# A Boolean Matrix Question

Last Updated : 22 Aug, 2023

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.

Examples:

Input: {{1, 0},
{0, 0}}
Output: {{1, 1}
{1, 0}}
Input: {{0, 0, 0},
{0, 0, 1}}
Output: {{0, 0, 1},
{1, 1, 1}}

Input: {{1, 0, 0, 1},
{0, 0, 1, 0},
{0, 0, 0, 0}}
Output: {{1, 1, 1, 1},
{1, 1, 1, 1},
{1, 0, 1, 1}}

Recommended Practice

### A Boolean Matrix Question using Brute Force:

Approach: Using brute force

Assuming all the elements in the matrix are non-negative. Traverse through the matrix and if you find an element with value 1, then change all the elements in its row and column to -1, except when an element is 1. The reason for not changing other elements to 1, but -1, is because that might affect other columns and rows. Now traverse through the matrix again and if an element is -1 change it to 1, which will be the answer.

## C++

 `#include`   `using` `namespace` `std;`   `void` `setZeroes(vector < vector < ``int` `>> & matrix) {` `  ``int` `rows = matrix.size(), cols = matrix[0].size();` `  ``for` `(``int` `i = 0; i < rows; i++) {` `    ``for` `(``int` `j = 0; j < cols; j++) {` `      ``if` `(matrix[i][j] == 1) {`   `        ``int` `ind = i - 1;` `        ``while` `(ind >= 0) {` `          ``if` `(matrix[ind][j] != 1) {` `            ``matrix[ind][j] = -1;` `          ``}` `          ``ind--;` `        ``}` `        ``ind = i + 1;` `        ``while` `(ind < rows) {` `          ``if` `(matrix[ind][j] != 1) {` `            ``matrix[ind][j] = -1;` `          ``}` `          ``ind++;` `        ``}` `        ``ind = j - 1;` `        ``while` `(ind >= 0) {` `          ``if` `(matrix[i][ind] != 1) {` `            ``matrix[i][ind] = -1;`   `          ``}` `          ``ind--;` `        ``}` `        ``ind = j + 1;` `        ``while` `(ind < cols) {` `          ``if` `(matrix[i][ind] != 1) {` `            ``matrix[i][ind] = -1;`   `          ``}` `          ``ind++;` `        ``}` `      ``}` `    ``}` `  ``}` `  ``for` `(``int` `i = 0; i < rows; i++) {` `    ``for` `(``int` `j = 0; j < cols; j++) {` `      ``if` `(matrix[i][j] < 0) {` `        ``matrix[i][j] = 1;` `      ``}` `    ``}` `  ``}`   `}`   `int` `main() {` `  ``vector < vector < ``int` `>> arr;` `  ``arr = {{1, 0, 2, 1}, {3, 4, 5, 2}, {0, 3, 0, 5}};` `  ``setZeroes(arr);` `  ``cout << ``"The Final Matrix is "` `<< endl;` `  ``for` `(``int` `i = 0; i < arr.size(); i++) {` `    ``for` `(``int` `j = 0; j < arr[0].size(); j++) {` `      ``cout << arr[i][j] << ``" "``;` `    ``}` `    ``cout << ``"\n"``;` `  ``}` `}`

