Combining Matrix Submatrices

Hello Coders! In this unit, we will explore the fascinating world of two-dimensional matrix manipulation. Our focus will be on combining submatrices from two different matrices to create a new one. While this may sound complex at first, we'll break down the process step by step, using Scala's powerful collection tools to make the task manageable and clear.

Are you ready for the challenge? Here it is: Imagine you have two different 2D matrices, A and B. Your task is to write a Scala function — let's call it submatrixConcatenation — which takes these two matrices as inputs, along with the coordinates specifying submatrices within A and B. This function should combine the two selected submatrices into a new matrix, C. The submatrices from A and B must have the same number of rows, and in the resulting matrix C, the elements from A's submatrix should appear on the left, and those from B's submatrix on the right.

Let's visualize this with an example. Given the matrix A:

Array(Array(1, 2, 3, 4),
      Array(5, 6, 7, 8),
      Array(9, 10, 11, 12))

and the matrix B:

Array(Array(11, 12, 13),
      Array(14, 15, 16),
      Array(17, 18, 19))

If we select 2x2 submatrices from each (comprising the 2nd to 3rd rows and 2nd to 3rd columns from A, and 1st to 2nd rows and 1st to 2nd columns from B), their concatenation would look like:

Array(Array(6, 7, 11, 12),
      Array(10, 11, 14, 15))

Our first step is to extract submatrices from A and B using the provided coordinates. In Scala, we can use the .slice method to select the required rows and columns from each matrix.

Here's how you can do it:

def submatrixConcatenation(
  matrixA: Array[Array[Int]],
  matrixB: Array[Array[Int]],
  submatrixCoords: ( // Tuple of two coordinate tuples
    (Int, Int, Int, Int), // (startRowA, endRowA, startColA, endColA)
    (Int, Int, Int, Int)  // (startRowB, endRowB, startColB, endColB)
  )
): Array[Array[Int]] = {
  val ((startRowA, endRowA, startColA, endColA), (startRowB, endRowB, startColB, endColB)) = submatrixCoords

  // Use .slice to extract the required rows, and then .slice again for columns
  val submatrixA = matrixA.slice(startRowA - 1, endRowA).map(row => row.slice(startColA - 1, endColA))
  val submatrixB = matrixB.slice(startRowB - 1, endRowB).map(row => row.slice(startColB - 1, endColB))