package ProjectEuler;

/**
 * The prime factors of 13195 are 5, 7, 13 and 29.
 *
 * <p>What is the largest prime factor of the number 600851475143 ?
 *
 * <p>Link: https://projecteuler.net/problem=3
 */
public class Problem03 {

 /**
 * Checks if a number is prime or not
 *
 * @param n the number
 * @return {@code true} if {@code n} is prime
 */
 public static boolean isPrime(int n) {
 if (n == 2) {
 return true;
 }
 if (n < 2 || n % 2 == 0) {
 return false;
 }
 for (int i = 3, limit = (int) Math.sqrt(n); i <= limit; i += 2) {
 if (n % i == 0) {
 return false;
 }
 }
 return true;
 }

 /**
 * Calculate all the prime factors of a number and return the largest
 *
 * @param n integer number
 * @return the maximum prime factor of the given number
 */
 static long maxPrimeFactor(long n) {
 for (int i = 2; i < n / 2; i++) {
 if (isPrime(i))
 while (n % i == 0) {
 n /= i;
 }
 }
 return n;
 }

 public static void main(String[] args) {
 int[][] testNumbers = {
 {87, 29},
 {10, 5},
 {21, 7},
 {657, 73},
 {777, 37}
 };
 for (int[] num : testNumbers) {
 assert Problem03.maxPrimeFactor(num[0]) == num[1];
 }
 assert Problem03.maxPrimeFactor(600851475143L) == 6857;
 }
}