Project Euler(43)

Posted on Saturday, January 17th, 2009 at 11:54 pm by Universe Queen

Problem 43:

The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it also has a rather interesting sub-string divisibility property.

Let d_(1) be the 1^(st) digit, d_(2) be the 2^(nd) digit, and so on. In this way, we note the following:

* d_(2)d_(3)d_(4)=406 is divisible by 2
* d_(3)d_(4)d_(5)=063 is divisible by 3
* d_(4)d_(5)d_(6)=635 is divisible by 5
* d_(5)d_(6)d_(7)=357 is divisible by 7
* d_(6)d_(7)d_(8)=572 is divisible by 11
* d_(7)d_(8)d_(9)=728 is divisible by 13
* d_(8)d_(9)d_(10)=289 is divisible by 17

Find the sum of all 0 to 9 pandigital numbers with this property.

Answer: 16695334890

Implementation in Java:

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public class Euler43 
{
	public static int factory( int n )
	{
		int result = 1;
 
		for( int i=1; i<=n; i++ )
		{
			result *= i;
		}
 
		return result; 
	}
 
	public static String[] getAllCombinations( String s )
	{
		String[] combinations = new String[factory(s.length())];
 
		if( combinations.length == 1 )
		{
			combinations[0] = s;
			return combinations;
		}
 
		int n = factory( s.length() - 1 );
 
		for( int i=0; i<s.length(); i++ )
		{
			String sub;
			String[] subs;
 
			if( i == 0 )
			{
				sub = s.substring( 1 );
			}
			else if( i == s.length()-1 )
			{
				sub = s.substring( 0, s.length()-1 );
			}
			else
			{
				sub = s.substring( 0, i ) + s.substring( i+1 );
			}
 
			subs = getAllCombinations( sub );
 
			for( int j=0; j<subs.length; j++ )
			{
				combinations[i*n+j] = s.charAt(i) + subs[j];
			}		
		}
 
		return combinations;
	}
 
	public static void main(String[] args) 
	{
		long result = 0;
		String[] s = new String[9];
		s[0] = new String( "023456789" );
		s[1] = new String( "013456789" );
		s[2] = new String( "021456789" );
		s[3] = new String( "023156789" );
		s[4] = new String( "023416789" );
		s[5] = new String( "023451789" );
		s[6] = new String( "023456189" );
		s[7] = new String( "023456719" );
		s[8] = new String( "023456781" );
		int tmp;
		String[] ss;
 
		for( int i=0; i<s.length; i++ )
		{
			ss = getAllCombinations( s[i] );
 
			for( int j=0; j<ss.length; j++ )
			{
				ss[j] = String.valueOf(i+1)+ss[j];
 
				tmp = Integer.valueOf( ss[j].substring( 1, 4 ) );
				if( tmp % 2 != 0 )
				{
					continue;
				}
 
				tmp = Integer.valueOf( ss[j].substring( 2, 5 ) );
				if( tmp % 3 != 0 )
				{
					continue;
				}
 
				tmp = Integer.valueOf( ss[j].substring( 3, 6 ) );
				if( tmp % 5 != 0 )
				{
					continue;
				}
 
				tmp = Integer.valueOf( ss[j].substring( 4, 7 ) );
				if( tmp % 7 != 0 )
				{
					continue;
				}
 
				tmp = Integer.valueOf( ss[j].substring( 5, 8 ) );
				if( tmp % 11 != 0 )
				{
					continue;
				}
 
				tmp = Integer.valueOf( ss[j].substring( 6, 9 ) );
				if( tmp % 13 != 0 )
				{
					continue;
				}
 
				tmp = Integer.valueOf( ss[j].substring( 7, 10 ) );
				if( tmp % 17 == 0 )
				{
					result += Long.valueOf( ss[j] );
				}
			}
		}
 
		System.out.println( result );
	}
}

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