Introduction

Rotating a two-dimensional array, or matrix, is a common problem in programming that can arise in different applications, particularly in computer graphics and data manipulation. In this blog post, we will dive into the process of rotating a 4x4 matrix by 90 degrees clockwise.

Understanding the Problem

Imagine you have a two-dimensional array structured like this:

[1][2][3][4]
[5][6][7][8]
[9][0][1][2]
[3][4][5][6]

After rotating this matrix 90 degrees clockwise, it should transform into:

[3][9][5][1]
[4][0][6][2]
[5][1][7][3]
[6][2][8][4]

In practical terms, each element in the original array shifts into a new position based on the rotation. But how do we implement this in a programming language like C#? Let’s break this down step by step.

Solution

Step 1: Initialize the Matrix

First, we need to initialize the matrix in our program. Here’s how you can do it:

int[,] array = new int[4,4] {
    { 1,2,3,4 },
    { 5,6,7,8 },
    { 9,0,1,2 },
    { 3,4,5,6 }
};

Step 2: Create a Function to Rotate the Matrix

Next, we will create a function called RotateMatrix that performs the required rotation. This function will take the original matrix and its size as parameters and return the rotated matrix.

Here’s the implementation of the RotateMatrix function:

static int[,] RotateMatrix(int[,] matrix, int n) {
    int[,] ret = new int[n, n];

    for (int i = 0; i < n; ++i) {
        for (int j = 0; j < n; ++j) {
            ret[i, j] = matrix[n - j - 1, i];
        }
    }

    return ret;
}

Step 3: Explanation of the Function

• Matrix Declaration: We declare a new matrix ret of the same size as the input.
• Nested Loops: We use a nested loop to traverse through each element of the matrix.
• Rotation Logic: For each element at position (i, j), we map it to the new position (j, n - i - 1). This formula helps in rotating the elements correctly by 90 degrees clockwise.

Step 4: Testing the Function

You can test the function by calling it and printing out the rotated matrix:

int[,] rotated = RotateMatrix(array, 4);

Just ensure to implement a method to print the matrix for verification.

Conclusion

Rotating a two-dimensional array is a straightforward task once you understand the mapping of indices. While the current approach runs in O(n^2) time complexity, optimizing algorithms for larger matrices (like 10000x10000) is an ongoing discussion in algorithms and data structures.

Now you can confidently rotate any two-dimensional array in C#. Happy coding!