1. Java Programming: From Problem Analysis to Program Design, 4e Chapter 13 Recursion

5. Recursive Definitions (continued) Java Programming: From Problem Analysis to Program Design, 4e

13. Recursive Factorial Method Java Programming: From Problem Analysis to Program Design, 4e public static int fact( int num) { if (num = = 0) return 1; else return num * fact(num – 1); }

14. Recursive Factorial Method (continued) Java Programming: From Problem Analysis to Program Design, 4e

15. Largest Value in Array Java Programming: From Problem Analysis to Program Design, 4e

17. Largest Value in Array (continued) Java Programming: From Problem Analysis to Program Design, 4e public static int largest( int [] list, int lowerIndex, int upperIndex) { int max; if (lowerIndex == upperIndex) return list[lowerIndex]; else { max = largest(list, lowerIndex + 1, upperIndex); if (list[lowerIndex] >= max) return list[lowerIndex]; else return max; } }

18. Execution of largest (list, 0, 3) Java Programming: From Problem Analysis to Program Design, 4e

19. Execution of largest (list, 0, 3) Java Programming: From Problem Analysis to Program Design, 4e

20. Recursive Fibonacci Java Programming: From Problem Analysis to Program Design, 4e

21. Recursive Fibonacci (continued) Java Programming: From Problem Analysis to Program Design, 4e public static int rFibNum( int a, int b, int n) { if (n == 1) return a; else if (n == 2) return b; else return rFibNum(a, b, n -1) + rFibNum(a, b, n - 2); }

22. Recursive Fibonacci (continued) Java Programming: From Problem Analysis to Program Design, 4e

23. Towers of Hanoi Problem with Three Disks Java Programming: From Problem Analysis to Program Design, 4e

24. Towers of Hanoi: Three Disk Solution Java Programming: From Problem Analysis to Program Design, 4e

25. Towers of Hanoi: Three Disk Solution (continued) Java Programming: From Problem Analysis to Program Design, 4e

26. Towers of Hanoi: Recursive Algorithm Java Programming: From Problem Analysis to Program Design, 4e public static void moveDisks( int count, int needle1, int needle3, int needle2) { if (count > 0) { moveDisks(count - 1, needle1, needle2, needle3); System.out.println( " Move disk " + count + " from needle " + needle1 + " to needle " + needle3 + " . " ); moveDisks(count - 1, needle2, needle3, needle1); } }

28. Programming Example: Decimal to Binary Java Programming: From Problem Analysis to Program Design, 4e

29. Java Programming: From Problem Analysis to Program Design, 4e

30. Sierpinski Gaskets of Various Orders Java Programming: From Problem Analysis to Program Design, 4e

32. Programming Example: Sierpinski Gasket (continued) Java Programming: From Problem Analysis to Program Design, 4e private void drawSierpinski(Graphics g, int lev, Point p1, Point p2, Point p3) { Point midP1P2; Point midP2P3; Point midP3P1; if (lev > 0) { g.drawLine(p1.x, p1.y, p2.x, p2.y); g.drawLine(p2.x, p2.y, p3.x, p3.y); g.drawLine(p3.x, p3.y, p1.x, p1.y); midP1P2 = midPoint(p1, p2); midP2P3 = midPoint(p2, p3); midP3P1 = midPoint(p3, p1); drawSierpinski(g, lev - 1, p1, midP1P2, midP3P1); drawSierpinski(g, lev - 1, p2, midP2P3, midP1P2); drawSierpinski(g, lev - 1, p3, midP3P1, midP2P3); } }

33. Programming Example: Sierpinski Gasket (continued) Java Programming: From Problem Analysis to Program Design, 4e