package com.thealgorithms.maths;

/*
 * Java program for liouville lambda function
 * For any positive integer n, define λ(n) as the sum of the primitive nth roots of unity. 
 * It has values in {−1, 1} depending on the factorization of n into prime factors:
 *   λ(n) = +1 if n is a positive integer with an even number of prime factors.
 *   λ(n) = −1 if n is a positive integer with an odd number of prime factors.
 * Wikipedia: https://en.wikipedia.org/wiki/Liouville_function
 * 
 * Author: Akshay Dubey (https://github.com/itsAkshayDubey)
 * 
 * */

public class LiouvilleLambdaFunction {

	/**
	 * This method returns λ(n) of given number n
	 *
	 * @param number Integer value which λ(n) is to be calculated 
	 * @return  1 when number has even number of prime factors
	 *         -1 when number has odd number of prime factors
	 * @throws IllegalArgumentException when number is negative
	 */
	static int liouvilleLambda(int number) {
		if(number <= 0) {
			//throw exception when number is less than or is zero
			throw new IllegalArgumentException("Number must be greater than zero.");
		}

		//return 1 if size of prime factor list is even, -1 otherwise
		return PrimeFactorization.pfactors(number).size() % 2 == 0 ? 1 : -1;
	}
}