Problem 12

歐拉項目

問題10：Highly divisible triangular number

The sequence of triangle numbers is generated by adding the natural numbers. So the 7^th 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?

分析

這道題目是找出第一個擁有500除數的三角數。，採用試除法可以得到。

Project Euler 網站的解決方案是採用素數表，效率很高。

解決方案（Java）

package Problem12;

public class HighlyDivisible {

    private static final int divisorsNumbers = 500;
    
    private int number = 1;
    
    public static void main(String[] args){
        HighlyDivisible hd = new HighlyDivisible();
        long startTime = System.currentTimeMillis();   
        hd.compute();
        long endTime = System.currentTimeMillis();       
        System.out.println("Time: "+(endTime-startTime));           
        hd.print();
    }
    
    private void compute(){
        
        int currDivisorsLevel = 1;
        int currDivisorsNumbers = 0;

        while(currDivisorsNumbers<divisorsNumbers){
            currDivisorsLevel++;
            number = number+currDivisorsLevel;//(currDivisorsLevel * (currDivisorsLevel + 1))/2;
            currDivisorsNumbers = getDivisorsNumbers(number);
//            System.out.println(number+":"+currDivisorsNumbers);
        }
        
    }
    
    private void print(){
        System.out.println("Number: "+ number + " is the first triangle number to have over "+divisorsNumbers+" divisors");
    }
    
    private int getDivisorsNumbers(int num){
        int currDivisorsNumbers = 0;
        
        int maxDivisiorNum = (int)Math.sqrt(num);
        
        for(int i=1;i<=maxDivisiorNum;i++){
            if(num%i==0)currDivisorsNumbers += 2;
        }
        
        return currDivisorsNumbers;
    }
    
}

結果

Time: 227(3.40GHz雙核 8G內存)
Number: 76576500 is the first triangle number to have over 500 divisors