package ProjectEuler;
/**
 * The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle
 * number would be 1 +たす 2 +たす 3 +たす 4 +たす 5 +たす 6 +たす 7 =わ 28. The first ten terms would be:
 *
 * <p>1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
 *
 * <p>Let us list the factors of the first seven triangle numbers:
 *
 * <p>1: 1 3: 1,3 6: 1,2,3,6 10: 1,2,5,10 15: 1,3,5,15 21: 1,3,7,21 28: 1,2,4,7,14,28 We can see
 * that 28 is the first triangle number to have over five divisors.
 *
 * <p>What is the value of the first triangle number to have over five hundred divisors?
 *
 * <p>link: https://projecteuler.net/problem=12
 */
public class Problem12 {

 /** Driver Code */
 public static void main(String[] args) {
 assert solution1(500) == 76576500;
 }

 /* returns the nth triangle number; that is, the sum of all the natural numbers less than, or equal to, n */
 public static int triangleNumber(int n) {
 int sum = 0;
 for (int i = 0; i <= n; i++) sum += i;
 return sum;
 }

 public static int solution1(int number) {
 int j = 0; // j represents the jth triangle number
 int n = 0; // n represents the triangle number corresponding to j
 int numberOfDivisors = 0; // number of divisors for triangle number n

 while (numberOfDivisors <= number) {

 // resets numberOfDivisors because it's now checking a new triangle number
 // and also sets n to be the next triangle number
 numberOfDivisors = 0;
 j++;
 n = triangleNumber(j);

 // for every number from 1 to the square root of this triangle number,
 // count the number of divisors
 for (int i = 1; i <= Math.sqrt(n); i++) if (n % i == 0) numberOfDivisors++;

 // 1 to the square root of the number holds exactly half of the divisors
 // so multiply it by 2 to include the other corresponding half
 numberOfDivisors *= 2;
 }
 return n;
 }
}