A Boolean Matrix Question

Difficulty Level : Medium
Last Updated : 09 Nov, 2020

Given a boolean matrix mat[M][N] of size M X N, modify it such that if a matrix cell mat[i][j] is 1 (or true) then make all the cells of ith row and jth column as 1.

Example 1
The matrix
1 0
0 0
should be changed to following
1 1
1 0

Example 2
The matrix
0 0 0
0 0 1
should be changed to following
0 0 1
1 1 1

Example 3
The matrix
1 0 0 1
0 0 1 0
0 0 0 0
should be changed to following
1 1 1 1
1 1 1 1
1 0 1 1

Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

Method 1 (Use two temporary arrays)
1) Create two temporary arrays row[M] and col[N]. Initialize all values of row[] and col[] as 0.
2) Traverse the input matrix mat[M][N]. If you see an entry mat[i][j] as true, then mark row[i] and col[j] as true.
3) Traverse the input matrix mat[M][N] again. For each entry mat[i][j], check the values of row[i] and col[j]. If any of the two values (row[i] or col[j]) is true, then mark mat[i][j] as true.

Thanks to Dixit Sethi for suggesting this method.

C++

// C++ Code For A Boolean Matrix Question 
#include <bits/stdc++.h> 
  
using namespace std; 
#define R 3 
#define C 4 
  
void modifyMatrix(bool mat[R][C]) 
{ 
    bool row[R]; 
    bool col[C]; 
  
    int i, j; 
      
    /* Initialize all values of row[] as 0 */
    for (i = 0; i < R; i++) 
    { 
    row[i] = 0; 
    } 
  
    /* Initialize all values of col[] as 0 */
    for (i = 0; i < C; i++) 
    { 
    col[i] = 0; 
    } 
  
    // Store the rows and columns to be marked as 
    // 1 in row[] and col[] arrays respectively 
    for (i = 0; i < R; i++) 
    { 
        for (j = 0; j < C; j++) 
        { 
            if (mat[i][j] == 1) 
            { 
                row[i] = 1; 
                col[j] = 1; 
            } 
        } 
    } 
  
    // Modify the input matrix mat[] using the  
    // above constructed row[] and col[] arrays 
    for (i = 0; i < R; i++) 
    { 
        for (j = 0; j < C; j++) 
        { 
            if ( row[i] == 1 || col[j] == 1 ) 
            { 
                mat[i][j] = 1; 
            } 
        } 
    } 
} 
  
/* A utility function to print a 2D matrix */
void printMatrix(bool mat[R][C]) 
{ 
    int i, j; 
    for (i = 0; i < R; i++) 
    { 
        for (j = 0; j < C; j++) 
        { 
            cout << mat[i][j]; 
        } 
        cout << endl; 
    } 
} 
  
// Driver Code 
int main() 
{ 
    bool mat[R][C] = { {1, 0, 0, 1}, 
                       {0, 0, 1, 0}, 
                       {0, 0, 0, 0}}; 
  
    cout << "Input Matrix \n"; 
    printMatrix(mat); 
  
    modifyMatrix(mat); 
  
    printf("Matrix after modification \n"); 
    printMatrix(mat); 
  
    return 0; 
} 
  
// This code is contributed  
// by Akanksha Rai(Abby_akku) 

Java

// Java Code For A Boolean Matrix Question 
class GFG 
{ 
    public static void modifyMatrix(int mat[ ][ ], int R, int C) 
    { 
        int row[ ]= new int [R]; 
        int col[ ]= new int [C]; 
        int i, j; 
      
        /* Initialize all values of row[] as 0 */
        for (i = 0; i < R; i++) 
        { 
        row[i] = 0; 
        } 
      
      
        /* Initialize all values of col[] as 0 */
        for (i = 0; i < C; i++) 
        { 
        col[i] = 0; 
        } 
      
      
        /* Store the rows and columns to be marked as 
        1 in row[] and col[] arrays respectively */
        for (i = 0; i < R; i++) 
        { 
            for (j = 0; j < C; j++) 
            { 
                if (mat[i][j] == 1) 
                { 
                    row[i] = 1; 
                    col[j] = 1; 
                } 
            } 
        } 
      
