Question

I’ve never really bothered with math programming, but today I’ve decided to give it a shot.

Here’s my code and it’s working as intended:

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Data;
using System.Windows.Documents;
using System.Windows.Input;
using System.Windows.Media;
using System.Windows.Media.Imaging;
using System.Windows.Navigation;
using System.Windows.Shapes;

namespace PrimeFactorization
{
    /// <summary>
    /// Interaction logic for MainWindow.xaml
    /// </summary>
    public partial class MainWindow : Window
    {
        public MainWindow()
        {
            InitializeComponent();
        }

        private void btnSubmit_Click(object sender, RoutedEventArgs e)
        {
            List<int> primeFactors = FindPrimeFactors(Convert.ToInt32(txtNumber.Text));
            primeFactors.Sort();
            for (int i = 0; i < primeFactors.Count; i++)
            {
                listBoxFoundNumbers.Items.Add(primeFactors[i]);
            }            
        }

        private List<int> FindPrimeFactors(int number)
        {
            List<int> factors = new List<int>();
            factors.Add(1);
            factors.Add(number);

            for (int i = 2; i < number; i++)
            {

                if (number % i == 0)
                {
                    int holder = number / i;
                    //If the number is in the list, don't add it again.
                    if (!factors.Contains(i))
                    {
                        factors.Add(i);
                    }
                    //If the number is in the list, don't add it again.
                    if (!factors.Contains(holder))
                    {
                        factors.Add(holder);
                    }
                }            
            }

            return factors;
        }
    }
}

The only problem I can see with my code is that it will iterate through to the bitter end, even though there will definitely not be any factors.

For example, imagine I wrote in 35. My loop will go up to 35 and check 24,25,26,27…etc. Not very good.

What do you recommend?

Answer 1

One thing you can do is avoid checking even numbers after 2, since they will never be prime.

So, check 2 and then declare your loop as such:

for (int i = 3; i < number; i+=2)

Re: stopping at sqrt(n) – this is an effective technique for determining whether a given number is prime, since any n that divides x where x > sqrt(n) also divides n/x which is necessarily less than sqrt(n). But a number may have prime factors larger than its own square root (for example, 1002 = 2 * 3 * 167).

That said, you could implement some kind of recursive solution where, for all prime factors p of n such that p < sqrt(n), you also calculate the prime factors of n / p. My gut feeling is that this will decrease the running time of your algorithm in general, but might increase it for small values of n.

Edit: if you’re interested in getting into more sophisticated techniques, the Wikipedia page on Integer Factorization links to all kinds of algorithms.