Construct a Matrix such that each cell consists of sum of adjacent elements of respective cells in given Matrix

Namachila November 18, 2025

0 6 7 minutes read

Given a matrix arr[][] of dimensions N * M, the task is to generate a matrix such that any cell (r, c) stores the sum of adjacent elements present horizontally, vertically, and diagonally in the given matrix.

Examples:

Input: arr[][] = {{1, 3}, {2, 4}}
Output: {{9, 7}, {8, 6}}
Explanation: Matrix is constructed by the following operations:
For cell (0, 0), arr[1][0] + arr[0][1] + arr[1][1] = 2 + 3 + 4 = 9.
For cell (0, 1), arr[1][0] + arr[0][0] + arr[1][1] = 2 + 1 + 4 = 7.
For cell (1, 0), arr[0][0] + arr[0][1] + arr[1][1] = 1 + 3 + 4 = 8.
For cell (1, 1), arr[1][0] + arr[0][1] + arr[0][0] = 2 + 3 + 1 = 6.

Input: arr[][] = {{1}}
Output: {{0}}

Approach: The idea is to traverse each cell of the given matrix and for each cell (r, c), store the sum of adjacent cells {{r-1, c-1}, {r+1, c+1}, {r-1, c+1}, {r+1, c-1}, {r, c-1}, {r-1, c}, {r+1, c}, {r, c+1}} if possible.

Initialize a matrix v[][] of dimension N * M to store the results of each cell.
Now, traverse each cell of the matrix. For each cell, check for valid adjacent cells and keep updating their sum.
After traversing, print the value stored in each cell of the matrix v[][].

Below is the implementation of the above approach:

C++

// C++ program for the above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Initialize rows and columns
int r, c;
 
// Store all 8 directions
vector<vector<int> > dir
    = { { 1, 0 },   { -1, 0 }, { 0, 1 }, { 0, -1 },
        { -1, -1 }, { -1, 1 }, { 1, 1 }, { 1, -1 } };
 
// Function to check if a cell
// (i, j) is valid or not
bool valid(int i, int j)
{
    if (i >= 0 && j >= 0 && i < r && j < c)
        return 1;
 
    return 0;
}
 
// Function to find sum of adjacent cells
// for cell (i, j)
int find(int i, int j, vector<vector<int> >& v)
{
    // Initialize sum
    int s = 0;
 
    // Visit all 8 directions
    for (auto x : dir) {
        int ni = i + x[0], nj = j + x[1];
 
        // Check if cell is valid
        if (valid(ni, nj))
            s += v[ni][nj];
    }
 
    // Return sum
    return s;
}
 
// Function to print sum of adjacent elements
void findsumofneighbors(vector<vector<int> >& M)
{
    // Stores the resultant matrix
    vector<vector<int> > v(r, vector<int>(c, 0));
 
    // Iterate each elements of matrix
    for (int i = 0; i < r; i++) {
        for (int j = 0; j < c; j++) {
 
            // Find adjacent sum
            v[i][j] = find(i, j, M);
            cout << v[i][j] << " ";
        }
        cout << "\n";
    }
}
 
// Driver Code
int main()
{
 
    // Given matrix
    vector<vector<int> > M
        = { { 1, 4, 1 }, { 2, 4, 5 }, { 3, 1, 2 } };
 
    // Size of matrix
    r = M.size(), c = M[0].size();
 
    // Function call
    findsumofneighbors(M);
}

Java

// Java program for the above approach
import java.util.*;
import java.lang.*;
 
public class GFG {
 
    // Initialize rows and columns
    private static int r, c;
 
    // Store all 8 directions
    static int[][] dir
        = { { 1, 0 },   { -1, 0 }, { 0, 1 }, { 0, -1 },
            { -1, -1 }, { -1, 1 }, { 1, 1 }, { 1, -1 } };
 
    // Function to check if a cell
    // (i, j) is valid or not
    public static boolean valid(int i, int j)
    {
        if (i >= 0 && j >= 0 && i < r && j < c)
            return true;
 
        return false;
    }
 
    // Function to find sum of adjacent cells
    // for cell (i, j)
    static int find(int i, int j, int[][] v)
    {
        // Initialize sum
        int s = 0;
 
        // Visit all 8 directions
        for (int k = 0; k < 8; k++) {
 
            int ni = i + dir[k][0], nj = j + dir[k][1];
 
            // Check if cell is valid
            if (valid(ni, nj))
                s += v[ni][nj];
        }
 
        // Return sum
        return s;
    }
 
    // Function to print sum of adjacent elements
    static void findsumofneighbors(int[][] M)
    {
        // Stores the resultant matrix
        int[][] v = new int[r];
 
        // Iterate each elements of matrix
        for (int i = 0; i < r; i++) {
            for (int j = 0; j < c; j++) {
 
                // Find adjacent sum
                v[i][j] = find(i, j, M);
                System.out.print(v[i][j] + " ");
            }
            System.out.println("");
        }
    }
 
    // Driver code
    public static void main(String[] args)
    {
        // Given matrix
        int[][] M
            = { { 1, 4, 1 },
               { 2, 4, 5 }, 
               { 3, 1, 2 } };
 
        // Size of matrix
        r = M.length;
        c = M[0].length;
 
