Given a 3X3 matrix mat with it’s left diagonal elements missing (set to 0), considering the sum of every row, column and diagonal of the original matrix was equal, the task is to find the missing diagonal elements and print the original matrix.
Examples:
Input: mat[][] = {{0, 7, 6}, {9, 0, 1}, {4, 3, 0}}
Output:
2 7 6
9 5 1
4 3 8
Row sum = Column sum = Diagonal sum = 15Input: mat[][] = {{0, 1, 1}, {1, 0, 1}, {1, 1, 0}}
Output:
1 1 1
1 1 1
1 1 1
Approach: Let Sum denote the total sum excluding the diagonal elements,
Sum = total sum of the given matrix – diagonalSum
Sum = (3 * rowSum) – diagonalSum
Sum = (2 * rowSum) [Since, columnSum = rowSum = diagonalSum]
rowSum = Sum / 2
Hence, we can insert an element in every row such that the sum of the row is rowSum
Below is the implementation of the above approach:
C++
// C++ program to fill blanks with numbers#include <bits/stdc++.h>using namespace std;// Function to print the original matrixint printFilledDiagonal(int sq[][3]){ // Calculate the sum of all the elements // of the matrix int sum = 0; for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) sum += sq[i][j]; // Required sum of each row (from the approach) sum /= 2; for (int i = 0; i < 3; i++) { // Row sum excluding the diagonal element int rowSum = 0; for (int j = 0; j < 3; j++) rowSum += sq[i][j]; // Element that must be inserted at // diagonal element of the current row sq[i][i] = sum - rowSum; } // Print the updated matrix for (int i = 0; i < 3; i++) { for (int j = 0; j < 3; j++) cout << sq[i][j] << " "; cout << endl; }}// Driver Program to test above functionint main(){ int sq[3][3] = { { 0, 7, 6 }, { 9, 0, 1 }, { 4, 3, 0 } }; printFilledDiagonal(sq); return 0;} |
Java
// Java program to fill blanks with numbersimport java.io.*;class GFG { // Function to print the original matrixstatic int printFilledDiagonal(int sq[][]){ // Calculate the sum of all the elements // of the matrix int sum = 0; for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) sum += sq[i][j]; // Required sum of each row (from the approach) sum /= 2; for (int i = 0; i < 3; i++) { // Row sum excluding the diagonal element int rowSum = 0; for (int j = 0; j < 3; j++) rowSum += sq[i][j]; // Element that must be inserted at // diagonal element of the current row sq[i][i] = sum - rowSum; } // Print the updated matrix for (int i = 0; i < 3; i++) { for (int j = 0; j < 3; j++) System.out.print( sq[i][j] + " "); System.out.println(); } return 0;}// Driver Program to test above function public static void main (String[] args) { int sq[][] = { { 0, 7, 6 }, { 9, 0, 1 }, { 4, 3, 0 } }; printFilledDiagonal(sq); } }// This code is contributed by anuj_67.. |
Python3
# Python3 program to fill blanks # with numbers # Function to print the original matrix def printFilledDiagonal(sq): # Calculate the sum of all the # elements of the matrix Sum = 0 for i in range(0, 3): for j in range(0, 3): Sum += sq[i][j] # Required sum of each # row (from the approach) Sum = Sum//2 for i in range(0, 3): # Row sum excluding the # diagonal element rowSum = 0 for j in range(0, 3): rowSum += sq[i][j] # Element that must be inserted # at diagonal element of the # current row sq[i][i] = Sum - rowSum # Print the updated matrix for i in range(0, 3): for j in range(0, 3): print(sq[i][j], end = " ") print()# Driver Codeif __name__ == "__main__": sq = [[0, 7, 6], [9, 0, 1], [4, 3, 0]] printFilledDiagonal(sq) # This code is contributed# by Rituraj Jain |
C#
// C# program to fill blanks with numbersusing System;class GFG { // Function to print the original matrixstatic int printFilledDiagonal(int [,]sq){ // Calculate the sum of all the elements // of the matrix int sum = 0; for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++) sum += sq[i,j]; // Required sum of each row (from the approach) sum /= 2; for (int i = 0; i < 3; i++) { // Row sum excluding the diagonal element int rowSum = 0; for (int j = 0; j < 3; j++) rowSum += sq[i,j]; // Element that must be inserted at // diagonal element of the current row sq[i,i] = sum - rowSum; } // Print the updated matrix for (int i = 0; i < 3; i++) { for (int j = 0; j < 3; j++) Console.Write( sq[i,j] + " "); Console.WriteLine(); } return 0;}// Driver Program to test above function public static void Main () { int [,]sq = { { 0, 7, 6 }, { 9, 0, 1 }, { 4, 3, 0 } }; printFilledDiagonal(sq); } }// This code is contributed by inder_verma |
PHP
<?php// PHP program to fill blanks with numbers// Function to print the original matrixfunction printFilledDiagonal($sq){ // Calculate the sum of all the // elements of the matrix $sum = 0; for ($i = 0; $i < 3; $i++) for ($j = 0; $j < 3; $j++) $sum += $sq[$i][$j]; // Required sum of each row // (from the approach) $sum = (int)($sum / 2); for ($i = 0; $i < 3; $i++) { // Row sum excluding the // diagonal element $rowSum = 0; for ($j = 0; $j < 3; $j++) $rowSum += $sq[$i][$j]; // Element that must be inserted at // diagonal element of the current row $sq[$i][$i] = $sum - $rowSum; } // Print the updated matrix for ($i = 0; $i < 3; $i++) { for ($j = 0; $j < 3; $j++) echo $sq[$i][$j] . " "; echo "\n"; }}// Driver Code$sq = array(array(0, 7, 6), array(9, 0, 1), array(4, 3, 0));printFilledDiagonal($sq);// This code is contributed // by Akanksha Rai?> |
Javascript
<script> // Javascript program to fill blanks with numbers // Function to print the original matrix function printFilledDiagonal(sq) { // Calculate the sum of all the elements // of the matrix let sum = 0; for (let i = 0; i < 3; i++) for (let j = 0; j < 3; j++) sum += sq[i][j]; // Required sum of each row (from the approach) sum /= 2; for (let i = 0; i < 3; i++) { // Row sum excluding the diagonal element let rowSum = 0; for (let j = 0; j < 3; j++) rowSum += sq[i][j]; // Element that must be inserted at // diagonal element of the current row sq[i][i] = sum - rowSum; } // Print the updated matrix for (let i = 0; i < 3; i++) { for (let j = 0; j < 3; j++) document.write(sq[i][j] + " "); document.write("</br>"); } return 0; } let sq = [ [ 0, 7, 6 ], [ 9, 0, 1 ], [ 4, 3, 0 ] ]; printFilledDiagonal(sq);</script> |
Output
2 7 6 9 5 1 4 3 8
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