TheAlgorithms-Java/ProjectEuler/Problem12.java at master · windNight/TheAlgorithms-Java · GitHub

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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:

* 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 {

/** 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;

}

TheAlgorithms-Java/ProjectEuler/Problem12.java at master · windNight/TheAlgorithms-Java · GitHub

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