        /* Modify the input matrix mat[] using the 
        above constructed row[] and col[] arrays */
        for (i = 0; i < R; i++) 
        { 
            for (j = 0; j < C; j++) 
            { 
                if ( row[i] == 1 || col[j] == 1 ) 
                { 
                    mat[i][j] = 1; 
                } 
            } 
        } 
    } 
      
    /* A utility function to print a 2D matrix */
    public static void printMatrix(int mat[ ][ ], int R, int C) 
    { 
        int i, j; 
        for (i = 0; i < R; i++) 
        { 
            for (j = 0; j < C; j++) 
            { 
                System.out.print(mat[i][j]+ " "); 
            } 
            System.out.println(); 
        } 
    } 
      
    /* Driver program to test above functions */
    public static void main(String[] args)  
    { 
        int mat[ ][ ] = { {1, 0, 0, 1}, 
                          {0, 0, 1, 0}, 
                          {0, 0, 0, 0},}; 
                      
                System.out.println("Matrix Intially"); 
                  
                printMatrix(mat, 3, 4); 
              
                modifyMatrix(mat, 3, 4); 
                System.out.println("Matrix after modification n"); 
                printMatrix(mat, 3, 4); 
              
    }  
  
} 
  
// This code is contributed by Kamal Rawal 

Python3

# Python3 Code For A Boolean Matrix Question 
R = 3
C = 4
  
def modifyMatrix(mat): 
    row = [0] * R  
    col = [0] * C  
      
    # Initialize all values of row[] as 0  
    for i in range(0, R): 
        row[i] = 0
          
    # Initialize all values of col[] as 0  
    for i in range(0, C) : 
        col[i] = 0
  
  
    # Store the rows and columns to be marked  
    # as 1 in row[] and col[] arrays respectively  
    for i in range(0, R) : 
          
        for j in range(0, C) : 
            if (mat[i][j] == 1) : 
                row[i] = 1
                col[j] = 1
              
    # Modify the input matrix mat[] using the  
    # above constructed row[] and col[] arrays  
    for i in range(0, R) : 
          
        for j in range(0, C): 
            if ( row[i] == 1 or col[j] == 1 ) : 
                mat[i][j] = 1
                  
# A utility function to print a 2D matrix  
def printMatrix(mat) : 
    for i in range(0, R): 
          
        for j in range(0, C) : 
            print(mat[i][j], end = " ") 
        print() 
          
# Driver Code 
mat = [ [1, 0, 0, 1], 
        [0, 0, 1, 0], 
        [0, 0, 0, 0] ]  
  
print("Input Matrix n") 
printMatrix(mat) 
  
modifyMatrix(mat) 
  
print("Matrix after modification n") 
printMatrix(mat) 
  
# This code is contributed by Nikita Tiwari. 

C#

// C# Code For A Boolean 
// Matrix Question 
using System; 
  
class GFG 
{ 
    public static void modifyMatrix(int [,]mat,  
                                    int R, int C) 
    { 
        int []row = new int [R]; 
        int []col = new int [C]; 
        int i, j; 
      
        /* Initialize all values 
        of row[] as 0 */
        for (i = 0; i < R; i++) 
        { 
        row[i] = 0; 
        } 
      
      
        /* Initialize all values 
        of col[] as 0 */
        for (i = 0; i < C; i++) 
        { 
        col[i] = 0; 
        } 
      
      
        /* Store the rows and columns  
        to be marked as 1 in row[]  
        and col[] arrays respectively */
        for (i = 0; i < R; i++) 
        { 
            for (j = 0; j < C; j++) 
            { 
                if (mat[i, j] == 1) 
                { 
                    row[i] = 1; 
                    col[j] = 1; 
                } 
            } 
        } 
      
        /* Modify the input matrix  
        mat[] using the above  
        constructed row[] and  
        col[] arrays */
        for (i = 0; i < R; i++) 
        { 
            for (j = 0; j < C; j++) 
            { 
                if (row[i] == 1 || col[j] == 1) 
                { 
                    mat[i, j] = 1; 
                } 
            } 
        } 
    } 
      
