Python – Test if all elements are unique in columns of a Matrix

When it is required to test if all elements are unique in columns of a matrix, a simple iteration and a list comprehension along with the 'set' operator are used.

Below is a demonstration of the same ?

Example

my_matrix = [[11, 24, 84], [24, 55, 11], [7, 11, 9]]

print("The matrix is:")
print(my_matrix)

my_result = True

for index in range(len(my_matrix[0])):
    column = [row[index] for row in my_matrix]
    
    if len(list(set(column))) != len(column):
        my_result = False
        break

if my_result == True:
    print("All columns are unique")
else:
    print("All columns are not unique")

Output

The matrix is:
[[11, 24, 84], [24, 55, 11], [7, 11, 9]]
All columns are unique

How It Works

The algorithm extracts each column from the matrix and converts it to a set. Since sets only contain unique elements, comparing the length of the original column with the set reveals if duplicates exist.

Example with Duplicate Elements

# Matrix with duplicate elements in column 1
matrix_with_duplicates = [[11, 24, 84], [24, 24, 11], [7, 24, 9]]

print("The matrix is:")
print(matrix_with_duplicates)

result = True

for index in range(len(matrix_with_duplicates[0])):
    column = [row[index] for row in matrix_with_duplicates]
    
    if len(set(column)) != len(column):
        result = False
        print(f"Column {index} has duplicates: {column}")
        break

if result:
    print("All columns are unique")
else:
    print("All columns are not unique")

The matrix is:
[[11, 24, 84], [24, 24, 11], [7, 24, 9]]
Column 1 has duplicates: [24, 24, 24]
All columns are not unique

Using a Function Approach

def check_unique_columns(matrix):
    """Check if all columns in matrix have unique elements"""
    for col_index in range(len(matrix[0])):
        column = [row[col_index] for row in matrix]
        if len(set(column)) != len(column):
            return False
    return True

# Test with different matrices
matrix1 = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
matrix2 = [[1, 2, 3], [1, 5, 6], [7, 8, 9]]

print("Matrix 1:", matrix1)
print("All columns unique:", check_unique_columns(matrix1))

print("\nMatrix 2:", matrix2)
print("All columns unique:", check_unique_columns(matrix2))

Matrix 1: [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
All columns unique: True

Matrix 2: [[1, 2, 3], [1, 5, 6], [7, 8, 9]]
All columns unique: False

Conclusion

Testing column uniqueness in a matrix involves extracting each column using list comprehension and comparing the original length with the set length. This approach efficiently identifies duplicate elements within any column of the matrix.