Python Program to Print Matrix in Z form

A Z-form traversal of a square matrix follows a specific pattern: traverse the first row, then the main diagonal (excluding elements already printed), and finally the last row. This creates a Z-like path through the matrix.

Understanding Z-Form Pattern

For a matrix of size n×n, Z-form traversal involves three steps ?

• Print all elements of the first row
• Print diagonal elements from top-right to bottom-left (excluding corners)
• Print all elements of the last row

Implementation

Here's how to implement Z-form matrix traversal ?

def print_z_form(matrix):
    n = len(matrix)
    
    # Print first row
    for j in range(n):
        print(matrix[0][j], end=' ')
    
    # Print diagonal elements (excluding first and last row)
    for i in range(1, n-1):
        diagonal_col = n - 1 - i
        print(matrix[i][diagonal_col], end=' ')
    
    # Print last row (if more than one row)
    if n > 1:
        for j in range(n):
            print(matrix[n-1][j], end=' ')

# Example matrix
arr = [[1, 2, 6, 9],
       [1, 2, 3, 1],
       [7, 1, 3, 5],
       [1, 8, 7, 5]]

print("Matrix in Z-form:")
print_z_form(arr)

Matrix in Z-form:
1 2 6 9 3 1 1 8 7 5

Step-by-Step Breakdown

Let's trace through the algorithm with our 4×4 matrix ?

matrix = [[1, 2, 6, 9],
          [1, 2, 3, 1],
          [7, 1, 3, 5],
          [1, 8, 7, 5]]

n = len(matrix)

print("Step 1 - First row:")
for j in range(n):
    print(f"matrix[0][{j}] = {matrix[0][j]}")

print("\nStep 2 - Diagonal elements:")
for i in range(1, n-1):
    diagonal_col = n - 1 - i
    print(f"matrix[{i}][{diagonal_col}] = {matrix[i][diagonal_col]}")

print("\nStep 3 - Last row:")
for j in range(n):
    print(f"matrix[{n-1}][{j}] = {matrix[n-1][j]}")

Step 1 - First row:
matrix[0][0] = 1
matrix[0][1] = 2
matrix[0][2] = 6
matrix[0][3] = 9

Step 2 - Diagonal elements:
matrix[1][2] = 3
matrix[2][1] = 1

Step 3 - Last row:
matrix[3][0] = 1
matrix[3][1] = 8
matrix[3][2] = 7
matrix[3][3] = 5

Alternative Approach

Here's a more concise version using a single loop ?

def print_z_form_compact(matrix):
    n = len(matrix)
    result = []
    
    # Collect all Z-form elements
    # First row
    result.extend(matrix[0])
    
    # Diagonal elements (middle rows)
    for i in range(1, n-1):
        result.append(matrix[i][n-1-i])
    
    # Last row (if matrix has more than 1 row)
    if n > 1:
        result.extend(matrix[n-1])
    
    return result

# Test with example
arr = [[1, 2, 6, 9],
       [1, 2, 3, 1], 
       [7, 1, 3, 5],
       [1, 8, 7, 5]]

z_elements = print_z_form_compact(arr)
print("Z-form elements:", z_elements)

Z-form elements: [1, 2, 6, 9, 3, 1, 1, 8, 7, 5]

Conclusion

Z-form matrix traversal prints the first row, diagonal elements from top-right to bottom-left, and the last row. This creates a Z-shaped path through the matrix, useful for specific data processing patterns.