Problem

This problem is a simplified version of problem 11 at Project Euler[1].

Using the provided array find 4 adjacent numbers along any row, column or diagonal with the greatest product. To keep things simple we will only worry about diagonals going down to the right. I have included some skeleton code to make problem a little easier.

For example at row 0, column 0 there are three lines to check.
8 x 2 x 22 x 97 = 34144
8 x 49 x 81 x 52 = 1651104
8 x 49 x 31 x 23 = 279496

public class matrix {

	static final int   lineLength = 4;		      //length of line to check 
	static       int[] bestNumbers = new int[lineLength]; //best line found so far
	static       int   bestNumber = 0;                    //product of the best line
	
	static final int array[][] ={ 
		{ 8, 2,22,97,38,15, 0,40, 0,75, 4, 5, 7,78,52,12,50,77,91, 8},
		{49,49,99,40,17,81,18,57,60,87,17,40,98,43,69,48, 4,56,62, 0},
		{81,49,31,73,55,79,14,29,93,71,40,67,53,88,30, 3,49,13,36,65},
		{52,70,95,23, 4,60,11,42,69,24,68,56, 1,32,56,71,37, 2,36,91},
		{22,31,16,71,51,67,63,89,41,92,36,54,22,40,40,28,66,33,13,80},
		{24,47,32,60,99, 3,45, 2,44,75,33,53,78,36,84,20,35,17,12,50},
		{32,98,81,28,64,23,67,10,26,38,40,67,59,54,70,66,18,38,64,70},
		{67,26,20,68, 2,62,12,20,95,63,94,39,63, 8,40,91,66,49,94,21},
		{24,55,58, 5,66,73,99,26,97,17,78,78,96,83,14,88,34,89,63,72},
		{21,36,23, 9,75, 0,76,44,20,45,35,14, 0,61,33,97,34,31,33,95},
		{78,17,53,28,22,75,31,67,15,94, 3,80, 4,62,16,14, 9,53,56,92},
		{16,39, 5,42,96,35,31,47,55,58,88,24, 0,17,54,24,36,29,85,57},
		{86,56, 0,48,35,71,89, 7, 5,44,44,37,44,60,21,58,51,54,17,58},
		{19,80,81,68, 5,94,47,69,28,73,92,13,86,52,17,77, 4,89,55,40},
		{04,52, 8,83,97,35,99,16, 7,97,57,32,16,26,26,79,33,27,98,66},
		{88,36,68,87,57,62,20,72, 3,46,33,67,46,55,12,32,63,93,53,69},
		{04,42,16,73,38,25,39,11,24,94,72,18, 8,46,29,32,40,62,76,36},
		{20,69,36,41,72,30,23,88,34,62,99,69,82,67,59,85,74, 4,36,16},
		{20,73,35,29,78,31,90, 1,74,31,49,71,48,86,81,16,23,57, 5,54},
		{01,70,54,71,83,51,54,69,16,92,33,48,61,43,52, 1,89,19,67,48} };


	public static void main(String[] args) {

		for( int row = 0; row < array[0].length; row++ )
		{
			for( int col = 0; col < array.length; col++ )
			{
				checkRow( row, col );
				checkCol( row, col );
				checkDiagonal( row, col );
			}
		}

		printLine( bestNumbers, bestNumber );

	}
	
	//prints a nice output for a provided line
	public static void printLine( int[] toPrintArray, int toPrintProd )
	{
	}
	
	//calculate the product for the line passed
	//if it the product is better than bestNumber update it
	public static void checkLine( int[] toCheck )
	{
		
	}
	
	//from (row,col) check product of the row
	public static void checkRow( int row, int col )
	{
		int[] tempRow = new int[ 4 ];
		...
		checkLine( tempRow );
	}
	
	//from (row,col) check product of the column
	public static void checkCol( int row, int col )
	{
		int[] tempRow = new int[ 4 ];
		...
		checkLine( tempRow );
	}
	
	//from (row,col) check product of the diagonal
	public static void checkDiagonal( int row, int col )
	{
		int[] tempRow = new int[ 4 ];
		...
		checkLine( tempRow );
	}