    /* A utility function to 
    print a 2D matrix */
    public static void printMatrix(int [,]mat,  
                                   int R, int C) 
    { 
        int i, j; 
        for (i = 0; i < R; i++) 
        { 
            for (j = 0; j < C; j++) 
            { 
                Console.Write(mat[i, j] + " "); 
            } 
            Console.WriteLine(); 
        } 
    } 
      
    // Driver code 
    static public void Main () 
    { 
        int [,]mat = {{1, 0, 0, 1}, 
                      {0, 0, 1, 0}, 
                      {0, 0, 0, 0}}; 
              
        Console.WriteLine("Matrix Intially"); 
          
        printMatrix(mat, 3, 4); 
      
        modifyMatrix(mat, 3, 4); 
        Console.WriteLine("Matrix after "+ 
                        "modification n"); 
        printMatrix(mat, 3, 4); 
          
    } 
} 
  
// This code is contributed by ajit 

PHP

<?php  
// PHP Code For A Boolean 
// Matrix Question 
$R = 3; 
$C = 4; 
  
function modifyMatrix(&$mat) 
{ 
    global $R,$C; 
    $row = array(); 
    $col = array(); 
  
    /* Initialize all values  
       of row[] as 0 */
    for ($i = 0; $i < $R; $i++) 
    { 
        $row[$i] = 0; 
    } 
  
  
    /* Initialize all values  
       of col[] as 0 */
    for ($i = 0; $i < $C; $i++) 
    { 
        $col[$i] = 0; 
    } 
  
  
    /* Store the rows and columns  
       to be marked as 1 in row[]  
       and col[] arrays respectively */
    for ($i = 0; $i < $R; $i++) 
    { 
        for ($j = 0; $j < $C; $j++) 
        { 
            if ($mat[$i][$j] == 1) 
            { 
                $row[$i] = 1; 
                $col[$j] = 1; 
            } 
        } 
    } 
  
    /* Modify the input matrix mat[] 
       using the above constructed  
       row[] and col[] arrays */
    for ($i = 0; $i < $R; $i++) 
    { 
        for ($j = 0; $j < $C; $j++) 
        { 
            if ($row[$i] == 1 ||  
                $col[$j] == 1 ) 
            { 
                $mat[$i][$j] = 1; 
            } 
        } 
    } 
} 
  
/* A utility function to 
   print a 2D matrix */
function printMatrix(&$mat) 
{ 
    global $R, $C; 
    for ($i = 0; $i < $R; $i++) 
    { 
        for ($j = 0; $j < $C; $j++) 
        { 
            echo $mat[$i][$j] . " "; 
        } 
        echo "\n"; 
    } 
} 
  
// Driver code  
$mat = array(array(1, 0, 0, 1), 
             array(0, 0, 1, 0), 
             array(0, 0, 0, 0)); 
  
echo "Input Matrix \n"; 
printMatrix($mat); 
  
modifyMatrix($mat); 
  
echo "Matrix after modification \n"; 
printMatrix($mat); 
  
// This code is contributed  
// by ChitraNayal 
?> 

Output:

Input Matrix
1 0 0 1
0 0 1 0
0 0 0 0
Matrix after modification
1 1 1 1
1 1 1 1
1 0 1 1

Time Complexity: O(M*N)
Auxiliary Space: O(M + N)

Method 2 (A Space Optimized Version of Method 1)
This method is a space optimized version of above method 1. This method uses the first row and first column of the input matrix in place of the auxiliary arrays row[] and col[] of method 1. So what we do is: first take care of first row and column and store the info about these two in two flag variables rowFlag and colFlag. Once we have this info, we can use first row and first column as auxiliary arrays and apply method 1 for submatrix (matrix excluding first row and first column) of size (M-1)*(N-1).

