Java 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:

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 columns
static 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 Code
public 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

Output:

6

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

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