We present below some simple algorithms to manipulate 2-dimensional (rectangular) arrays.
Summing the values row per row
The following code sum the values contained in a 2-dimensional array row per row, and display the result each time before moving on to the next row:
int[,] numbers =
{
{1, 2, 3, 4},
{5, 6, 7, 8}
};
int acc;
for (int row = 0; row < numbers.GetLength(0); row++)
{
acc = 0;
for (int col = 0; col < numbers.GetLength(1); col++)
{
acc += numbers[row, col];
}
Console.WriteLine("Total for row #" + row +
" is " + acc + ".");
}This code can easily be adapted to compute the sums column per column if needed.
Computing Magic Square
A magic square is a square matrix where the sums of the numbers in each row, each column, and both the diagonal and the anti-diagonal are the same.
The following is an example of a magic square:
int[,] magicSquare = {
{ 4, 9, 2 },
{ 3, 5, 7 },
{ 8, 1, 6 }
};as we have, diagonally,
and anti-diagonally,
and on the rows,
and finally on the columns
A method to return true if the 2d-matrix of int passed as an
argument is a magic square is as follows:
bool isMagic(int[,] arrayP)
{
bool magicSoFar = true;
if (arrayP.GetLength(0) == arrayP.GetLength(1))
{ // The array is a square.
int magicConstant = 0;
for (int i = 0; i < arrayP.GetLength(1); i++)
{
magicConstant += arrayP[i, i];
}
int testedValue = 0;
for (int i = 0; i < arrayP.GetLength(1); i++)
{
testedValue += arrayP[i, arrayP.GetLength(1) - i - 1];
}
if (testedValue == magicConstant)
{// The diagonal and anti-diagonal have the same sums.
// We test the rows.
for (int row = 0; row < arrayP.GetLength(0); row++)
{
testedValue = 0;
for (int col = 0; col < arrayP.GetLength(1); col++)
{
testedValue += arrayP[row, col];
}
if (testedValue != magicConstant)
{
magicSoFar = false;
}
}
// We test the columns.
for (int col = 0; col < arrayP.GetLength(1); col++)
{
testedValue = 0;
for (int row = 0; row < arrayP.GetLength(0); row++)
{
testedValue += arrayP[row, col];
}
if (testedValue != magicConstant)
{
magicSoFar = false;
}
}
}
else
{// The diagonal and anti-diagonal have different same sums.
magicSoFar = false;
}
}
else
{ // The array is not a square.
magicSoFar = false;
}
return magicSoFar;
} That code can be tested using for example this code.