Combining Submatrices from Multiple Matrices Using Java

Hello Coder! This unit's exciting programming lesson will involve traversing the labyrinth of two-dimensional matrices. We're going to apply our Java 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.

Are you ready for the task? Here it is: Imagine having two different 2D arrays, A and B. Our job is to devise a Java method — let's name it submatrixConcatenation() — which takes these two matrices as inputs, along with the coordinates specifying submatrices within A and B. The coordinate system uses 1-based indexing (meaning the first row and column are numbered 1, not 0). This method 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 Java to get the rows and then the required columns from those rows:

class Solution {

    public static int[][] submatrixConcatenation(
        int[][] matrixA, 
        int[][] matrixB, 
        int[][] submatrixCoords) {

        int startRowA = submatrixCoords[0][0];
        int endRowA = submatrixCoords[0][1];
        int startColA = submatrixCoords[0][2];
        int endColA = submatrixCoords[0][3];
        int startRowB = submatrixCoords[1][0];
        int endRowB = submatrixCoords[1][1];
        int startColB = submatrixCoords[1][2];
        int endColB = submatrixCoords[1][3];

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

        int[][] submatrixA = new int[numRows][numColsA];
        for (int i = 0; i < numRows; i++) {
            for (int j = 0; j < numColsA; j++) {
                submatrixA[i][j] = matrixA[startRowA + i - 1][startColA + j - 1];
            }
        }
        
        int[][] submatrixB = new int[numRows][numColsB];
        for (int i = 0; i < numRows; i++) {
            for (int 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
    }
}