55 lines
1.9 KiB
Java
55 lines
1.9 KiB
Java
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:
|
|
*
|
|
* <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;
|
|
}
|
|
}
|