Sum of all parts of a square Matrix divided by its diagonals

Last Updated : 12 Jul, 2025

Given a 2D matrix arr[][] of N*N dimensions, the task is to find the sum of elements of all four parts of the matrix divided by the diagonals without including the diagonal elements in any of the four parts.
Example:

Input: arr[][] = { {1, 2, 3}, {4, 5, 6}, {7, 8, 9} }
Output: 2 4 6 8
Explanation:
(1, 5, 9) and (3, 5, 7) are diagonals of arr[][] matrix. Therefore sum of parts are:
Top = 2
Left = 4
Right = 6
Bottom = 8
Input: arr[][] = { {1, 3, 1, 5}, {2, 2, 4, 1}, {5, 0, 2, 3}, { 1, 3, 3, 5} }
Output: 4 7 4 6
Explanation:
(1, 2, 2, 5) and (5, 4, 0, 1) are diagonals of arr[][] matrix. Therefore sum of parts are:
Top = 3 + 1 = 4
Left = 2 + 5 = 7
Right = 1 + 3 = 4
Bottom = 3 + 3 = 6

Approach:

As shown in the above figure, After the matrix of size NxN is divided by diagonals. We observe the following properties:

If sum of index of row and column is less than N - 1 then, it belongs to either Top part or Left part.
- If column index is greater than row index it belongs to Top part.
- Else it belongs to Left part.
Else it belongs to either Right part or Down part.
- If column index is greater than row index it belongs to Right part.
- Else it belongs to Down part.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include "bits/stdc++.h"
using namespace std;

// Function to calculate the
// sum of all parts of matrix
void SumOfPartsOfMetrics(int* arr,
                         int N)
{

    // To store the sum of all four
    // parts of the diagonals
    int top, bottom, left, right;

    // Initialise respective sum
    // as zero
    top = bottom = right = left = 0;

    // Traversing the matrix
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {

            // If i + j < N -1
            // then it belongs to
            // top or left
            if (i + j < N - 1 && i != j) {

                // Belongs to top
                if (i < j) {
                    top += (arr + i * N)[j];
                }

                // Belongs to left
                else {
                    left += (arr + i * N)[j];
                }
            }

            // If i+j > N - 1 then
            // it belongs to right
            // or bottom
            else if (i + j > N - 1 && i != j) {

                // Belongs to right
                if (i > j) {
                    bottom += (arr + i * N)[j];
                }

                // Belongs to bottom
                else {
                    right += (arr + i * N)[j];
                }
            }
        }
    }
    cout << top << ' ' << left
         << ' ' << right << ' '
         << bottom << endl;
}

// Driver Code
int main()
{
    int N = 4;
    int arr[N][N] = { { 1, 3, 1, 5 },
                      { 2, 2, 4, 1 },
                      { 5, 0, 2, 3 },
                      { 1, 3, 3, 5 } };
    // Function call to find print
    // sum of al parts
    SumOfPartsOfMetrics((int*)arr, N);
    return 0;
}

Java

// Java program for the above approach 
class GFG {

// Function to calculate the 
// sum of all parts of matrix 
static void SumOfPartsOfMetrics(int [][]arr, 
                                int N) 
{ 
    
    // To store the sum of all four 
    // parts of the diagonals 
    // Initialise respective sum 
    // as zero 
    int top = 0, bottom = 0;
    int left = 0, right = 0; 

    // Traversing the matrix 
    for(int i = 0; i < N; i++)
    { 
       for(int j = 0; j < N; j++)
       { 
          
          // If i + j < N -1 
          // then it belongs to 
          // top or left 
          if (i + j < N - 1 && i != j)
          { 
              
              // Belongs to top 
              if (i < j)
              { 
                  top += arr[i][j]; 
              } 
              
              // Belongs to left 
              else
              { 
                  left += arr[i][j]; 
              } 
          } 
          
          // If i+j > N - 1 then 
          // it belongs to right 
          // or bottom 
          else if (i + j > N - 1 && i != j)
          { 
              
              // Belongs to right 
              if (i > j)
              { 
                  bottom += arr[i][j]; 
              } 
              
              // Belongs to bottom 
              else 
              { 
                  right += arr[i][j]; 
              } 
          } 
       } 
    } 
    System.out.println(top + " " + left + " " +
                     right + " " + bottom); 
} 
    
// Driver Code 
public static void main (String[] args) 
{ 
    int N = 4; 
    int arr[][] = { { 1, 3, 1, 5 }, 
                    { 2, 2, 4, 1 }, 
                    { 5, 0, 2, 3 }, 
                    { 1, 3, 3, 5 } }; 
                        
    // Function call to find print 
    // sum of al parts 
    SumOfPartsOfMetrics(arr, N); 
} 
}

