PROJECT EULER #55

Link to Project Euler problem 55

If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.

Not all numbers produce palindromes so quickly. For example,

349 + 943 = 1292,
1292 + 2921 = 4213
4213 + 3124 = 7337

That is, 349 took three iterations to arrive at a palindrome.

Although no one has proved it yet, it is thought that some numbers, like 196, never produce a palindrome. A number that never forms a palindrome through the reverse and add process is called a Lychrel number. Due to the theoretical nature of these numbers, and for the purpose of this problem, we shall assume that a number is Lychrel until proven otherwise. In addition you are given that for every number below ten-thousand, it will either (i) become a palindrome in less than fifty iterations, or, (ii) no one, with all the computing power that exists, has managed so far to map it to a palindrome. In fact, 10677 is the first number to be shown to require over fifty iterations before producing a palindrome: 4668731596684224866951378664 (53 iterations, 28-digits).

Surprisingly, there are palindromic numbers that are themselves Lychrel numbers; the first example is 4994.

How many Lychrel numbers are there below ten-thousand?

NOTE: Wording was modified slightly on 24 April 2007 to emphasise the theoretical nature of Lychrel numbers.

I used BigInt again here.

using System;

namespace project_euler
{
class Program
{
   static void Main()
   {
       //Problem 55
       DateTime start = DateTime.Now;
       int lychrel=0;
       for (int i = 1; i < 10000; i++)
       {
           BigInt j = i;
           int count = 0;
           while(count<51)
           {
               j =ReverseAndAdd(j);
               if (IsPalindrome(j.ToString()))
                   break;
               count++;
               if (count == 50)
                   lychrel++;
           }
       }
       Console.WriteLine(lychrel);
       TimeSpan time = DateTime.Now - start;
       Console.WriteLine("This took {0}", time);
       Console.ReadKey();
   }
   public static BigInt ReverseAndAdd(BigInt n)
   {
       char[] c = n.ToString().ToCharArray();
       Array.Reverse(c);
       string s = new string(c);
       return n + s;
   }
   public static bool IsPalindrome(string s)
   {
       char[] q = s.ToCharArray();
       Array.Reverse(q);
       string r = new string(q);
       if (s.Equals(r))
           return true;
       return false;
   }
}
}

PROJECT EULER #36

Link to Project Euler problem 36

The decimal number, 585 = 1001001001₂ (binary), is palindromic in both bases.

Find the sum of all numbers, less than one million, which are palindromic in base 10 and base 2.

(Please note that the palindromic number, in either base, may not include leading zeros.)

using System;
using System.Text;

namespace ProjectEuler
{
 class Program
 {
     static void Main()
     {
         //Problem 36
         DateTime start = DateTime.Now;
         int sum = 0;
         for (int i = 1; i < 1000000; i++)
         {
             if(IsPalindrome(i.ToString()))
             {
                 sum += IsPalindrome(ToBinary(i))
                            ? i
                            : 0;
             }
         }
         Console.WriteLine(sum);
         TimeSpan time = DateTime.Now-start;
         Console.WriteLine("This took {0}", time);
         Console.ReadKey();
     }
     public static string ToBinary(int n)
     {
         var number = new StringBuilder();
         int rem;
         while(n!=0)
         {
             n=Math.DivRem(n, 2, out rem);
             switch (rem)
             {
                 case 0:
                     number.Append(0);
                     break;
                 case 1:
                     number.Append(1);
                     break;
                 default:
                     break;
             }
         }
         var c = number.ToString().ToCharArray();
         Array.Reverse(c);
         string s = new string(c);
         while (s.StartsWith("0"))
         {
             s.Remove(0, 1);
         }
         return s;
     }
     public static bool IsPalindrome (string s)
     {
         char[] q = s.ToCharArray();
         Array.Reverse(q);
         string r = new string(q);
         if (s.Equals(r))
             return true;
         return false;
     }
 }
}

PROJECT EULER #4

Link to Project Euler problem 4

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.

Int to string to char[], reverse, back to string etc. is another recurring pattern in these problems.

using System;
using System.Collections.Generic;

namespace ProjectEuler
{
  class Program
  {
      static void Main(string[] args)
      {
          //Problem 4
          DateTime start = DateTime.Now;
          List<int> palindromes = new List<int>();
          for(int i = 999;i>99;i--)
          {
              for(int j = 999;j>99;j--)
              {
                  string p = (i*j).ToString();
                  char[] q = p.ToCharArray();
                  Array.Reverse(q);
                  string r = new string(q);
                  if(p.Equals(r))
                      palindromes.Add(i*j);
              }
          }
          palindromes.Sort();
          TimeSpan time = DateTime.Now-start;
          Console.WriteLine("{0}\nThis took {1}",palindromes[palindromes.Count-1] ,time);
          Console.ReadKey();
      }
  }
}