Filling diagonal to make the sum of every row, column and diagonal equal of 3x3 matrix

Given 9 elements in a 3 x 3 matrix where the value of diagonals are 0. We need to find the values in diagonal to make the sum of every row, column and diagonal equal.

Examples:

Input: 
0 3 6 
5 0 5
4 7 0
Output: 
6 3 6
5 5 5
4 7 4
Explanation: 
    Now the value of the sum of 
    any row or column is 15

Input: 
0 4 4
4 0 4
4 4 0
Output: 
4 4 4
4 4 4
4 4 4

Approach:

Let’s say the diagonal is x, y and z.
The value of x will be ( x_{2, 3} + x_{3, 2} ) / 2.
The value of z will be ( x_{1, 2} + x_{2, 1} ) / 2.
The value of y will be ( x + z ) / 2.

Below is the implementation of the above approach:

Program:

C++

// C++ program to implement 
// the above problem 
  
#include <bits/stdc++.h> 
using namespace std; 
  
// Function to print the matrix 
void print(int arr[3][3]) 
{ 
    int i = 0, j = 0; 
  
    for (i = 0; i < 3; i++) { 
        for (j = 0; j < 3; j++) 
            cout << arr[i][j] << " "; 
        cout << endl; 
    } 
} 
  
// Function to find the diagonal values 
void find(int arr[3][3]) 
{ 
    arr[0][0] = (arr[1][2] + arr[2][1]) / 2; 
    arr[2][2] = (arr[0][1] + arr[1][0]) / 2; 
    arr[1][1] = (arr[0][0] + arr[1][1]) / 2; 
  
    // Print the new matrix with diagonals 
    cout << "Matrix with diagonals:\n"; 
    print(arr); 
} 
  
// Driver code 
int main() 
{ 
    // Initialize all the elements of a matrix 
    int arr[3][3] = { { 0, 54, 48 }, 
                      { 36, 0, 78 }, 
                      { 66, 60, 0 } }; 
  
    cout << "Matrix initially:\n"; 
    print(arr); 
  
    find(arr); 
  
    return 0; 
} 

Java

// Java program to implement  
// the above problem  
class GFG 
{ 
  
// Function to print the matrix  
static void print(int arr[][])  
{  
    int i = 0, j = 0;  
  
    for (i = 0; i < 3; i++) 
    {  
        for (j = 0; j < 3; j++)  
            System.out.print( arr[i][j] + " ");  
        System.out.println(); 
    }  
}  
  
// Function to find the diagonal values  
static void find(int arr[][])  
{  
    arr[0][0] = (arr[1][2] + arr[2][1]) / 2;  
    arr[2][2] = (arr[0][1] + arr[1][0]) / 2;  
    arr[1][1] = (arr[0][0] + arr[1][1]) / 2;  
  
    // Print the new matrix with diagonals  
    System.out.print( "Matrix with diagonals:\n");  
    print(arr);  
}  
  
// Driver code  
public static void main(String args[]) 
{  
    // Initialize all the elements of a matrix  
    int arr[][] = { { 0, 54, 48 },  
                    { 36, 0, 78 },  
                    { 66, 60, 0 } };  
  
    System.out.print( "Matrix initially:\n");  
    print(arr);  
  
    find(arr);  
}  
} 
  
// This code is contributed by Arnab Kundu 

Python3

# Python3 program to implement 
# the above problem 
  
# Function to print the matrix 
def print_(arr, n): 
    for i in range(n): 
        for j in range(n): 
            print(arr[i][j], end = " ") 
        print("\n", end= "") 
  
# Function to find the diagonal values 
def find(arr, n): 
    arr[0][0] = (arr[1][2] + arr[2][1]) // 2
    arr[2][2] = (arr[0][1] + arr[1][0]) // 2
    arr[1][1] = (arr[0][0] + arr[1][1]) // 2
    print("\nMatrix with diagonals:") 
    print_(arr, n) 
  
# Driver code 
arr = [[0, 54, 48], 
       [36, 0, 78], 
       [66, 60, 0]] 
  
n = 3
print("Matrix initally:") 
print_(arr, n) 
find(arr, n) 
  
# This code is contributed by Shrikant13 

C#

// C# program to implement  
// the above problem  
using System; 
  
class GFG  
{  
  
    // Function to print the matrix  
    static void print(int [,]arr)  
    {  
        int i = 0, j = 0;  
      
        for (i = 0; i < 3; i++)  
        {  
            for (j = 0; j < 3; j++)  
                Console.Write( arr[i, j] + " ");  
                  
            Console.WriteLine();  
        }  
    }  
      
    // Function to find the diagonal values  
    static void find(int [,]arr)  
    {  
        arr[0, 0] = (arr[1, 2] + arr[2, 1]) / 2;  
        arr[2, 2] = (arr[0, 1] + arr[1, 0]) / 2;  
        arr[1, 1] = (arr[0, 0] + arr[1, 1]) / 2;  
      
        // Print the new matrix with diagonals  
        Console.Write( "Matrix with diagonals:\n");  
        print(arr);  
    }  
      
    // Driver code  
    public static void Main()  
    {  
        // Initialize all the elements of a matrix  
        int [,]arr = { { 0, 54, 48 },  
                        { 36, 0, 78 },  
                        { 66, 60, 0 } };  
      
        Console.Write( "Matrix initially:\n");  
        print(arr);  
      
        find(arr);  
    }  
}  
  
// This code is contributed by Ryuga 

PHP

<?php 
// PHP program to implement 
// the above problem Function 
// to print the matrix 
function printt( $arr) 
{ 
    $i = 0; 
    $j = 0; 
  
    for ($i = 0; $i < 3; $i++)  
    { 
        for ($j = 0; $j < 3; $j++) 
            echo $arr[$i][$j], " "; 
        echo "\n"; 
    } 
} 
  
// Function to find the diagonal values 
function find( $arr) 
{ 
    $arr[0][0] = ($arr[1][2] + $arr[2][1]) / 2; 
    $arr[2][2] = ($arr[0][1] + $arr[1][0]) / 2; 
    $arr[1][1] = ($arr[0][0] + $arr[1][1]) / 2; 
  
    // Print the new matrix with diagonals 
    echo "Matrix with diagonals:\n"; 
    printt($arr); 
} 
  
// Driver code 
  
// Initialize all the elements of a matrix 
$arr =array(array( 0, 54, 48 ), 
        array( 36, 0, 78 ), 
        array( 66, 60, 0 )); 
  
echo "Matrix initially:\n"; 
printt($arr); 
  
find($arr); 
  
#This Code is contributed by ajit.. 
?> 

Output:

Matrix initially:
0 54 48 
36 0 78 
66 60 0 

Matrix with diagonals:
69 54 48 
36 34 78 
66 60 45

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My Personal Notes

Filling diagonal to make the sum of every row, column and diagonal equal of 3×3 matrix

C++

Java

Python3

C#

PHP

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