## Java

 `import` `java.util.*;`   `class` `Main {`   `    ``// Given an m x n matrix, if an element is 0, set its` `    ``// entire row and column to 0.` `    ``static` `void` `setZeroes(``int``[][] matrix)` `    ``{`   `        ``int` `rows = matrix.length;` `        ``int` `cols = matrix[``0``].length;`   `        ``// Iterate through each element of the matrix` `        ``for` `(``int` `i = ``0``; i < rows; i++) {` `            ``for` `(``int` `j = ``0``; j < cols; j++) {`   `                ``// If the element is 1, mark its` `                ``// corresponding row and column using -1` `                ``if` `(matrix[i][j] == ``1``) {`   `                    ``// Mark all elements in the same column` `                    ``// as -1, except for other 1's` `                    ``int` `ind = i - ``1``;` `                    ``while` `(ind >= ``0``) {` `                        ``if` `(matrix[ind][j] != ``1``) {` `                            ``matrix[ind][j] = -``1``;` `                        ``}` `                        ``ind--;` `                    ``}` `                    ``ind = i + ``1``;` `                    ``while` `(ind < rows) {` `                        ``if` `(matrix[ind][j] != ``1``) {` `                            ``matrix[ind][j] = -``1``;` `                        ``}` `                        ``ind++;` `                    ``}`   `                    ``// Mark all elements in the same row as` `                    ``// -1, except for other 1's` `                    ``ind = j - ``1``;` `                    ``while` `(ind >= ``0``) {` `                        ``if` `(matrix[i][ind] != ``1``) {` `                            ``matrix[i][ind] = -``1``;` `                        ``}` `                        ``ind--;` `                    ``}` `                    ``ind = j + ``1``;` `                    ``while` `(ind < cols) {` `                        ``if` `(matrix[i][ind] != ``1``) {` `                            ``matrix[i][ind] = -``1``;` `                        ``}` `                        ``ind++;` `                    ``}` `                ``}` `            ``}` `        ``}`   `        ``// Iterate through the matrix again, setting all` `        ``// -1's to 0` `        ``for` `(``int` `i = ``0``; i < rows; i++) {` `            ``for` `(``int` `j = ``0``; j < cols; j++) {` `                ``if` `(matrix[i][j] < ``0``) {` `                    ``matrix[i][j] = ``1``;` `                ``}` `            ``}` `        ``}` `    ``}`   `    ``// Test the setZeroes function with a sample input` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``int``[][] arr = { { ``1``, ``0``, ``2``, ``1` `},` `                        ``{ ``3``, ``4``, ``5``, ``2` `},` `                        ``{ ``0``, ``3``, ``0``, ``5` `} };` `        ``setZeroes(arr);` `        ``System.out.println(``"The Final Matrix is:"``);` `        ``for` `(``int` `i = ``0``; i < arr.length; i++) {` `            ``for` `(``int` `j = ``0``; j < arr[``0``].length; j++) {` `                ``System.out.print(arr[i][j] + ``" "``);` `            ``}` `            ``System.out.println();` `        ``}` `    ``}` `}`

## Python3

 `# Python equivalent of above code `   `# define a function to set the zeroes in the matrix` `def` `setZeroes(matrix):` `    ``# get the length of the matrix` `    ``rows ``=` `len``(matrix)` `    ``cols ``=` `len``(matrix[``0``])`   `    ``# Iterate through each element of the matrix` `    ``for` `i ``in` `range``(``0``, rows):` `        ``for` `j ``in` `range``(``0``, cols):`   `            ``# If the element is 1, mark its` `            ``# corresponding row and column using -1` `            ``if` `matrix[i][j] ``=``=` `1``:`   `                ``# Mark all elements in the same column` `                ``# as -1, except for other 1's` `                ``ind ``=` `i ``-` `1` `                ``while` `ind >``=` `0``:` `                    ``if` `matrix[ind][j] !``=` `1``:` `                        ``matrix[ind][j] ``=` `-``1` `                    ``ind ``-``=` `1`   `                ``ind ``=` `i ``+` `1` `                ``while` `ind < rows:` `                    ``if` `matrix[ind][j] !``=` `1``:` `                        ``matrix[ind][j] ``=` `-``1` `                    ``ind ``+``=` `1`   `                ``# Mark all elements in the same row as` `                ``# -1, except for other 1's` `                ``ind ``=` `j ``-` `1` `                ``while` `ind >``=` `0``:` `                    ``if` `matrix[i][ind] !``=` `1``:` `                        ``matrix[i][ind] ``=` `-``1` `                    ``ind ``-``=` `1`   `                ``ind ``=` `j ``+` `1` `                ``while` `ind < cols:` `                    ``if` `matrix[i][ind] !``=` `1``:` `                        ``matrix[i][ind] ``=` `-``1` `                    ``ind ``+``=` `1`   `    ``# Iterate through the matrix again, setting all` `    ``# -1's to 0` `    ``for` `i ``in` `range``(``0``, rows):` `        ``for` `j ``in` `range``(``0``, cols):` `            ``if` `matrix[i][j] < ``0``:` `                ``matrix[i][j] ``=` `1`   `# Test the setZeroes function with a sample input` `if` `__name__ ``=``=` `"__main__"``:` `    ``arr ``=` `[[``1``, ``0``, ``2``, ``1``],` `           ``[``3``, ``4``, ``5``, ``2``],` `           ``[``0``, ``3``, ``0``, ``5``]]` `    ``setZeroes(arr)` `    ``print``(``"The Final Matrix is:"``)` `    ``for` `i ``in` `range``(``len``(arr)):` `        ``for` `j ``in` `range``(``len``(arr[``0``])):` `            ``print``(arr[i][j], end``=``" "``)` `        ``print``()`

