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Problem12.java
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54 lines (47 loc) · 1.86 KB
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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;
}
}