JavaScript Program for Mirror of Matrix Across Diagonal

To write a javascript program for mirror of matrix across diagonal, we will be discussing two approaches with their code examples and explanations.

In this article we have a 2D matrix. Our task is to write a JavaScript program that creates a mirror of the matrix across its diagonal. This operation is also known as matrix transpose, where rows become columns and columns become rows.

Example

Input:
matrix = [[1, 2, 3],
          [4, 5, 6],
          [7, 8, 9]]

Output:
[[1, 4, 7],
 [2, 5, 8],
 [3, 6, 9]]

Approaches for Mirror of Matrix Across Diagonal

Here are two approaches to create a mirror of matrix across diagonal with stepwise explanation and complete example codes:

• Using a New Matrix
• Using In-Place Swapping

Using a New Matrix

This approach creates a new matrix to store the mirrored elements of the original matrix. The element at position [i][j] in the original matrix is placed at position [j][i] in the new matrix.

• We declare a 2D matrix mat and define a function mirror() that accepts mat as argument.
• We get the matrix size using length property and declare an empty matrix mirrorMatrix.
• Using nested for loops, we traverse the matrix and store mat[i][j] at mirrorMatrix[j][i].
• The function returns the new mirrored matrix.

Example

let mat = [
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]
];
console.log("Original matrix:");
console.log(mat);

function mirror(mat) {
    let n = mat.length;
    let mirrorMatrix = [];

    for (let i = 0; i < n; i++) {
        mirrorMatrix[i] = [];
        for (let j = 0; j < n; j++) {
            mirrorMatrix[i][j] = mat[j][i];
        }
    }
    return mirrorMatrix;
}

console.log("Mirror of the matrix across diagonal:");
console.log(mirror(mat));

Original matrix:
[ [ 1, 2, 3 ], [ 4, 5, 6 ], [ 7, 8, 9 ] ]
Mirror of the matrix across diagonal:
[ [ 1, 4, 7 ], [ 2, 5, 8 ], [ 3, 6, 9 ] ]

Using In-Place Swapping

This approach modifies the original matrix by swapping elements across the diagonal. We swap mat[i][j] with mat[j][i] for all elements above the diagonal.

• We declare a 2D matrix mat and define a function mirror() that accepts mat as argument.
• We get the matrix size using the length property.
• Using nested for loops, we traverse only the upper triangle of the matrix (j starts from i+1).
• We swap mat[i][j] with mat[j][i] using a temporary variable.
• This creates the mirror without needing additional space.

Example

let mat = [
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]
];
console.log("Original matrix:");
console.log(mat);

function mirror(mat) {
    let n = mat.length;
    for (let i = 0; i < n; i++) {
        for (let j = i + 1; j < n; j++) {
            let temp = mat[i][j];
            mat[i][j] = mat[j][i];
            mat[j][i] = temp;
        }
    }
    return mat;
}

console.log("Mirror of the matrix across diagonal:");
console.log(mirror(mat));

Original matrix:
[ [ 1, 2, 3 ], [ 4, 5, 6 ], [ 7, 8, 9 ] ]
Mirror of the matrix across diagonal:
[ [ 1, 4, 7 ], [ 2, 5, 8 ], [ 3, 6, 9 ] ]

Complexity Comparison

Here is a comparison of time and space complexity of both approaches:

Conclusion

Both approaches effectively create a mirror of the matrix across its diagonal. The in-place swapping method is more space-efficient with O(1) space complexity, while the new matrix approach preserves the original matrix but requires additional O(n²) space.

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