## C#

 `using` `System;` `using` `System.Collections.Generic;`   `class` `Program {`   `    ``// Given an m x n matrix, if an element is 0, set its` `    ``// entire row and column to 0.` `    ``static` `void` `SetZeroes(List > matrix)` `    ``{` `        ``int` `rows = matrix.Count, cols = matrix[0].Count;`   `        ``// Iterate through each element of the matrix` `        ``for` `(``int` `i = 0; i < rows; i++) {` `            ``for` `(``int` `j = 0; j < cols; j++) {`   `                ``// If the element is 1, mark its` `                ``// corresponding row and column using -1` `                ``if` `(matrix[i][j] == 1) {`   `                    ``// Mark all elements in the same column` `                    ``// as -1, except for other 1's` `                    ``int` `ind = i - 1;` `                    ``while` `(ind >= 0) {` `                        ``if` `(matrix[ind][j] != 1) {` `                            ``matrix[ind][j] = -1;` `                        ``}` `                        ``ind--;` `                    ``}` `                    ``ind = i + 1;` `                    ``while` `(ind < rows) {` `                        ``if` `(matrix[ind][j] != 1) {` `                            ``matrix[ind][j] = -1;` `                        ``}` `                        ``ind++;` `                    ``}`   `                    ``// Mark all elements in the same row as` `                    ``// -1, except for other 1's` `                    ``ind = j - 1;` `                    ``while` `(ind >= 0) {` `                        ``if` `(matrix[i][ind] != 1) {` `                            ``matrix[i][ind] = -1;` `                        ``}` `                        ``ind--;` `                    ``}` `                    ``ind = j + 1;` `                    ``while` `(ind < cols) {` `                        ``if` `(matrix[i][ind] != 1) {` `                            ``matrix[i][ind] = -1;` `                        ``}` `                        ``ind++;` `                    ``}` `                ``}` `            ``}` `        ``}`   `        ``// Iterate through the matrix again, setting all` `        ``// -1's to 0` `        ``for` `(``int` `i = 0; i < rows; i++) {` `            ``for` `(``int` `j = 0; j < cols; j++) {` `                ``if` `(matrix[i][j] < 0) {` `                    ``matrix[i][j] = 1;` `                ``}` `            ``}` `        ``}` `    ``}`   `    ``// Test the setZeroes function with a sample input` `    ``static` `void` `Main(``string``[] args)` `    ``{` `        ``List > arr = ``new` `List >{` `            ``new` `List<``int``>{ 1, 0, 2, 1 },` `            ``new` `List<``int``>{ 3, 4, 5, 2 },` `            ``new` `List<``int``>{ 0, 3, 0, 5 }` `        ``};` `        ``SetZeroes(arr);` `        ``Console.WriteLine(``"The Final Matrix is "``);` `        ``for` `(``int` `i = 0; i < arr.Count; i++) {` `            ``for` `(``int` `j = 0; j < arr[0].Count; j++) {` `                ``Console.Write(arr[i][j] + ``" "``);` `            ``}` `            ``Console.WriteLine();` `        ``}` `    ``}` `}`