        // Function call
        findsumofneighbors(M);
    }
}
 
// This code is contributed by ajaykr00kj

Python3

# Python program for the above approach
 
# Initialize rows and columns
r, c = 0, 0;
 
# Store all 8 directions
dir = [[1, 0], [-1, 0], [0, 1], [0, -1],
       [-1, -1], [-1, 1], [1, 1], [1, -1]];
 
# Function to check if a cell
# (i, j) is valid or not
def valid(i, j):
    if (i >= 0 and j >= 0 and i < r and j < c):
        return True;
 
    return False;
 
# Function to find sum of adjacent cells
# for cell (i, j)
def find(i, j, v):
   
    # Initialize sum
    s = 0;
 
    # Visit all 8 directions
    for k in range(8):
 
        ni = i + dir[k][0];
        nj = j + dir[k][1];
 
        # Check if cell is valid
        if (valid(ni, nj)):
            s += v[ni][nj];
 
    # Return sum
    return s;
 
# Function to print sum of adjacent elements
def findsumofneighbors(M):
   
    # Stores the resultant matrix
    v = [[0 for i in range(c)] for j in range(r)];
 
    # Iterate each elements of matrix
    for i in range(r):
        for j in range(c):
           
            # Find adjacent sum
            v[i][j] = find(i, j, M);
            print(v[i][j], end=" ");
 
        print("");
 
# Driver code
if __name__ == '__main__':
   
    # Given matrix
    M = [[1, 4, 1], [2, 4, 5], [3, 1, 2]];
 
    # Size of matrix
    r = len(M[0]);
    c = len(M[1]);
 
    # Function call
    findsumofneighbors(M);
 
# This code is contributed by 29AjayKumar

C#

// C# program for the above approach
using System;
public class GFG {
 
    // Initialize rows and columns
    private static int r, c;
 
    // Store all 8 directions
    static int[,] dir
        = { { 1, 0 },   { -1, 0 }, { 0, 1 }, { 0, -1 },
            { -1, -1 }, { -1, 1 }, { 1, 1 }, { 1, -1 } };
 
    // Function to check if a cell
    // (i, j) is valid or not
    public static bool valid(int i, int j)
    {
        if (i >= 0 && j >= 0 && i < r && j < c)
            return true;
 
        return false;
    }
 
    // Function to find sum of adjacent cells
    // for cell (i, j)
    static int find(int i, int j, int[,] v)
    {
        // Initialize sum
        int s = 0;
 
        // Visit all 8 directions
        for (int k = 0; k < 8; k++) {
 
            int ni = i + dir[k, 0], nj = j + dir[k, 1];
 
            // Check if cell is valid
            if (valid(ni, nj))
                s += v[ni, nj];
        }
 
        // Return sum
        return s;
    }
 
    // Function to print sum of adjacent elements
    static void findsumofneighbors(int[,] M)
    {
        // Stores the resultant matrix
        int[,] v = new int[r, c];
 
        // Iterate each elements of matrix
        for (int i = 0; i < r; i++) {
            for (int j = 0; j < c; j++) {
 
                // Find adjacent sum
                v[i,j] = find(i, j, M);
                Console.Write(v[i, j] + " ");
            }
            Console.WriteLine("");
        }
    }
 
    // Driver code
    public static void Main(String[] args)
    {
        // Given matrix
        int[,] M
            = { { 1, 4, 1 },
               { 2, 4, 5 }, 
               { 3, 1, 2 } };
 
        // Size of matrix
        r = M.GetLength(0);
        c = M.GetLength(1);
 
        // Function call
        findsumofneighbors(M);
    }
}
 
// This code is contributed by Rajput-Ji 

Javascript

<script>
 
// JavaScript program for the above approach
 
    // Initialize rows and columns
    let r, c;
  
    // Store all 8 directions
    let dir
        = [[ 1, 0 ],   [ -1, 0 ], [ 0, 1 ], [ 0, -1 ],
            [ -1, -1 ], [ -1, 1 ], [ 1, 1 ], [ 1, -1 ]];
  
    // Function to check if a cell
    // (i, j) is valid or not
   function valid(i, j)
    {
        if (i >= 0 && j >= 0 && i < r && j < c)
            return true;
  
        return false;
    }
  
    // Function to find sum of adjacent cells
    // for cell (i, j)
    function find(i, j, v)
    {
        // Initialize sum
        let s = 0;
  
        // Visit all 8 directions
        for (let k = 0; k < 8; k++) {
  
            let ni = i + dir[k][0], nj = j + dir[k][1];
  
            // Check if cell is valid
            if (valid(ni, nj))
                s += v[ni][nj];
        }
  
        // Return sum
        return s;
    }
  
    // Function to print sum of adjacent elements
    function findsumofneighbors(M)
    {
        // Stores the resultant matrix
        let v = new Array(r);
         
        // Loop to create 2D array using 1D array
    for (var i = 0; i < v.length; i++) {
        v[i] = new Array(2);
    }
  
        // Iterate each elements of matrix
        for (let i = 0; i < r; i++) {
            for (let j = 0; j < c; j++) {
  
                // Find adjacent sum
                v[i][j] = find(i, j, M);
                document.write(v[i][j] + " ");
            }
            document.write("<br/>" );
        }
    }
 
// Driver Code
 
     // Given matrix
      let M
            = [[ 1, 4, 1 ],
               [ 2, 4, 5 ],
               [ 3, 1, 2 ]];
  
        // Size of matrix
        r = M.length;
        c = M[0].length;
  
        // Function call
        findsumofneighbors(M);
 
</script>

Output

10 13 13 
13 19 12 
7 16 10

Time Complexity: O(N*M) where N * M are the dimensions of the matrix.
Auxiliary Space: O(N*M)

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