Chapter 17
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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.
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
- 4. 17 Calculate Factorials Using Recursion The Java solution: private int doFactorial(int N) { if ( N == 0 ) { return 1; } return N * doFactorial(N – 1); }
- 5. 17 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
- 6. 17 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
- 7. 17 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