5 Best Ways to Find the Sum of All Elements in a Matrix Except the Elements in Row or Column of a Given Cell in Python

💡 Problem Formulation: Given a matrix (a list of lists in Python) and a specific cell (identified by its row and column indices), the task is to calculate the sum of all elements in the matrix except those that are in the same row or column as the specified cell. For example, given the matrix [[1, 2, 3], [4, 5, 6], [7, 8, 9]] and the cell at (1, 1) (the middle cell with value 5), the desired output is 20.

Method 1: Slicing and Summation

This approach involves creating a new matrix without the specified row and column, and then summing all the remaining elements. The built-in sum() function is used to calculate the sum of the elements in the remaining matrix.

Here’s an example:

def matrix_sum_excluding_row_col(matrix, row, col):
        reduced_matrix = [r[:col] + r[col+1:] for i, r in enumerate(matrix) if i != row]
        return sum(map(sum, reduced_matrix))

    matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
    sum_excluding = matrix_sum_excluding_row_col(matrix, 1, 1)
    print(sum_excluding)
    

Output: 20

This method relies on list comprehensions to remove the selected row and column. Using list slicing and the enumerate function identifies the row index, while slicing within the generator expression excludes the column. The result is a smaller matrix from which the sum is then calculated with a combination of the map() and sum() functions.

Method 2: Manual Iteration and Summation

Using nested loops allows for manually iterating over each element and summing them, excluding elements from the specified row and column. This method provides fine-grained control over the summation process.

Here’s an example:

def matrix_sum_excluding_row_col(matrix, row, col):
        total_sum = 0
        for i, r in enumerate(matrix):
            for j, val in enumerate(r):
                if i != row and j != col:
                    total_sum += val
        return total_sum

    matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
    sum_excluding = matrix_sum_excluding_row_col(matrix, 1, 1)
    print(sum_excluding)
    

Output: 20

This function iterates over the matrix with a nested loop, checking the indices to ensure the current element is not in the same row or column as the specified cell. When this condition is met, it adds the element’s value to a running total, yielding the desired sum.

Method 3: Using NumPy Library

If performance is a concern, utilizing the NumPy library to work with the matrix can be significantly faster, especially for large matrices. The NumPy array slicing features enable concise code for excluding the specified row and column.

Here’s an example:

import numpy as np

    def matrix_sum_excluding_row_col(matrix, row, col):
        np_matrix = np.array(matrix)
        return np.sum(np_matrix) - np.sum(np_matrix[row, :]) - np.sum(np_matrix[:, col]) + np_matrix[row, col]

    matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
    sum_excluding = matrix_sum_excluding_row_col(matrix, 1, 1)
    print(sum_excluding)
    

Output: 20

This method converts the list of lists into a NumPy array, allowing the use of powerful array slicing and aggregation functions. The total sum of the array is calculated, then the sums of the specified row and column are subtracted, adding back the intersecting cell as it’s subtracted twice.

Method 4: Set-based Exclusion

This method treats the matrix as a flat list of tuples representing coordinates and their values. By creating sets for exclusion, we can easily filter out the elements to be summed.

Here’s an example:

def matrix_sum_excluding_row_col(matrix, row, col):
        flat_coords = {(i, j): val for i, r in enumerate(matrix) for j, val in enumerate(r)}
        exclude_coords = set((row, j) for j in range(len(matrix[0]))) | set((i, col) for i in range(len(matrix)))
        return sum(val for coord, val in flat_coords.items() if coord not in exclude_coords)

    matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
    sum_excluding = matrix_sum_excluding_row_col(matrix, 1, 1)
    print(sum_excluding)
    

Output: 20

The function enumerates through the matrix to create a dictionary mapping coordinates to their corresponding values. It then creates sets of coordinates to exclude based on the given row and column, and sums the values of the remaining coordinates.

Bonus One-Liner Method 5: Functional Python Magic

This one-liner uses functional programming features in Python, like filter and lambda, to compactly express the summation excluding a specified row and column.

Here’s an example:

matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
    row, col = 1, 1
    sum_excluding = sum(val for i, r in enumerate(matrix) for j, val in enumerate(r) if i != row and j != col)
    print(sum_excluding)
    

Output: 20

This one-liner uses a generator expression to iterate over each cell of the matrix, using enumerate to obtain row and column indices, and conditionally adds the cell value to the sum if it’s not in the excluded row or column.

Summary/Discussion

• Method 1: Slicing and Summation. Strengths: Intuitive and uses list comprehensions effectively. Weaknesses: Slightly slower for larger matrices.
• Method 2: Manual Iteration and Summation. Strengths: Simple to understand, does not require additional libraries. Weaknesses: Potentially slow due to the explicit iteration.
• Method 3: Using NumPy Library. Strengths: Fast and efficient for large matrices. Weaknesses: Requires the installation of the NumPy library.
• Method 4: Set-based Exclusion. Strengths: Clear separation of inclusion and exclusion logic. Weaknesses: Additional memory for set creation and less intuitive.
• Bonus Method 5: Functional Python Magic. Strengths: Compact and Pythonic one-liner. Weaknesses: May be less readable for those not familiar with functional programming paradigms.