Recursion!. Can a method call another method? YES.

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Presentation transcript:

Recursion!

Can a method call another method?

YES

Can a method itself? Also YES

Rules: 1. Recursive call must be to a smaller version of the problem. 2. Recursion must be heading for the base case.

public static int fact(int n) { if (n == 0) return 1; else return n*fact(n-1); }

public static void main(String[] args) { int f; f = fact(4); System.out.println(f); } Call to fact(4)

public static int fact(int n) { if (n == 0) return 1; else return n *fact(n -1); }

public static int fact(int 4) { if (4 == 0) return 1; else return 4 *fact(4 -1); } Call to fact(3)

public static int fact(int 4) { if (4 == 0) return 1; else return 4 *fact(4 -1); } public static int fact(int 3) { if (3 == 0) return 1; else return 3 *fact(3 -1); } Call to fact(2)

public static int fact(int 4) { if (4 == 0) return 1; else return 4 *fact(4 -1); } public static int fact(int 3) { if (3 == 0) return 1; else return 3 *fact(3 -1); } public static int fact(int 2) { if (2 == 0) return 1; else return 2 *fact(2 -1); } Call to fact(1)

public static int fact(int 4) { if (4 == 0) return 1; else return 4 *fact(4 -1); } public static int fact(int 3) { if (3 == 0) return 1; else return 3 *fact(3 -1); } public static int fact(int 2) { if (2 == 0) return 1; else return 2 *fact(2 -1); } public static int fact(int 1) { if (1 == 0) return 1; else return 1 *fact(1 -1); } Call to fact(0)

public static int fact(int 4) { if (4 == 0) return 1; else return 4 *fact(4 -1); } public static int fact(int 3) { if (3 == 0) return 1; else return 3 *fact(3 -1); } public static int fact(int 2) { if (2 == 0) return 1; else return 2 *fact(2 -1); } public static int fact(int 1) { if (1 == 0) return 1; else return 1 *fact(1 -1); } public static int fact(int 0) { if (0 == 0) return 1; else return 0 *fact(0 -1); }

public static int fact(int 4) { if (4 == 0) return 1; else return 4 *fact(4 -1); } public static int fact(int 3) { if (3 == 0) return 1; else return 3 *fact(3 -1); } public static int fact(int 2) { if (2 == 0) return 1; else return 2 *fact(2 -1); } public static int fact(int 1) { if (1 == 0) return 1; else return 1 *fact(1 -1); } public static int fact(int 0) { if (0 == 0) return 1; else return 0 *fact(0 -1); }

public static int fact(int 4) { if (4 == 0) return 1; else return 4 *fact(4 -1); } public static int fact(int 3) { if (3 == 0) return 1; else return 3 *fact(3 -1); } public static int fact(int 2) { if (2 == 0) return 1; else return 2 *fact(2 -1); } public static int fact(int 1) { if (1 == 0) return 1; else return 1 *fact(1 -1); } Returned 1

public static int fact(int 4) { if (4 == 0) return 1; else return 4 *fact(4 -1); } public static int fact(int 3) { if (3 == 0) return 1; else return 3 *fact(3 -1); } public static int fact(int 2) { if (2 == 0) return 1; else return 2 *fact(2 -1); } Returned 1

public static int fact(int 4) { if (4 == 0) return 1; else return 4 *fact(4 -1); } public static int fact(int 3) { if (3 == 0) return 1; else return 3 *fact(3 -1); } Returned 2

public static int fact(int 4) { if (4 == 0) return 1; else return 4 *fact(4 -1); } Returned 6

public static void main(String[] args) { int f; f = fact(4); System.out.println(f); } Returned 24

public static void main(String[] args) { int f; f = fact(4); System.out.println(f); } Displays 24

?

Comments about recursion 1.Recursion is never necessary. Can always be done iteratively. 2.Can hide inefficiency. 3.But may be the easiest, clearest, shortest way to write a program.

public static int fib(int n) { // pre: n>=0 // post: returned value is fib(n) if (n==0 || n==1) return n; else return fib(n-1)+fib(n-2); }

Fib(8)

Fib(6)Fib(7)

Fib(8) Fib(6) Fib(5)Fib(6) Fib(7)

Fib(8) Fib(4)Fib(5) Fib(6) Fib(5) Fib(6) Fib(7) Fib(4)

Yadda yadda yadda

Fib(8) Fib(4)Fib(5) Fib(6) Fib(5) Fib(6) Fib(7) Fib(2)Fib(3) Fib(4)Fib(3)Fib(4)

Fib(8) Fib(4)Fib(5) Fib(6) Fib(5) Fib(6) Fib(7) Fib(2)Fib(3) Fib(4)Fib(3)Fib(4)

To compute fib(8), we call: fib(8)1 time fib(7)1 times fib(6)2 times fib(5)3 times fib(4)5 times fib(3)8 times fib(2)13 times fib(1)21 times fib(0)13 times A total of 67 method calls!