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Check if a Matrix is Symmetric

Certification: Basic Level Accuracy: 25% Submissions: 16 Points: 10

Write a C++ program to check if a given square matrix is symmetric. A matrix is symmetric if it is equal to its transpose.

Example 1
    
  
  • Input: matrix = [
    [1, 2, 3],
    [2, 4, 5],
    [3, 5, 6]
  ]
    • 
  
  • Output: true
    • 
  
  • Explanation: 
      
    
    • Step 1: Calculate the transpose of the matrix by swapping elements across the diagonal.
      • 
    
    • Step 2: Check if element at position (i,j) equals element at position (j,i) for all valid i,j.
      • 
    
    • Step 3: Verify that matrix[0][1] = matrix[1][0] = 2, matrix[0][2] = matrix[2][0] = 3, and matrix[1][2] = matrix[2][1] = 5.
      • 
    
    • Step 4: Since all elements match their counterparts across the diagonal, return true.
      • 
  
    •
Example 2
    
  
  • Input: matrix = [
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]
  ]
    • 
  
  • Output: false
    • 
  
  • Explanation: 
      
    
    • Step 1: Calculate the transpose of the matrix by swapping elements across the diagonal.
      • 
    
    • Step 2: Check if element at position (i,j) equals element at position (j,i) for all valid i,j.
      • 
    
    • Step 3: Verify that matrix[0][1] = 2 ≠ matrix[1][0] = 4, which means the matrix is not symmetric.
      • 
    
    • Step 4: Return false as we found elements that don't match across the diagonal.
      • 
  
    •
Constraints
    
  
  • The matrix must be a square matrix
    • 
  
  • The matrix can have a maximum size of 100x100
    • 
  
  • Time Complexity: O(n²), where n is the size of the matrix
    • 
  
  • Space Complexity: O(1) (no extra space needed for in-place checking)
    •
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Hint
Solution

Solution Hints

    
  
  • Compare the matrix with its transpose.
    • 
  
  • Use nested loops to check if each element at position (i, j) is equal to the element at position (j, i).
    •

Steps to solve by this approach:

 Step 1: Define a function is_symmetric that takes a constant 2D vector as parameter.
 Step 2: Get the size of the matrix (number of rows/columns).
 Step 3: Use nested loops to compare each element with its transpose position.
 Step 4: If any element doesn't match its transpose counterpart, return false.
 Step 5: If all elements match their transpose counterparts, return true.
 Step 6: In main, create a matrix, call the function, and print the result.

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