Project Euler #4 - Java

Question:

A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91  99.

Find the largest palindrome made from the product of two 3-digit numbers.

Solution:

So, a there are two basic facts about this problem to keep in mind. One, any two 3-digit numbers will have a 6 digit product. Second, a 6-digit palindrome will be in the form ijkkji, where j and k are integers from 0-9 and i is an integer from 1-9. We know that i cannot be zero because of the fact that the product must be a 6-digit number. If i were 0, the product would only contain 5 digits (ie: leading zeroes do not count). 

So with this in mind, this problem is simple. Since we are looking for the largest palindrome with two 3-digit products, begin at 999999 and check whether this number is the product of two 3 digit numbers. If it is not, we must decrement our palindrome from the inside out. In other words, our loop is structured as i -> j -> k. We decrement k, then j, then i as we loop through our possible palindromes. 

Lets put these ideas in concrete with some code. 

public class euler_04 {


    final static int MIN3 = 100;
    final static int MAX3 = 999;
    
    public static void main (String args[])
    {
        int i, j, k, m;
        int subj; 


        for (i = 9; i > 0; i--)
        {
            for (j = 9; j >= 0; j--)
            {
                for (k = 9; k >= 0; k--)
                {
                    subj = k*1100 + j*10010 + i*100001; // create our test subject
                    
                    for (m = MAX3; m >= MIN3 ; m--) 
                    {
                        if ( (subj % m) > 0) // if the number is not divisible go to the next value of m
                            continue;
     
                        int div = subj / m; 
                        if (div >= 100 && div <= 999) // we found our subject!
                        {
                            System.out.printf("Largest palindrome with 3 digit multipliers is %d\n", subj);
                            System.exit(1);
                        }
                    }
                }
            }
        }  
    }
}