1) Scan the first row and set a variable rowFlag to indicate whether we need to set all 1s in first row or not.
2) Scan the first column and set a variable colFlag to indicate whether we need to set all 1s in first column or not.
3) Use first row and first column as the auxiliary arrays row[] and col[] respectively, consider the matrix as submatrix starting from second row and second column and apply method 1.
4) Finally, using rowFlag and colFlag, update first row and first column if needed.

Time Complexity: O(M*N)
Auxiliary Space: O(1)

Thanks to Sidh for suggesting this method.

C++

#include <bits/stdc++.h> 
using namespace std; 
#define R 3 
#define C 4 
  
void modifyMatrix(int mat[R][C]) 
{ 
    // variables to check if there are any 1 
    // in first row and column 
    bool row_flag = false; 
    bool col_flag = false; 
  
    // updating the first row and col if 1 
    // is encountered 
    for (int i = 0; i < R; i++) { 
        for (int j = 0; j < C; j++) { 
            if (i == 0 && mat[i][j] == 1) 
                row_flag = true; 
  
            if (j == 0 && mat[i][j] == 1) 
                col_flag = true; 
  
            if (mat[i][j] == 1) { 
  
                mat[0][j] = 1; 
                mat[i][0] = 1; 
            } 
        } 
    } 
  
    // Modify the input matrix mat[] using the 
    // first row and first column of Matrix mat 
    for (int i = 1; i < R; i++) { 
        for (int j = 1; j < C; j++) { 
  
            if (mat[0][j] == 1 || mat[i][0] == 1) { 
                mat[i][j] = 1; 
            } 
        } 
    } 
  
    // modify first row if there was any 1 
    if (row_flag == true) { 
        for (int i = 0; i < C; i++) { 
            mat[0][i] = 1; 
        } 
    } 
  
    // modify first col if there was any 1 
    if (col_flag == true) { 
        for (int i = 0; i < R; i++) { 
            mat[i][0] = 1; 
        } 
    } 
} 
  
/* A utility function to print a 2D matrix */
void printMatrix(int mat[R][C]) 
{ 
    for (int i = 0; i < R; i++) { 
        for (int j = 0; j < C; j++) { 
            cout << mat[i][j]; 
        } 
        cout << "\n"; 
    } 
} 
  
// Driver function to test the above function 
int main() 
{ 
  
    int mat[R][C] = { { 1, 0, 0, 1 }, 
                      { 0, 0, 1, 0 }, 
                      { 0, 0, 0, 0 } }; 
  
    cout << "Input Matrix :\n"; 
    printMatrix(mat); 
  
    modifyMatrix(mat); 
  
    cout << "Matrix After Modification :\n"; 
    printMatrix(mat); 
    return 0; 
} 
  
// This code is contributed by Nikita Tiwari 

Java

class GFG 
{  
    public static void modifyMatrix(int mat[][]){ 
                  
        // variables to check if there are any 1  
        // in first row and column 
        boolean row_flag = false; 
        boolean col_flag = false; 
                  
        // updating the first row and col if 1 
        // is encountered 
        for (int i = 0; i < mat.length; i++ ){ 
                for (int j = 0; j < mat[0].length; j++){ 
                        if (i == 0 && mat[i][j] == 1) 
                            row_flag = true; 
                          
                        if (j == 0 && mat[i][j] == 1) 
                            col_flag = true; 
                          
                        if (mat[i][j] == 1){ 
                              
                            mat[0][j] = 1; 
                            mat[i][0] = 1; 
                        } 
                          
                    } 
                } 
                  
        // Modify the input matrix mat[] using the  
        // first row and first column of Matrix mat 
        for (int i = 1; i < mat.length; i ++){ 
                for (int j = 1; j < mat[0].length; j ++){ 
                          
                    if (mat[0][j] == 1 || mat[i][0] == 1){ 
                            mat[i][j] = 1; 
                        } 
                    } 
                } 
                  
        // modify first row if there was any 1 
        if (row_flag == true){ 
            for (int i = 0; i < mat[0].length; i++){ 
                        mat[0][i] = 1; 
                    } 
                } 
                  
        // modify first col if there was any 1 
        if (col_flag == true){ 
            for (int i = 0; i < mat.length; i ++){ 
                        mat[i][0] = 1; 
            } 
        } 
    } 
              
