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 |
6
Time Complexity: O(N2)
Auxiliary Space: O(1)
Please refer complete article on Maximize sum of diagonal of a matrix by rotating all rows or all columns for more details!
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