Transpose 2D Matrix in Java - Time & Space Complexity?

Question

Here's my algorithm / approach for transposing a 2D Matrix on the main diagonal.

Before:

a L M d 
b G c N 
H K e F 
I J O P 

After:

a b H I 
L G K J 
M c e O 
d N F P 

---

My code:

public class Matrix {

    static String[][] matrix = {

            {"a", "L", "M", "d"},
            {"b", "G", "c", "N"},
            {"H", "K", "e", "F"},
            {"I", "J", "O", "P"}
    };

    public void transpose(String[][] matrix) {
       String[][] transposedArray = new String [4][4];
       for (int row =0; row < 4; row ++) {
           for (int col = 0; col < 4; col++) {
               transposedArray[row][col] = matrix[col][row];  
           }
       }
    }
}

What is the time & space complexity of this approach?

Is there a better optimal solution?

Answer 1

The time complexity for your algorithm will be O(n). If you pass in a 16 element matrix (4x4) it will take approximately 16 units of time. If you pass in a 100 element matrix (10x10) it will take approximately 100 units of time.

The space complexity will be O(n) - in other words the amount of memory required is approximately proportional to the input matrix size. In your case, you could say it would be O(2n) - since it will take approximately twice the space of your input matrix (inc the input matrix).

The reason I say approximate is that there is minimal additional time and space required for loops and their variables, but these become insignificant for any reasonably sized input matrix.