Check If the Given Two Matrices Are Mirror Images of One Another in Java

In Java programming, determining if two matrices are mirror images of each other involves comparing corresponding elements in reverse order. A matrix is considered a mirror image of another if its rows or columns are reversed versions of the corresponding rows or columns in the other matrix.

Examples of Matrices Mirror Image

Example 1:

Input:

Output:

 
Yes   

Explanation:

• For i = 0 (first row): mat1[0][0] = 1, mat2[0][2] = 1
• For i = 1 (second row): mat1[1][1] = 4, mat2[1][1] = 4
• For i = 2 (third row): mat1[2][2] = 8, mat2[2][0] = 8

All corresponding elements satisfy the mirror image condition; hence the output is "Yes".

Example 2:

Input:

Output:

 
No   

Explanation:

• For i = 0 (first row): mat1[0][0] = 1, mat2[0][2] = 1
• For i = 1 (second row): mat1[1][1] = 4, mat2[1][1] = 4
• For i = 2 (third row): mat1[2][2] = 2, mat2[2][0] = 2

However, for i = 0 (first row): mat1[0][1] = 2, mat2[0][1] = 2 does not match (mat1[0][1] = 2, mat2[0][1] = 1) which does not satisfy the mirror image condition, hence the output is "No".

Example 3:

Input:

Output:

 
Yes   

Explanation:

• For i = 0 (first row): mat1[0][0] = 1, mat2[0][2] = 1
• For i = 1 (second row): mat1[1][1] = 5, mat2[1][1] = 5
• For i = 2 (third row): mat1[2][2] = 9, mat2[2][0] = 9

All corresponding elements satisfy the mirror image condition, hence the output is "Yes".

Approach

The code checks if matrix2 is the horizontal mirror image of matrix1 by comparing each row of matrix1 with the corresponding row of matrix2 read from right to left.

Algorithm

Step 1: Define a function checkMirror(matrix1, matrix2, size) to compare two square matrices matrix1 and matrix2 of size size x size.

Step 2: Initialize row to 0 and col to 0 to track current indices in matrix2 and also initialize isMirrorImage to true as an initial assumption that matrices are mirror images.

Step 3: Use an outer loop (i iterating over rows of matrix1):

• Inside, use an inner loop (j iterating backwards over columns of matrix1):
  
  • Compare matrix2[row][col] with matrix1[i][j].
  • If they differ, set isMirrorImage to false and break out of the inner loop.
  • Increment col to move to the next column in matrix2.

Step 4: Reset col to 0 after completing the inner loop for each row comparison and Increment row to move to the next row in matrix2 for comparison with the next row in matrix1.

Step 5: If isMirrorImage remains true, print "Yes" indicating matrix2 is a mirror image of matrix1. Otherwise, print "No" indicating they are not mirror images.

Step 6: Define size as the size of the matrices (for example, 3 for 3x3 matrices).

• Define matrix1 and matrix2 with specific values.
• Call checkMirror(matrix1, matrix2, size) to execute the comparison.

Implementation

Let's implement the above algorithm in a Java program.

File Name: MirrorImageCheck.java

Output:

 
Yes   

Time Complexity: The time complexity of the code is O(n^2), where n is the size of the matrix (assuming the matrix is n×n).

Auxiliary Space: The auxiliary space of the code is O(1)