diff --git a/ProjectEuler/Problem12.java b/ProjectEuler/Problem12.java index 72e1b5b71..89ea3e0ac 100644 --- a/ProjectEuler/Problem12.java +++ b/ProjectEuler/Problem12.java @@ -1,24 +1,34 @@ -/* - The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. - The first ten terms would be: +package ProjectEuler; +/** + * The sequence of triangle numbers is generated by adding the natural numbers. + * So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. + * The first ten terms would be: + *

+ * 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ... + *

+ * Let us list the factors of the first seven triangle numbers: + *

+ * 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. + *

+ * What is the value of the first triangle number to have over five hundred divisors? + *

+ * link: https://projecteuler.net/problem=12 + */ +public class Problem12 { - 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ... - - Let us list the factors of the first seven triangle numbers: - - 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. - - What is the value of the first triangle number to have over five hundred divisors? -*/ - -public class Problem_12 { + /** + * 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) { @@ -28,36 +38,29 @@ public class Problem_12 { return sum; } - public static void main(String[] args) { - - long start = System.currentTimeMillis(); // start the stopwatch - + 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 <= 500) { + + 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; } - - long finish = System.currentTimeMillis(); // stop the stopwatch - - System.out.println(n); - System.out.println("Time taken: " + (finish - start) + " milliseconds"); + return n; } }