Submatrix Concatenation and Matrix Manipulation in PHP

Introduction

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.

Task Statement

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: text [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]] and the matrix $B as: text [[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: text [[6, 7, 11, 12], [10, 11, 14, 15]]

Solution Building: Step 1

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

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text

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

text

[[11, 12, 13],
 [14, 15, 16],
 [17, 18, 19]]

text

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

PHP

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
}

PHP

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];
        }
    }

    // The part for the concatenation process
    $resultMatrix = [];
    for ($i = 0; $i < $numRows; $i++) {
        $resultMatrix[$i] = array_merge($submatrixA[$i], $submatrixB[$i]);
    }

    return $resultMatrix;
}

// Example usage
$matrixA = [
    [1, 2, 3, 4],
    [5, 6, 7, 8],
    [9, 10, 11, 12]
];

$matrixB = [
    [11, 12, 13],
    [14, 15, 16],
    [17, 18, 19]
];

$submatrixCoords = [
    [2, 3, 2, 3],
    [1, 2, 1, 2]
];

$result = submatrixConcatenation($matrixA, $matrixB, $submatrixCoords);
foreach ($result as $row) {
    echo implode(' ', $row) . "\n";
}
// 6 7 11 12
// 10 11 14 15

PHP

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];
        }
    }

    // The part for the concatenation process
    $resultMatrix = [];
    for ($i = 0; $i < $numRows; $i++) {
        $resultMatrix[$i] = array_merge($submatrixA[$i], $submatrixB[$i]);
    }

    return $resultMatrix;
}

// Example usage
$matrixA = [
    [1, 2, 3, 4],
    [5, 6, 7, 8],
    [9, 10, 11, 12]
];

$matrixB = [
    [11, 12, 13],
    [14, 15, 16],
    [17, 18, 19]
];

$submatrixCoords = [
    [2, 3, 2, 3],
    [1, 2, 1, 2]
];

$result = submatrixConcatenation($matrixA, $matrixB, $submatrixCoords);
foreach ($result as $row) {
    echo implode(' ', $row) . "\n";
}
// 6 7 11 12
// 10 11 14 15

Introduction

Task Statement

Solution Building: Step 1

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Solution Building: Step 2

Lesson Summary