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Question

Hello fellow programmers

I'm currently trying to solve some problems on Project Euler in C# to improve my knowledge. However, one solution I made for Problem #4 isn't working even though it should.

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.

Any ideas?

    namespace ProjectEuler_4
{
    class Program
    {
        static void Main(string[] args)
        {

            for (int i = 999; i >= 100; i--)
            {
                for (int j = 999; j >= 100; j--)
                {
                    if (isPalindome(i *j) == true)
                    {
                        Console.WriteLine("Digit1: " + i);
                        Console.WriteLine("Digit2: " + j);
                        Console.WriteLine("Outcome: " + i * j);
                          Console.ReadLine();
                    }
                    else
                    {

                        Console.WriteLine(i + " " + j + " =nope");

                    }
                }


            }
            Console.ReadLine();
        }
        public static bool isPalindome(int num)
        {
            string sNum = num.ToString();
            for (int i = 0; i < sNum.Length / 2; i++)
                if (sNum[i] != sNum[sNum.Length - 1 - i]) return false;

            return true;
        }

    }
}

Outcome is :

Digit1: 995 Digit2: 583 Total: 580085

Though, that is not the right answer. Anything I did wrong? I'm not asking for a finished solution, just want to understand what the problem is with this one.

Answer 1

Try checking all combinations. For example, 994 * 994 is larger, and you didn't even check it.

Answer 2

Your program actually works and finds the right answer. However, it doesn't print the biggest number first, it's the third output instead.

For example, i=999 j=2 comes before i=998 j=998, but the second product is much bigger. See, you don't find the products in descending order.

The good solution is a simple max-finding loop (kinda-pseudo-code):

var best = -1;
for (i, j) {
  if (isPalindrome(i*j) && i*j > best) {
    best = i*j;
  }
}
Console.WriteLine(best);

Answer 3

I have a few notes:

• It's better to start the inner loop from i .
• We are able to leave the inner loop if a palindrome has been found, because it's guaranteed that for the current i there is no numbers greater than number .
• It makes sense to search for the multiplicands that gives the biggest product in the range 99..9 - 90..0 , because they are definitely exist in this range.
• The fastest condition should be the first in the if statement.
• I've used a long type for variables to make the code below work for bigger numbers.

Try this code sample:

// Store the maximum palindrome number here:
long maxNumber = 0;

// The maximum multiplicand (typically: 9...9):
const int NMax = 999;
// The minimum multiplicand.
// Obviously, it couldn't be less than 90...0:
const int NMin = NMax - (NMax + 1) / 10 + 1;

for (int i = NMax; i > NMin; i--)
{
    // Starting from i since i * j = j * i for any i, j:
    for (int j = i; j > NMin; j--)
    {
        long number = Math.BigMul(i, j);
        // The fastest condition should be the first in the `if` statement:
        if (number > maxNumber && isPalindome(number))
        {
            maxNumber = number;
            Console.WriteLine("{0} = {1} * {2}", number, i, j);
            break; // Leave the `j` loop, because it's guaranteed that there is
                   // no numbers greater than `number` for the current `i`
        }
    }
}

Output:

for NMax=999:     906609 = 993 * 913
for NMax=9999:    99000099 = 9999 * 9901
for NMax=9999999: 99956644665999 = 9998017 * 9997647