## Javascript

 `function` `setZeroes(matrix) {` `  ``const rows = matrix.length;` `  ``const cols = matrix[0].length;`   `  ``for` `(let i = 0; i < rows; i++) {` `    ``for` `(let j = 0; j < cols; j++) {` `      ``if` `(matrix[i][j] === 1) {` `        ``let ind = i - 1;` `        ``while` `(ind >= 0) {` `          ``if` `(matrix[ind][j] !== 1) {` `            ``matrix[ind][j] = -1;` `          ``}` `          ``ind--;` `        ``}`   `        ``ind = i + 1;` `        ``while` `(ind < rows) {` `          ``if` `(matrix[ind][j] !== 1) {` `            ``matrix[ind][j] = -1;` `          ``}` `          ``ind++;` `        ``}`   `        ``ind = j - 1;` `        ``while` `(ind >= 0) {` `          ``if` `(matrix[i][ind] !== 1) {` `            ``matrix[i][ind] = -1;` `          ``}` `          ``ind--;` `        ``}`   `        ``ind = j + 1;` `        ``while` `(ind < cols) {` `          ``if` `(matrix[i][ind] !== 1) {` `            ``matrix[i][ind] = -1;` `          ``}` `          ``ind++;` `        ``}` `      ``}` `    ``}` `  ``}`   `  ``for` `(let i = 0; i < rows; i++) {` `    ``for` `(let j = 0; j < cols; j++) {` `      ``if` `(matrix[i][j] < 0) {` `        ``matrix[i][j] = 1;` `      ``}` `    ``}` `  ``}` `}`   `function` `printMatrix(matrix) {` `  ``for` `(let i = 0; i < matrix.length; i++) {` `    ``console.log(matrix[i].join(``' '``));` `  ``}` `}`   `// Main` `const arr = [` `  ``[1, 0, 2, 1],` `  ``[3, 4, 5, 2],` `  ``[0, 3, 0, 5]` `];` `setZeroes(arr);` `console.log(``"The Final Matrix is:"``);` `printMatrix(arr);`

Output

```The Final Matrix is
1 1 1 1
1 4 5 1
1 3 0 1

```

Time Complexity:O((N*M)*(N + M)). O(N*M) for traversing through each element and (N+M)for traversing to row and column of elements having value 1.
Space Complexity:O(1)

Another Approach:

Follow the steps below to solve the problem

• Create two temporary arrays row[M] and col[N]. Initialize all values of row[] and col[] as 0.
• 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.
• 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.

Below is the implementation of the above approach:

## C++

 `// C++ Code For A Boolean Matrix Question` `#include `   `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 Aditya Kumar (adityakumar129)`

## C

 `// C Code For A Boolean Matrix Question` `#include ` `#include `   `#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++)` `            ``printf``(``"%d "``, mat[i][j]);` `        ``printf``(``"\n"``);` `    ``}` `}`   `// Driver Code` `int` `main()` `{` `    ``bool` `mat[R][C] = { { 1, 0, 0, 1 },` `                       ``{ 0, 0, 1, 0 },` `                       ``{ 0, 0, 0, 0 } };`   `    ``printf``(``"Input Matrix \n"``);` `    ``printMatrix(mat);` `    ``modifyMatrix(mat);` `    ``printf``(``"Matrix after modification \n"``);` `    ``printMatrix(mat);` `    ``return` `0;` `}`   `// This code is contributed by Aditya Kumar (adityakumar129)`

