A Boolean Matrix Question - GeeksforGeeks

25 Feb, 2022
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
 
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++
Java
Python3
C#
PHP
Javascript
// 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 Codeint 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 Code For A Boolean Matrix Questionclass 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 Initially");                                 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 Code For A Boolean Matrix QuestionR = 3C = 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 matrixdef printMatrix(mat) :    for i in range(0, R):                 for j in range(0, C) :            print(mat[i][j], end = " ")        print()         # Driver Codemat = [ [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# Code For A Boolean// Matrix Questionusing 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 Initially");                 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 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?>
<script> // Javascript Code For A Boolean Matrix Question         function modifyMatrix(mat,R,C)    {        let row=new Array(R);        let col = new Array(C);                 /* 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,R,C)    {        let i, j;        for (i = 0; i < R; i++)        {            for (j = 0; j < C; j++)            {                document.write(mat[i][j]+ " ");            }            document.write("<br>");        }    }         /* Driver program to test above functions */         let mat = [[1, 0, 0, 1],[0, 0, 1, 0],[0, 0, 0, 0]];    document.write("Matrix Initially <br>")    printMatrix(mat, 3, 4);    modifyMatrix(mat, 3, 4);    document.write("Matrix after modification n <br>");    printMatrix(mat, 3, 4);         // This code is contributed by avanitrachhadiya2155     </script>
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++
Java
Python3
C#
PHP
Javascript
#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 functionint 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
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 Code For A Boolean Matrix Questiondef 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 matrixdef printMatrix(mat) :         for i in range(0, len(mat)) :        for j in range(0, len(mat) + 1) :            print( mat[i][j], end = "" )                 print()         # Driver Codemat = [ [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# Code For A Boolean// Matrix Questionusing 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 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 functionto 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?>
<script> function modifyMatrix(mat){    // variables to check if there are any 1        // in first row and column        let row_flag = false;        let col_flag = false;                          // updating the first row and col if 1        // is encountered        for (let i = 0; i < mat.length; i++ ){                for (let 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 (let i = 1; i < mat.length; i ++){                for (let 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 (let i = 0; i < mat[0].length; i++){                        mat[0][i] = 1;                    }                }                          // modify first col if there was any 1        if (col_flag == true){            for (let i = 0; i < mat.length; i ++){                        mat[i][0] = 1;            }        }} /* A utility function to print a 2D matrix */function printMatrix(mat){    for (let i = 0; i < mat.length; i ++){            for (let j = 0; j < mat[0].length; j ++){                document.write( mat[i][j] );            }                document.write("<br>");        }} // Driver function to test the above functionlet mat=[[1, 0, 0, 1],                [0, 0, 1, 0],                [0, 0, 0, 0]];document.write("Input Matrix :<br>");printMatrix(mat); modifyMatrix(mat); document.write("Matrix After Modification :<br>");printMatrix(mat); // This code is contributed by ab2127 </script>
Output:  
Input Matrix :
1001
0010
0000
Matrix After Modification :
1111
1111
1011
 
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