Submatrix Concatenation and Matrix Manipulation in PHP

Hello, Explorer! This unit's exciting programming lesson will involve traversing the labyrinth of two-dimensional matrices. We're going to apply our PHP skills to combine submatrices from two different matrices, creating a new one. It appears to be quite a complex task, doesn't it? But don't fret. We'll go through this together, one step at a time, using PHP arrays as our primary structure for matrix handling.

Are you ready for the task? Here it is: Imagine having two different 2D arrays in PHP, $A and $B. Our job is to devise a PHP function — let's name it submatrixConcatenation() — which takes these two matrices as inputs, along with the coordinates specifying submatrices within $A and $B. This function is expected to stitch the two chosen submatrices together, forming a new one, $C. Notably, the submatrices from $A and $B should have the same number of rows, and in the final matrix $C, elements from $A's submatrix should be on the left and those from $B's submatrix on the right.

Let's visualize this with a couple of matrices.

Given the matrix $A as:

[[1, 2, 3, 4],
 [5, 6, 7, 8],
 [9, 10, 11, 12]]

and the matrix $B as:

[[11, 12, 13],
 [14, 15, 16],
 [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:

[[6, 7, 11, 12],
 [10, 11, 14, 15]]

Our first step toward the solution is to extract submatrices from $A and $B from the given coordinates. For this, we'll use nested loops in PHP to get the rows and then the required columns from those rows:

function submatrixConcatenation($matrixA, $matrixB, $submatrixCoords) {
    $startRowA = $submatrixCoords[0][0];
    $endRowA = $submatrixCoords[0][1];
    $startColA = $submatrixCoords[0][2];
    $endColA = $submatrixCoords[0][3];
    $startRowB = $submatrixCoords[1][0];
    $endRowB = $submatrixCoords[1][1];
    $startColB = $submatrixCoords[1][2];
    $endColB = $submatrixCoords[1][3];

    $numRows = $endRowA - $startRowA + 1;
    $numColsA = $endColA - $startColA + 1;
    $numColsB = $endColB - $startColB + 1;

    $submatrixA = [];
    for ($i = 0; $i < $numRows; $i++) {
        for ($j = 0; $j < $numColsA; $j++) {
            $submatrixA[$i][$j] = $matrixA[$startRowA + $i - 1][$startColA + $j - 1];
        }
    }
    
    $submatrixB = [];
    for ($i = 0; $i < $numRows; $i++) {
        for ($j = 0; $j < $numColsB; $j++) {
            $submatrixB[$i][$j] = $matrixB[$startRowB + $i - 1][$startColB + $j - 1];
        }
    }
    
    // At this point, we have extracted submatrices from matrixA and matrixB
}