Recursion AP Computer Science A Mr. Langner By: Thomas Robbins

 Recursion happens whenever a method has a statement inside it that causes the method to call itself.  Example: Public int recursion(int a, int b) { //other body statements return 1 + recursion(int a, int b-1); } Overview

Two Important Things  There are two things to know when coding with recursion;  1)If the problem is simple and easy, solve it right away.  2)If the problem isn’t so simple and appears very difficult, you need to break it down into smaller parts.  Then solve these.

Example  Say you want to divide a piece of wood into x amount of parts.

Example  You will use recursion until all the pieces of wood are small enough.  Remember the two important things:  1)If the wood is small enough, stop dividing  2)Else, divide the wood in two pieces and do the same for the next pieces.

Example Etc, etc, until the pieces are small enough

Coding Examples  Now that we understand the principle behind recursion, we can take a look at some specific examples.  Probably the easiest way to describe recursion to someone would be to relate factorials. Ex: 5! = 5 * 4 * 3 * 2 * 1 = 120 Ex: 3! = 3 * 2 * 1 = 6

Psuedocode 1. If the number is equal to one, then the factorial equals one. 2. Else, the factorial of the number equals itself times itself minus one.  factorial(0) = 1, factorial(1) = 1  factorial(N) = N * factorial( N-1 )

Simple Code The Recursion that progresses towards the base case. Code similar to this is nearly mandatory on all recursive methods. It’s called a “Base case” and prevents the method from entering an infinite loop. static int fact(int n) { if (n <= 1) { return 1; return 1;} else { return n * fact(n-1); return n * fact(n-1);}

Break it down!  Terrible pun aside, here’s a good break down of the factorial method’s process:  factorial(5) = 5 * factorial(4) = 5 * ( 4 * factorial(3)) = 5 * ( 4 * factorial(3)) = 5 * ( 4 * (3 * factorial(2))) = 5 * ( 4 * (3 * factorial(2))) = 5 * ( 4 * (3 * (2 * factorial(1)))) = 5 * ( 4 * (3 * (2 * factorial(1)))) = 5 * ( 4 * (3 * (2 * (1 * factorial(0))))) = 5 * ( 4 * (3 * (2 * (1 * factorial(0))))) = 5 * ( 4 * (3 * (2 * (1 * 1)))) = 5 * ( 4 * (3 * (2 * (1 * 1)))) = 5 * 4 * 3 * 2 * 1 * 1 = 120 = 5 * 4 * 3 * 2 * 1 * 1 = 120

Another example of Recursion!  Counting the number of bowling pins in a triangle: trianglePins(int N) //N is the number of rows { if ( N == 1 ) if ( N == 1 ) return 1; return 1; else else return N + Triangle( N-1 ); return N + Triangle( N-1 ); }

The breakdown trianglePins(5 ) = 5 + trianglePins (4) = 5 + (4 + trianglePins(3)) = 5 + (4 + trianglePins(3)) = 5 + (4 + (3 + trianglePins(2))) = 5 + (4 + (3 + trianglePins(2))) = 5 + (4 + (3 + (2 + trianglePins(1)))) = 5 + (4 + (3 + (2 + trianglePins(1)))) = 5 + (4 + (3 + (2 + 1))) = 5 + (4 + (3 + (2 + 1))) = 5 + (4 + (3 + 3)) = 5 + (4 + (3 + 3)) = 5 + (4 + 6) = 5 + (4 + 6) = = = 15 = 15