}

More with Arrays

Solution

First a quick overview of how we are going to solve the problem. The main body is a good place to start. The body reads a lot like the description of the problem. The two for loops scan the array, and at each cell we check the row, column and diagonal.

public static void main(String[] args) {

	//for each row
	for( int row = 0; row < array[0].length; row++ )
	{
		//and each column
		for( int col = 0; col < array.length; col++ )
		{
			checkRow( row, col ); //check the row starting here
			checkCol( row, col ); //check the column starting here
			checkDiagonal( row, col ); //check the diagonal starting here
		}
	}

	//print the best numbers we found
	printLine( bestNumbers, bestNumber );
}

Next, filling in the printLine method is a good idea as it is useful in debugging. Given an array and an int this method prints the output like in my example. The main loop here should look a little strange to you. We want to print "x" between the numbers but not at the end. So we will print toPrintArray[ 0 ] first, then add a "x" and the next value in the loop.

//prints a nice output for a provided line
//8 x  2 x 22 x 97 = 34144
public static void printLine( int[] toPrintArray, int toPrintProd )
{
	System.out.print( toPrintArray[ 0 ] );
	
	for( int i = 1; i < toPrintArray.length; i++ )
	{
		System.out.print( " x " + toPrintArray[ i ] );
	}
	
	System.out.println( " = " + toPrintProd );
}

With printing out of the way the next method to write is checkLine. This method checks if a set of numbers is the new highest. The current highest set of number and their product is stored in bestNumbers and bestNumber. Manually check a few lines to make sure you are getting the right results.

static int[] bestNumbers = new int[lineLength];
static int   bestNumber = 0;

public static void checkLine( int[] toCheck )
{
	int tempProduct = 1;
	
	for( int i = 0; i < toCheck.length; i++ )
	{
		tempProduct = tempProduct * toCheck[i];			
	}
	
	if( tempProduct > bestNumber )
	{
		bestNumber = tempProduct;
		bestNumbers = toCheck;
	}
}

The only things left are checkRow, checkCol and checkDiagonal. These three methods are very similar. checkRow copies lineLength<4> numbers from the row and column provided. Next checkRow passes the resulting array to to checkLine to see if we have a new winner.

//from (row,col) check product of the row
public static void checkRow( int row, int col )
{
	//make sure the row we are checking does not exceed the array row length
	if( col + lineLength <=  array[0].length )
	{
		int[] tempRow = new int[ 4 ];
		
		for( int i = 0; i < lineLength; i++ )
		{
			tempRow[ i ] = array[ row ][ col + i ];
		}
		
		checkLine( tempRow );
	}
	
}//checkRow

You're almost there, fill in checkCol, checkDiagonal, and verify that you are getting the right answer.

BONUS

1. Can you find the line with the highest average?
2. Whats the best line of length 5?
3. How about with diagonals going lines down to the left?

Code

Solution Code

public class matrix {

	static final int   lineLength = 4;		      //length of line to check 
	static       int[] bestNumbers = new int[lineLength]; //best line found so far
	static       int   bestNumber = 0;                    //product of the best line
	
