Python3 Program to Maximize sum of diagonal of a matrix by rotating all rows or all columns

Given a square matrix, mat[][] of dimensions N * N, the task is find the maximum sum of diagonal elements possible from the given matrix by rotating either all the rows or all the columns of the matrix by a positive integer.

Examples:

Input: mat[][] = { { 1, 1, 2 }, { 2, 1, 2 }, { 1, 2, 2 } }
Output: 6 
Explanation:
Rotating all the columns of matrix by 1 modifies mat[][] to { {2, 1, 2}, {1, 2, 2}, {1, 1, 2} }. 
Therefore, the sum of diagonal elements of the matrix = 2 + 2 + 2 = 6 which is the maximum possible.

Input: A[][] = { { -1, 2 }, { -1, 3 } }
Output: 2

Approach: The idea is to rotate all the rows and columns of the matrix in all possible ways and calculate the maximum sum obtained. Follow the steps to solve the problem:

• Initialize a variable, say maxDiagonalSum to store the maximum possible sum of diagonal elements the matrix by rotating all the rows or columns of the matrix.
• Rotate all the rows of the matrix by a positive integer in the range [0, N – 1] and update the value of maxDiagonalSum.
• Rotate all the columns of the matrix by a positive integer in the range [0, N – 1] and update the value of maxDiagonalSum.
• Finally, print the value of maxDiagonalSum.

Below is the implementation of the above approach:

Python3

# Python3 program to implement
# the above approach
import sys

N = 3

# Function to find maximum sum of diagonal
# elements of matrix by rotating either
# rows or columns
def findMaximumDiagonalSumOMatrixf(A):

    # Stores maximum diagonal sum of elements
    # of matrix by rotating rows or columns
    maxDiagonalSum = -sys.maxsize - 1

    # Rotate all the columns by an integer
    # in the range [0, N - 1]
    for i in range(N):

        # Stores sum of diagonal elements
        # of the matrix
        curr = 0

        # Calculate sum of diagonal
        # elements of the matrix
        for j in range(N):

            # Update curr
            curr += A[j][(i + j) % N]

        # Update maxDiagonalSum
        maxDiagonalSum = max(maxDiagonalSum,
                             curr)

    # Rotate all the rows by an integer
    # in the range [0, N - 1]
    for i in range(N):

        # Stores sum of diagonal elements
        # of the matrix
        curr = 0

        # Calculate sum of diagonal
        # elements of the matrix
        for j in range(N):

            # Update curr
            curr += A[(i + j) % N][j]

        # Update maxDiagonalSum
        maxDiagonalSum = max(maxDiagonalSum,
                             curr)

    return maxDiagonalSum

# Driver code
if __name__ == "__main__":

    mat = [ [ 1, 1, 2 ],
            [ 2, 1, 2 ],
            [ 1, 2, 2 ] ]

    print(findMaximumDiagonalSumOMatrixf(mat))

# This code is contributed by chitranayal

Output:

6

Time Complexity: O(N²)
Auxiliary Space: O(1)

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