This articles shows a java program that finds a greatest common divisor between two input integers and also prints the intermediate steps of recursion. Can you think about the complexity of this algorithm? It is O(Log(N)) where N is the largest number of the two. See the analysis here.

package com.icodejava.research.ready; /** * * @author Kushal Paudyal * Created on: 2/8/2017 * Last Modified on: 2/8/2017 * * Recursive way of finding the GCD (Greatest Common Divisor) */ public class GCDRecursive { public static int gcd(int a, int b) { System.out.println("First Number: " + a + " Second Number: " + b); if (a < 0 || b < 0) { throw new IllegalArgumentException("No GCD of negative integers"); } return b == 0 ? a : gcd(b, a % b); } public static void main(String args []) { System.out.println("Greatest Common Divisor of 35 and 21 is " + gcd(35,21)); } }

The following is the output of this program.

First Number: 35 Second Number: 21 First Number: 21 Second Number: 14 First Number: 14 Second Number: 7 First Number: 7 Second Number: 0 Greatest Common Divisor of 35 and 21 is 7