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:
C++
// C++ program to implement// the above approach#include <bits/stdc++.h>using namespace std;#define N 3// Function to find maximum sum of diagonal elements // of matrix by rotating either rows or columnsint findMaximumDiagonalSumOMatrixf(int A[][N]){ // Stores maximum diagonal sum of elements // of matrix by rotating rows or columns int maxDiagonalSum = INT_MIN; // 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 = 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 = max(maxDiagonalSum, curr); } return maxDiagonalSum;}// Driver codeint main(){ int mat[N][N] = { { 1, 1, 2 }, { 2, 1, 2 }, { 1, 2, 2 } }; cout<< findMaximumDiagonalSumOMatrixf(mat); return 0;} |
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 |
Python3
# Python3 program to implement# the above approachimport sysN = 3# Function to find maximum sum of diagonal# elements of matrix by rotating either # rows or columnsdef 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 codeif __name__ == "__main__": mat = [ [ 1, 1, 2 ], [ 2, 1, 2 ], [ 1, 2, 2 ] ] print(findMaximumDiagonalSumOMatrixf(mat)) # This code is contributed by chitranayal |
C#
// C# program to implement// the above approach using System; 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 = Int32.MinValue; // 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(){ int[,] mat = { { 1, 1, 2 }, { 2, 1, 2 }, { 1, 2, 2 } }; Console.Write(findMaximumDiagonalSumOMatrixf(mat));}}// This code is contributed by code_hunt |
Javascript
<script>// Javascript program to implement// the above approachlet N = 3; // Function to find maximum sum of// diagonal elements of matrix by// rotating either rows or columnsfunction findMaximumDiagonalSumOMatrixf(A){ // Stores maximum diagonal sum of elements // of matrix by rotating rows or columns let maxDiagonalSum = Number.MIN_VALUE; // Rotate all the columns by an integer // in the range [0, N - 1] for(let i = 0; i < N; i++) { // Stores sum of diagonal elements // of the matrix let curr = 0; // Calculate sum of diagonal // elements of the matrix for(let 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(let i = 0; i < N; i++) { // Stores sum of diagonal elements // of the matrix let curr = 0; // Calculate sum of diagonal // elements of the matrix for(let j = 0; j < N; j++) { // Update curr curr += A[(i + j) % N][j]; } // Update maxDiagonalSum maxDiagonalSum = Math.max(maxDiagonalSum, curr); } return maxDiagonalSum;} // Driver Code let mat = [[ 1, 1, 2 ], [ 2, 1, 2 ], [ 1, 2, 2 ]]; document.write( findMaximumDiagonalSumOMatrixf(mat));// This code is contributed by souravghosh0416.</script> |
Output:
6
Time Complexity: O(N2)
Auxiliary Space: O(1)
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