Recursion is a method that calls itself, directly or indirectly. It is used to solve repetitive problems like calculating factorials and solving the Towers of Hanoi puzzle. The factorial example shows recursion can be used to calculate N! by defining it as N * (N-1)! and base cases where 0! = 1. Similarly, the Towers of Hanoi is solved recursively by breaking it down into moving all disks but the largest, moving the largest disk, and moving the remaining disks.

1. Recursion
Chapter 17

2. 17
What is recursion?
Recursion occurs when a method calls
itself, either directly or indirectly.
Used to solve difficult, repetitive
problems

3. 17
Factorial Example
N! (N Factorial)
N! = N * (N – 1)! for N >= 0 and 0! = 1
5! = 5 * 4! or 5 * 4 * 3 * 2 * 1 * 1 = 120
4! = 4 * 3! or 4 * 3 * 2 * 1 * 1 = 24
3! = 3 * 2! or 3 * 2 * 1 * 1 = 6
2! = 2 * 1! or 2 * 1 * 1 = 2
1! = 1 * 0! or 1 * 1 = 1
0! = 1

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Calculate Factorials Using Recursion
The Java solution:
private int doFactorial(int N)
{
if ( N == 0 )
{
return 1;
}
return N * doFactorial(N – 1);
}

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Towers of Hanoi
Three towers hold rings stacked in order
from largest to smallest (bottom to top)
Player can only move one ring at a time
Larger rings cannot be stacked on top of
smaller ring
Player must move stack to another tower

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The Towers of Hanoi Algorithm
Classic problem can be solved with
recursion.
Move N–1 rings to storage tower
Move Nth ring to destination tower
Move N–1 rings to destination tower

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Towers of Hanoi Solution
Final graphical solution includes the files:
TowerRing.java
Tower.java
TowerMove.java
ThreeTowers.java
TowersOfHanoi.java
TowerPanel.java

8. 17
Graphical Towers of Hanoi
Applet in progress