	static final int array[][] ={ 
		{ 8, 2,22,97,38,15, 0,40, 0,75, 4, 5, 7,78,52,12,50,77,91, 8},
		{49,49,99,40,17,81,18,57,60,87,17,40,98,43,69,48, 4,56,62, 0},
		{81,49,31,73,55,79,14,29,93,71,40,67,53,88,30, 3,49,13,36,65},
		{52,70,95,23, 4,60,11,42,69,24,68,56, 1,32,56,71,37, 2,36,91},
		{22,31,16,71,51,67,63,89,41,92,36,54,22,40,40,28,66,33,13,80},
		{24,47,32,60,99, 3,45, 2,44,75,33,53,78,36,84,20,35,17,12,50},
		{32,98,81,28,64,23,67,10,26,38,40,67,59,54,70,66,18,38,64,70},
		{67,26,20,68, 2,62,12,20,95,63,94,39,63, 8,40,91,66,49,94,21},
		{24,55,58, 5,66,73,99,26,97,17,78,78,96,83,14,88,34,89,63,72},
		{21,36,23, 9,75, 0,76,44,20,45,35,14, 0,61,33,97,34,31,33,95},
		{78,17,53,28,22,75,31,67,15,94, 3,80, 4,62,16,14, 9,53,56,92},
		{16,39, 5,42,96,35,31,47,55,58,88,24, 0,17,54,24,36,29,85,57},
		{86,56, 0,48,35,71,89, 7, 5,44,44,37,44,60,21,58,51,54,17,58},
		{19,80,81,68, 5,94,47,69,28,73,92,13,86,52,17,77, 4,89,55,40},
		{04,52, 8,83,97,35,99,16, 7,97,57,32,16,26,26,79,33,27,98,66},
		{88,36,68,87,57,62,20,72, 3,46,33,67,46,55,12,32,63,93,53,69},
		{04,42,16,73,38,25,39,11,24,94,72,18, 8,46,29,32,40,62,76,36},
		{20,69,36,41,72,30,23,88,34,62,99,69,82,67,59,85,74, 4,36,16},
		{20,73,35,29,78,31,90, 1,74,31,49,71,48,86,81,16,23,57, 5,54},
		{01,70,54,71,83,51,54,69,16,92,33,48,61,43,52, 1,89,19,67,48} };

	public static void main(String[] args) {

		for( int row = 0; row < array[0].length; row++ )
		{
			for( int col = 0; col < array.length; col++ )
			{
				checkRow( row, col );
				checkCol( row, col );
				checkDiagonal( row, col );
			}
		}

		printLine( bestNumbers, bestNumber );

	}
	
	//prints a nice output for a provided line
	//8 x  2 x 22 x 97 = 34144
	public static void printLine( int[] toPrintArray, int toPrintProd )
	{
		System.out.print( toPrintArray[ 0 ] );
		
		for( int i = 1; i < toPrintArray.length; i++ )
		{
			System.out.print( " x " + toPrintArray[ i ] );
		}
		
		System.out.println( " = " + toPrintProd );
	}
	
	//calculate the product for the line passed
	//if it the product is better than bestNumber update it
	public static void checkLine( int[] toCheck )
	{
		int tempProduct = 1;
		
		for( int i = 0; i < toCheck.length; i++ )
		{
			tempProduct = tempProduct * toCheck[i];			
		}
		
		if( tempProduct > bestNumber )
		{
			bestNumber = tempProduct;
			bestNumbers = toCheck;
		}
	}
	
	//from (row,col) check product of the row
	public static void checkRow( int row, int col )
	{
		//make sure the row we are checking does not exceed the array row length
		if( col + lineLength <=  array[0].length )
		{
			int[] tempRow = new int[ 4 ];
			
			for( int i = 0; i < lineLength; i++ )
			{
				tempRow[ i ] = array[ row ][ col + i ];
			}
			
			checkLine( tempRow );
		}
		
	}//checkRow
	
	//from (row,col) check product of the column
	public static void checkCol( int row, int col )
	{
		//make sure the column we are checking does not exceed the array column length
		if( row + lineLength <=  array.length )
		{
			int[] tempRow = new int[ 4 ];
			
			for( int i = 0; i < lineLength; i++ )
			{
				tempRow[ i ] = array[ row + i ][ col ];
			}
			
			checkLine( tempRow );
		}
		
	}//checkCol
	
	//from (row,col) check product of the diagonal
	public static void checkDiagonal( int row, int col )
	{
		//for diagonals we need to check row and column
		if( ( row + lineLength <=  array.length ) && (col + lineLength <=  array[0].length) )
		{
			int[] tempRow = new int[ 4 ];
			
			for( int i = 0; i < lineLength; i++ )
			{
				tempRow[ i ] = array[ row + i ][col + i ];
			}
			
			checkLine( tempRow );
		}
		
	}//checkDiagonal
	
}


Output
======
66 x 91 x 88 x 97 = 51267216