    /* A utility function to print a 2D matrix */
    public static void printMatrix(int mat[][]){ 
        for (int i = 0; i < mat.length; i ++){ 
            for (int j = 0; j < mat[0].length; j ++){ 
                System.out.print( mat[i][j] ); 
            } 
                System.out.println(""); 
        } 
    } 
              
    // Driver function to test the above function 
    public static void main(String args[] ){ 
                  
        int mat[][] = {{1, 0, 0, 1}, 
                {0, 0, 1, 0}, 
                {0, 0, 0, 0}}; 
                  
        System.out.println("Input Matrix :"); 
        printMatrix(mat); 
              
        modifyMatrix(mat); 
              
        System.out.println("Matrix After Modification :"); 
        printMatrix(mat); 
              
    } 
} 
  
// This code is contributed by Arnav Kr. Mandal. 

Python3

# Python3 Code For A Boolean Matrix Question 
def modifyMatrix(mat) : 
      
    # variables to check if there are any 1  
    # in first row and column 
    row_flag = False
    col_flag = False
              
    # updating the first row and col  
    # if 1 is encountered 
    for i in range(0, len(mat)) : 
          
        for j in range(0, len(mat)) : 
            if (i == 0 and mat[i][j] == 1) : 
                row_flag = True
                      
            if (j == 0 and mat[i][j] == 1) : 
                col_flag = True
              
            if (mat[i][j] == 1) : 
                mat[0][j] = 1
                mat[i][0] = 1
                  
    # Modify the input matrix mat[] using the  
    # first row and first column of Matrix mat 
    for i in range(1, len(mat)) : 
          
        for j in range(1, len(mat) + 1) : 
            if (mat[0][j] == 1 or mat[i][0] == 1) : 
                mat[i][j] = 1
                  
    # modify first row if there was any 1 
    if (row_flag == True) : 
        for i in range(0, len(mat)) : 
            mat[0][i] = 1
              
    # modify first col if there was any 1 
    if (col_flag == True) : 
        for i in range(0, len(mat)) : 
            mat[i][0] = 1
              
# A utility function to print a 2D matrix 
def printMatrix(mat) : 
      
    for i in range(0, len(mat)) : 
        for j in range(0, len(mat) + 1) : 
            print( mat[i][j], end = "" ) 
          
        print() 
          
# Driver Code 
mat = [ [1, 0, 0, 1], 
        [0, 0, 1, 0], 
        [0, 0, 0, 0] ] 
          
print("Input Matrix :") 
printMatrix(mat) 
      
modifyMatrix(mat) 
      
print("Matrix After Modification :") 
printMatrix(mat) 
  
# This code is contributed by Nikita tiwari. 

C#

// C# Code For A Boolean 
// Matrix Question 
using System; 
  
class GFG 
{  
    public static void modifyMatrix(int[,] mat) 
    { 
                  
        // variables to check  
        // if there are any 1  
        // in first row and column 
        bool row_flag = false; 
        bool col_flag = false; 
                  
        // updating the first 
        // row and col if 1 
        // is encountered 
        for (int i = 0; 
                 i < mat.GetLength(0); i++ ) 
        { 
                for (int j = 0;  
                         j < mat.GetLength(1); j++) 
                { 
                        if (i == 0 && mat[i, j] == 1) 
                            row_flag = true; 
                          
                        if (j == 0 && mat[i, j] == 1) 
                            col_flag = true; 
                          
                        if (mat[i, j] == 1) 
                        { 
                            mat[0, j] = 1; 
                            mat[i,0] = 1; 
                        } 
                          
                    } 
                } 
                  
        // Modify the input matrix mat[]  
        // using the first row and first 
        // column of Matrix mat 
        for (int i = 1;  
                 i < mat.GetLength(0); i ++) 
        { 
                for (int j = 1;  
                         j < mat.GetLength(1); j ++) 
                { 
                          
                    if (mat[0, j] == 1 ||  
                        mat[i, 0] == 1) 
                    { 
                            mat[i, j] = 1; 
                        } 
                    } 
                } 
                  
