Saturday 18 April 2009

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;
}
}
}

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