Rotating a matrix by 90 degrees clockwise is a common problem in computer science and technical interviews. This problem can be particularly interesting because the goal is to perform the rotation in place, without using additional memory for a new matrix. In this guide, we will explore how to achieve this with a clear explanation and example code.

Problem Description

You are given an n x n 2D matrix A representing an image. Your task is to rotate the image clockwise at 90 degrees in place. If you use an additional array, you will only receive partial credit.

Problem Constraints

1≤n≤1000

Input Format

A 2D matrix A of integers

Output Format

The 2D rotated matrix

Example Input

[
    [1, 2],
    [3, 4]
]

Example Output

[
    [3, 1],
    [4, 2]
]

Example Explanation

After rotating the matrix by 90 degrees:

• 1 goes to position 2
• 2 goes to position 4
• 4 goes to position 3
• 3 goes to position 1

Step-by-Step Solution

Step 1: Transpose the Matrix

• Transposing a matrix means converting its rows into columns and columns into rows. This can be done by swapping elements across the main diagonal (top-left to bottom-right diagonal).

Step 2: Reverse Each Row

• Once the matrix is transposed, the next step is to reverse each row. This will effectively rotate the matrix by 90 degrees clockwise.

Example Code

Here’s a JavaScript function to perform the rotation:

function rotateMatrix(A) {
    const n = A.length;

    // Step 1: Transpose the matrix
    for (let i = 0; i < n; i++) {
        for (let j = i; j < n; j++) {
            let temp = A[i][j];
            A[i][j] = A[j][i];
            A[j][i] = temp;
        }
    }

    // Step 2: Reverse each row
    for (let i = 0; i < n; i++) {
        A[i].reverse();
    }

    return A;
}

// Example usage:
let matrix = [
    [1, 2],
    [3, 4]
];

console.log(rotateMatrix(matrix));

Explanation of the Code

Transpose the Matrix:

• Loop through the matrix using two nested loops.
• Swap elements A[i][j] and A[j][i] to transpose the matrix.

Reverse Each Row:

• Use the built-in reverse() method to reverse each row in the transposed matrix.

Return the Rotated Matrix:

• After transposing and reversing each row, the matrix is rotated by 90 degrees clockwise.

Conclusion

Rotating a matrix in place is a valuable skill that showcases your understanding of array manipulation and in-place algorithms. By transposing the matrix and then reversing each row, you can achieve the desired rotation without using extra space. Practice this method to enhance your problem-solving abilities in technical interviews and coding challenges.