        // modify first row 
        // if there was any 1 
        if (row_flag == true) 
        { 
            for (int i = 0;  
                     i < mat.GetLength(1); i++) 
            { 
                        mat[0, i] = 1; 
            } 
        } 
                  
        // modify first col if 
        // there was any 1 
        if (col_flag == true) 
        { 
            for (int i = 0;  
                     i < mat.GetLength(0); i ++) 
            { 
                        mat[i, 0] = 1; 
            } 
        } 
    } 
              
    /* A utility function  
    to print a 2D matrix */
    public static void printMatrix(int[,] mat) 
    { 
        for (int i = 0;  
                 i < mat.GetLength(0); i ++) 
        { 
            for (int j = 0;  
                     j < mat.GetLength(1); j ++) 
            { 
                Console.Write(mat[i, j] + " " ); 
            } 
                Console.Write("\n"); 
        } 
    } 
              
    // Driver Code 
    public static void Main() 
    { 
        int[,] mat = {{1, 0, 0, 1}, 
                      {0, 0, 1, 0}, 
                      {0, 0, 0, 0}}; 
                  
        Console.Write("Input Matrix :\n"); 
        printMatrix(mat); 
              
        modifyMatrix(mat); 
              
        Console.Write("Matrix After " +  
                      "Modification :\n"); 
        printMatrix(mat); 
    } 
} 
  
// This code is contributed 
// by ChitraNayal 

PHP

<?php  
// PHP Code For A Boolean 
// Matrix Question 
$R = 3; 
$C = 4; 
  
function modifyMatrix(&$mat) 
{ 
    global $R, $C; 
      
    // variables to check if  
    // there are any 1 in  
    // first row and column 
    $row_flag = false; 
    $col_flag = false; 
  
    // updating the first  
    // row and col if 1 
    // is encountered 
    for ($i = 0; $i < $R; $i++)  
    { 
        for ($j = 0; $j < $C; $j++)  
        { 
            if ($i == 0 && $mat[$i][$j] == 1) 
                $row_flag = true; 
  
            if ($j == 0 && $mat[$i][$j] == 1) 
                $col_flag = true; 
  
            if ($mat[$i][$j] == 1)  
            { 
                $mat[0][$j] = 1; 
                $mat[$i][0] = 1; 
            } 
        } 
    } 
  
    // Modify the input matrix  
    // mat[] using the first  
    // row and first column of  
    // Matrix mat 
    for ($i = 1; $i < $R; $i++)  
    { 
        for ($j = 1; $j < $C; $j++) 
        { 
            if ($mat[0][$j] == 1 ||  
                $mat[$i][0] == 1) 
            { 
                $mat[$i][$j] = 1; 
            } 
        } 
    } 
  
    // modify first row  
    // if there was any 1 
    if ($row_flag == true)  
    { 
        for ($i = 0; $i < $C; $i++) 
        { 
            $mat[0][$i] = 1; 
        } 
    } 
  
    // modify first col  
    // if there was any 1 
    if ($col_flag == true)  
    { 
        for ($i = 0; $i < $R; $i++) 
        { 
            $mat[$i][0] = 1; 
        } 
    } 
} 
  
/* A utility function 
to print a 2D matrix */
function printMatrix(&$mat) 
{ 
    global $R, $C; 
    for ($i = 0; $i < $R; $i++)  
    { 
        for ($j = 0; $j < $C; $j++) 
        { 
            echo $mat[$i][$j]." "; 
        } 
        echo "\n"; 
    } 
} 
  
// Driver Code 
$mat = array(array(1, 0, 0, 1 ), 
             array(0, 0, 1, 0 ), 
             array(0, 0, 0, 0 )); 
  
echo "Input Matrix :\n"; 
printMatrix($mat); 
  
modifyMatrix($mat); 
  
echo "Matrix After Modification :\n"; 
printMatrix($mat); 
  
// This code is conrtributed  
// by ChitraNayal 
?> 

Output:

Input Matrix :
1001
0010
0000
Matrix After Modification :
1111
1111
1011

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