Wednesday, January 25, 2012

Problem 12

Problem Statement :Problem12

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?

Algorithm:

  • We  solve the problem on a basic assumption that if one factor of the number is present within root of the number the we need not iterate over all the factors till n/2.
  • count can be incremented twice just because of the above reason.
  • The value of  n = i * (i+1) / 2 is evident for i in the  


Solution:
    public class problem12 {
     public static void main(String args[]) {
      for (int i = 10;; i++) {
       int n = i * (i + 1) / 2;
       int count = 2;
       for (int k = 2; k * k <= n; k++) {
        if (n % k == 0)
         count += 2;
       }
       if (count >= 500) {
        System.out.println(n);
        break;
       }
      }
     }
    }
    
    
    

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