1. Recursion Definition: A method that calls itself. Examples
public int factorial(int n)
{ if (n==1) return 1; return n * factorial(n-1); }
public void hello(int n)
{ if (n>=0)
{ System.out.println("Hello"); hello(n-1);

2. Addr of the println() call.
Why does it work?
Example call:
int i = do(9, -1);
System.out.println(i);
Declaration:
public int do(int n,int k)
{ int num = 5; return n + k + num; }
Java creates an activation record for every method call Definition: An activation record is a block of memory on the call stack containing parameter values, local variables, the return address, and return value.
The activation record exists only while the method executes
The activation record is released when the method returns
A stack is a last-in first-out list
A list is an ordered collection of elements.
Activation Record
n: 9
k: -1
num: 5 valueToReturn: 13
Return addr:
Addr of the println() call.

3. Another Example Simple Example: Notes: Question:
See ../demos/SumByRecursion.java
Notes:
The then branch of the 'if' statement is the non-recursive part (the basis case)
The else branch contains the recursive call
A stack overflow occurs if the basis case never executes
Question:
What happens if startIndex is negative?

4. Designing a recursive method
There are two requirements
Define the basis case
Define the relationship between the problem and one or more smaller problems of the same kind
When is recursion beneficial?
Recursive algorithms are ALWAYS slower than their non-recursive counterparts. Why?
Recursive algorithms can often reduce a problem to just a few statements.
Non-recursive algorithms can be sometimes more difficult to program and maintain.
Recursion is useful when the recursion step significantly reduces the problem size.

5. Some more examples Fibonacci sequence: 1, 1, 2, 3, 5, 8, …
Basis case: n<2; Recursive step: return f(n-2)+f(n-1)
Greatest common denominator
Basis case: y%x = 0; Recursive step: return gcd(y%x,x)
See ../demos/GCD.java
Palindrome Tester
Basis case: length <=1 or first character <> last character
Recursive step: pal(s.substring(1,s.length()-2))
Print a string (Question: How would you reverse a string?)
Basis case: length=1; Recursive step: print char 0 and call with remainder

6. Towers of Hanoi A disk is represented by its size 0 == smallest
A tower is represented by a char: A, B, or C
src == tower holding the disks to be moved
dest == tower to which to move the disks
spare == tower to use as a temporary holding place
FUNCTION recursiveMove(disk, src, dest, spare):
IF disk == 0, THEN:
move disk from src to dest
ELSE:
recursiveMove(disk - 1, src, spare, dest)
recursiveMove(disk - 1, spare, dest, src)
END IF

7. Graphics and Fractals Definition: A recursive geometric pattern
Examples:
Drawing a tree visually
Sierpinski's triangles
Koch's Snowflake -
See demos/KochFlakeLeaf.java
Mandelbrot set – uses complex numbers
Our lab4: Recursively generate an image