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:
Java
// Java program to implement // the above approach import java.util.*; class GFG{ static int N = 3; // Function to find maximum sum of // diagonal elements of matrix by// rotating either rows or columnsstatic int findMaximumDiagonalSumOMatrixf(int A[][]){ // Stores maximum diagonal sum of elements // of matrix by rotating rows or columns int maxDiagonalSum = Integer.MIN_VALUE; // Rotate all the columns by an integer // in the range [0, N - 1] for(int i = 0; i < N; i++) { // Stores sum of diagonal elements // of the matrix int curr = 0; // Calculate sum of diagonal // elements of the matrix for(int j = 0; j < N; j++) { // Update curr curr += A[j][(i + j) % N]; } // Update maxDiagonalSum maxDiagonalSum = Math.max(maxDiagonalSum, curr); } // Rotate all the rows by an integer // in the range [0, N - 1] for(int i = 0; i < N; i++) { // Stores sum of diagonal elements // of the matrix int curr = 0; // Calculate sum of diagonal // elements of the matrix for(int j = 0; j < N; j++) { // Update curr curr += A[(i + j) % N][j]; } // Update maxDiagonalSum maxDiagonalSum = Math.max(maxDiagonalSum, curr); } return maxDiagonalSum;} // Driver Codepublic static void main(String[] args){ int[][] mat = { { 1, 1, 2 }, { 2, 1, 2 }, { 1, 2, 2 } }; System.out.println( findMaximumDiagonalSumOMatrixf(mat));}} // This code is contributed by susmitakundugoaldanga |
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!
