Maths for Coders : Chapter 1

#codenewbie #java #tutorial #career

Starting a thread where I will be adding some common math problems expected from developers in interview rounds or aptitude tests.

These will always come in handy - so I have added the cleanest version of some common functions


	import java.util.ArrayList;
	import java.util.List;

	public class MathsForCodersV1 {

	/**
	* Brief idea about the logic behind the code-
	* <p>
	* LCM(a,b)=a*b/HCF(a,b)
	*
	* <p>
	* LCM of 10, 18, 24 =>
	* 10 = 2 x 5
	* 18 = 2 x 3^2
	* 24 = 2^3 x 3
	* <p>
	* so for lcm we take all unique primes and there max powers => 2^3 x 3^2 x 5 = 8 x 9 x 5 = 360
	* </p>
	*/
	public static int smallestNumberDivisibleBy(int[] list) {
	int lcm = 1;
	int first = lcm;

	for (int i : list) {
	lcm = (first * i) / hcf(first, i);
	first = lcm;
	}

	return lcm;
	}

	protected static List<Integer> getPrimeFactors(int n) {
	final List<Integer> result = new ArrayList<>();

	// handle 2
	while (n % 2 == 0) {
	n /= 2;
	result.add(2);
	}

	// handle rest
	for (int i = 3; i <= Math.sqrt(n); i += 2) {
	// if ((i & 1) != 0) { // already odd by design
	while (n % i == 0) {
	n /= i;
	result.add(i);
	}
	// }
	}

	// This condition is to handle the case when n is a prime number greater than 2 and Math.sqrt(n/2)
	if (n > 2) {
	result.add(n);
	}

	return result;
	}

	/**
	* <p>
	* HCF of 10, 24
	* 10 = 2 x 5
	* 24 = 2^3 x 3
	* HCF = 2 (the only common factor
	* </p>
	*/
	static int hcf(int a, int b) {
	if (b == 0) {
	return a;
	}
	return hcf(b, a % b);
	}

	static boolean isOdd(int num) {
	return (num & 1) != 0;
	}
	}