Recursion

Chapter 17

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What is recursion?Recursion occurs when a method calls itself, either directly or indirectly.

Used to solve difficult, repetitive problems

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Factorial ExampleN! (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

17Calculate Factorials Using

RecursionThe Java solution:

private int doFactorial(int N){ if ( N == 0 ) { return 1; } return N * doFactorial(N – 1);}

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Towers of HanoiThree 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

17The Towers of Hanoi

AlgorithmClassic 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 SolutionFinal graphical solution includes the files:

TowerRing.java

Tower.java

TowerMove.java

ThreeTowers.java

TowersOfHanoi.java

TowerPanel.java

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Graphical Towers of HanoiApplet in progress