// This code is contributed by AnkitRai01

Python3

# Python3 program for the above approach 

# Function to calculate the 
# sum of all parts of matrix 
def SumOfPartsOfMetrics(arr, N): 

    # To store the sum of all four 
    # parts of the diagonals 
    # Initialise respective sum 
    # as zero 
    top = bottom = right = left = 0; 

    # Traversing the matrix 
    for i in range(N):
        for j in range(N):

            # If i + j < N -1 
            # then it belongs to 
            # top or left 
            if (i + j < N - 1 and i != j):

                # Belongs to top 
                if (i < j):
                    top += arr[i][j]; 
            
                # Belongs to left 
                else:
                    left += arr[i][j]; 

            # If i+j > N - 1 then 
            # it belongs to right 
            # or bottom 
            elif (i + j > N - 1 and i != j):

                # Belongs to right 
                if (i > j):
                    bottom += arr[i][j]; 

                # Belongs to bottom 
                else:
                    right += arr[i][j]; 
            
    print(top, left, right, bottom); 

# Driver Code 
if __name__ == "__main__":

    N = 4; 
    arr = [ [ 1, 3, 1, 5 ], 
            [ 2, 2, 4, 1 ], 
            [ 5, 0, 2, 3 ], 
            [ 1, 3, 3, 5 ] ];
            
    # Function call to find print 
    # sum of al parts 
    SumOfPartsOfMetrics(arr, N); 
    
# This code is contributed by AnkitRai01

// C# program for the above approach 
using System;

class GFG {

// Function to calculate the 
// sum of all parts of matrix 
static void SumOfPartsOfMetrics(int [,]arr, 
                                int N) 
{ 
        
    // To store the sum of all four 
    // parts of the diagonals 
    // Initialise respective sum 
    // as zero 
    int top = 0, bottom = 0;
    int left = 0, right = 0; 
    
    // Traversing the matrix 
    for(int i = 0; i < N; i++)
    { 
       for(int j = 0; j < N; j++)
       { 

          // If i + j < N -1 
          // then it belongs to 
          // top or left 
          if (i + j < N - 1 && i != j)
          { 
              
              // Belongs to top 
              if (i < j)
              {
                  top += arr[i, j]; 
              } 
              
              // Belongs to left 
              else
              { 
                  left += arr[i, j]; 
              } 
          } 
          
          // If i+j > N - 1 then 
          // it belongs to right 
          // or bottom 
          else if (i + j > N - 1 && i != j)
          { 
                
            // Belongs to right 
            if (i > j)
            { 
                bottom += arr[i, j]; 
            } 
            
            // Belongs to bottom 
            else
            { 
                right += arr[i, j]; 
            } 
          } 
       } 
    } 
    Console.WriteLine(top + " " + left + " " +
                    right + " " + bottom); 
} 
        
// Driver Code 
public static void Main (string[] args) 
{ 
    int N = 4; 
    int [,]arr = { { 1, 3, 1, 5 }, 
                   { 2, 2, 4, 1 }, 
                   { 5, 0, 2, 3 }, 
                   { 1, 3, 3, 5 } }; 
                            
    // Function call to find print 
    // sum of al parts 
    SumOfPartsOfMetrics(arr, N); 
} 
}

// This code is contributed by AnkitRai01

JavaScript

<script>
// Javascript program for the above approach

// Function to calculate the
// sum of all parts of matrix
function SumOfPartsOfMetrics(arr, N)
{

    // To store the sum of all four
    // parts of the diagonals
    let top, bottom, left, right;

    // Initialise respective sum
    // as zero
    top = bottom = right = left = 0;

    // Traversing the matrix
    for (let i = 0; i < N; i++) {
        for (let j = 0; j < N; j++) {

            // If i + j < N -1
            // then it belongs to
            // top or left
            if (i + j < N - 1 && i != j) {

                // Belongs to top
                if (i < j) {
                    top += arr[i][j];
                }

                // Belongs to left
                else {
                    left += arr[i][j];
                }
            }

            // If i+j > N - 1 then
            // it belongs to right
            // or bottom
            else if (i + j > N - 1 && i != j) {

                // Belongs to right
                if (i > j) {
                    bottom += arr[i][j];
                }

                // Belongs to bottom
                else {
                    right += arr[i][j];
                }
            }
        }
    }
    document.write(top + ' ' + left
         + ' ' + right + ' '
         + bottom + "<br>");
}

// Driver Code
    let N = 4;
    let arr = [ [ 1, 3, 1, 5 ],
                      [ 2, 2, 4, 1 ],
                      [ 5, 0, 2, 3 ],
                      [ 1, 3, 3, 5 ] ];
    // Function call to find print
    // sum of al parts
    SumOfPartsOfMetrics(arr, N);

// This code is contributed by rishavmahato348.
</script>

Output:

4 7 4 6

Time Complexity: O(N²)

Auxiliary Space: O(1) because It is using constant variable

Asymptotic Notations for Analysis of Algorithms

manthanpandey039

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