion - What is it? - When is it used? - Examples

2. A Recursive Method – A method that calls itself.
Very important concept for:
Fast sort algorithms
Binary tree traversals (Computer Science AB)
Fractal Generation

3. The parts of a Recursive Method
1. The Recursive Call: generally, the method calls
itself to perform a simpler version of the original problem.
2. The Stop Condition: each recursive method needs
a condition which does not call itself. This is where the
“winding up” occurs.
NO STOP CONDITION LEADS TO INFINITE RECURSION!!

4. Handout and Examples Please enter your value of n here when
it is your turn _____________
public void mystery (int n) {
if (n <= 0)
System.out.print(0);
else if (n%2 == 0)
mystery(n-1);
System.out.print("," + n*n); }
else
System.out.print(n*n + ",");

5. Handout and Examples 2. Consider the following recursive method:
public int foo(int x, int y) {
if (x < y)
return x;
else
return foo(x-y, y); }
For each function call below, indicate what value is returned:
Method call Value Returned
foo(6, 13) ____________
foo(14, 10) ____________
foo(37, 10) ____________
foo(8, 2) ____________
foo(50, 7) ____________

6. Handout and Examples 1. What is returned by the call compute(1, 5)?
public static int compute(int x, int y) {
if(x == y) return x;
else return (compute(x+1, y-1)); }
1. What is returned by the call compute(1, 5)?
2. Which of the following calls leads to infinite recursion?
I. compute(2, 8)
II. compute(8, 2)
III. compute(2, 5)

7. Programming Example
Write a recursive method that computes the number of cubes in a pyramid of cubes that is n cubes high.