## Java

 `// Java Code For A Boolean Matrix Question` `import` `java.io.*;`   `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 Initially"``);` `        ``printMatrix(mat, ``3``, ``4``);` `        ``modifyMatrix(mat, ``3``, ``4``);` `        ``System.out.println(``"Matrix after modification"``);` `        ``printMatrix(mat, ``3``, ``4``);` `    ``}` `}`   `// This code is contributed by Aditya Kumar (adityakumar129)`

## 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"``)` `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, ``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"``);` `        ``printMatrix(mat, 3, 4);` `    ``}` `}`   `// This code is contributed by ajit`

## Javascript

 ``

## PHP

 ``

Output

```Input Matrix
1001
0010
0000
Matrix after modification
1111
1111
1011

```

Time Complexity: O(M*N), Traversing over the matrix two times.
Auxiliary Space: O(M + N), Taking two arrays one of size M and another of size N.

Thanks to Dixit Sethi for suggesting this method.

## A Boolean Matrix Question using O(1) Space:

Intuition: Instead of taking two dummy arrays we can use the first row and column of the matrix for the same work. This will help to reduce the space complexity of the problem. While traversing for the second time the first row and column will be computed first, which will affect the values of further elements thatâ€™s why we traversing in the reverse direction.

Approach: Instead of taking two separate dummy arrays, take the first row and column of the matrix as the array for checking whether the particular column or row has the value 1 or not.Since matrix[0][0] are overlapping.Therefore take separate variable col0(say) to check if the 0th column has 1 or not and use matrix[0][0] to check if the 0th row has 1 or not. Now traverse from the last element to the first element and check if matrix[i][0]==1 || matrix[0][j]==1 and if true set matrix[i][j]=1, else continue.

Below is the implementation of above approach:

## C++

 `#include` `using` `namespace` `std;` `void` `setZeroes(vector < vector < ``int` `>> & matrix) {` `  ``int` `col0 = 0, rows = matrix.size(), cols = matrix[0].size();` `  ``for` `(``int` `i = 0; i < rows; i++) {` `    ``//checking if 0 is present in the 0th column or not` `    ``if` `(matrix[i][0] == 1) col0 = 1;` `    ``for` `(``int` `j = 1; j < cols; j++) {` `      ``if` `(matrix[i][j] == 1) {` `        ``matrix[i][0] = 1;` `        ``matrix[0][j] = 1;` `      ``}` `    ``}` `  ``}` `  ``//traversing in the reverse direction and` `  ``//checking if the row or col has 0 or not` `  ``//and setting values of matrix accordingly.` `  ``for` `(``int` `i = rows - 1; i >= 0; i--) {` `    ``for` `(``int` `j = cols - 1; j >= 1; j--) {` `      ``if` `(matrix[i][0] == 1 || matrix[0][j] == 1) {` `        ``matrix[i][j] = 1;` `      ``}` `    ``}` `    ``if` `(col0 == 1) {` `      ``matrix[i][0] = 1;` `    ``}`   `  ``}`   `}`   `int` `main() {` `  ``vector < vector < ``int` `>> arr;` `  ``arr = {{1, 0, 2, 1}, {3, 4, 5, 2}, {0, 3, 0, 5}};` `  ``setZeroes(arr);` `  ``cout<<``"The Final Matrix is "``<

## C

 `#include ` `#include `   `#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++)` `            ``printf``(``"%d "``, mat[i][j]);` `        ``printf``(``"\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 } };`   `    ``printf``(``"Input Matrix :\n"``);` `    ``printMatrix(mat);` `    ``modifyMatrix(mat);` `    ``printf``(``"Matrix After Modification :\n"``);` `    ``printMatrix(mat);` `    ``return` `0;` `}`   `// This code is contributed by Aditya Kumar (adityakumar129)`

## Java

 `import` `java.io.*;` `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 Aditya Kumar (adityakumar129)`

## 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`

## Javascript

 ``

## PHP

 ``

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), Traversing over the matrix two times.
Auxiliary Space: O(1)

Thanks to Sidh for suggesting this method.

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