Set Matrix Rows and Columns to Zeroes
Last Updated :
22 Jul, 2025
Given a matrix mat[][] of size nxm, the task is to update the matrix such that if an element is zero, set its entire row and column to zeroes.
Examples:
Input: mat[][] = [[1, -1, 1],
[-1, 0, 1],
[1, -1, 1]]
Output: [[1, 0, 1],
[0, 0, 0],
[1, 0, 1]]
Explanation: mat[1][1] = 0, so all elements in row 1 and column 1 are updated to zeroes.
Input: mat[][] = [[0, 1, 2, 0],
[3, 4, 0, 2],
[1, 3, 1, 5]]
Output: [[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 3, 0, 0]]
Explanation: mat[0][0], mat[1][2] and mat[0][3] are 0s, so all elements in row 0, row 1, column 0, column 2 and column 3 are updated to zeroes.
[Naive Approach] Using Two Auxiliary Arrays - O(n*m) Time and O(n+m) Space
The idea is to maintain two additional arrays, say rows[] and cols[] to store the rows and columns which contains at least one element equal to 0. So, first traverse the entire matrix and for each mat[i][j] = 0, mark rows[i] = true and cols[j] = true. Now in the second traversal, for each cell (i, j), if either rows[i] or cols[j] is marked as true, update mat[i][j] = 0 else continue to the next cell.
Illustration:
C++
#include <iostream>
#include <vector>
using namespace std;
void setMatrixZeroes(vector<vector<int>> &mat) {
int n = mat.size(), m = mat[0].size();
// To store which rows and columns are
// supposed to mark with zeroes
vector<bool> rows(n, false), cols(m, false);
// Traverse the matrix to fill rows[] and cols[]
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
// If the cell contains zero then mark
// its row and column as zero
if (mat[i][j] == 0) {
rows[i] = true;
cols[j] = true;
}
}
}
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
// Mark cell (i, j) with zero if either
// of rows[i] or cols[j] is true
if (rows[i] || cols[j])
mat[i][j] = 0;
}
}
}
int main() {
vector<vector<int> > mat = { { 0, 1, 2, 0 },
{ 3, 4, 0, 2 },
{ 1, 3, 1, 5 } };
setMatrixZeroes(mat);
for (int i = 0; i < mat.size(); i++) {
for (int j = 0; j < mat[0].size(); j++) {
cout << mat[i][j] << " ";
}
cout << endl;
}
return 0;
}
class GfG {
static void setMatrixZeroes(int[][] mat) {
int n = mat.length, m = mat[0].length;
// To store which rows and columns are
// supposed to mark with zeroes
boolean[] rows = new boolean[n];
boolean[] cols = new boolean[m];
// Traverse the matrix to fill rows[] and cols[]
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
// If the cell contains zero then mark
// its row and column as zero
if (mat[i][j] == 0) {
rows[i] = true;
cols[j] = true;
}
}
}
// Set matrix elements to zero if they
// belong to a marked row or column
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
// Mark cell (i, j) with zero if either
// of rows[i] or cols[j] is true
if (rows[i] || cols[j]) {
mat[i][j] = 0;
}
}
}
}
public static void main(String[] args) {
int[][] mat = {
{ 0, 1, 2, 0 },
{ 3, 4, 0, 2 },
{ 1, 3, 1, 5 }
};
setMatrixZeroes(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();
}
}
}
def setMatrixZeroes(mat):
n = len(mat)
m = len(mat[0])
# To store which rows and columns are
# supposed to mark with zeroes
rows = [False] * n
cols = [False] * m
# Traverse the matrix to fill rows[] and cols[]
for i in range(n):
for j in range(m):
# If the cell contains zero then mark
# its row and column as zero
if mat[i][j] == 0:
rows[i] = True
cols[j] = True
# Set matrix elements to zero if they
# belong to a marked row or column
for i in range(n):
for j in range(m):
# Mark cell (i, j) with zero if either
# of rows[i] or cols[j] is true
if rows[i] or cols[j]:
mat[i][j] = 0
if __name__ == "__main__":
mat = [
[0, 1, 2, 0],
[3, 4, 0, 2],
[1, 3, 1, 5]
]
setMatrixZeroes(mat)
for row in mat:
print(" ".join(map(str, row)))
using System;
using System.Collections.Generic;
class GfG {
static void setMatrixZeroes(int[,] mat) {
int n = mat.GetLength(0);
int m = mat.GetLength(1);
// To store which rows and columns are
// supposed to mark with zeroes
bool[] rows = new bool[n];
bool[] cols = new bool[m];
// Traverse the matrix to fill rows[] and cols[]
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
// If the cell contains zero then mark
// its row and column as zero
if (mat[i, j] == 0) {
rows[i] = true;
cols[j] = true;
}
}
}
// Mark cells with zero if either of
// rows[i] or cols[j] is true
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
// Mark cell (i, j) with zero if either
// of rows[i] or cols[j] is true
if (rows[i] || cols[j])
mat[i, j] = 0;
}
}
}
static void Main(string[] args) {
int[,] mat = {
{ 0, 1, 2, 0 },
{ 3, 4, 0, 2 },
{ 1, 3, 1, 5 }
};
setMatrixZeroes(mat);
int n = mat.GetLength(0), m = mat.GetLength(1);
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
Console.Write(mat[i, j] + " ");
}
Console.WriteLine();
}
}
}
function setMatrixZeroes(mat) {
const n = mat.length, m = mat[0].length;
// To store which rows and columns are
// supposed to mark with zeroes
const rows = new Array(n).fill(false);
const cols = new Array(m).fill(false);
// Traverse the matrix to fill rows[] and cols[]
for (let i = 0; i < n; i++) {
for (let j = 0; j < m; j++) {
// If the cell contains zero then mark
// its row and column as zero
if (mat[i][j] === 0) {
rows[i] = true;
cols[j] = true;
}
}
}
// Mark cells with zero if either of rows[i]
// or cols[j] is true
for (let i = 0; i < n; i++) {
for (let j = 0; j < m; j++) {
// Mark cell (i, j) with zero if either
// of rows[i] or cols[j] is true
if (rows[i] || cols[j]) {
mat[i][j] = 0;
}
}
}
}
// Driver Code
let mat = [
[0, 1, 2, 0],
[3, 4, 0, 2],
[1, 3, 1, 5]
];
setMatrixZeroes(mat);
for (let row of mat) {
console.log(row.join(" "));
}
Output0 0 0 0
0 0 0 0
0 3 0 0
[Expected Approach] Using First Row and Column - O(n*m) Time and O(1) Space
In the previous approach we took two arrays to store the row's and column's status. Now instead of two auxiliary arrays, we can use the first row and first column of mat[][] to store which row elements and column elements are to be marked as zeroes.
So if the first cell of a row is set to 0, then all cells of that row should be updated with 0. Similarly, if the first cell of a column is set to 0, then all cells of that column should be updated to 0. Since cell (0, 0) is first cell of the first row as well as the first column, so maintain another variable, say c0 to store the status of the first column and cell(0, 0) will store the status of the first row.
Step By Step Algorithm:
- Traverse the matrix, and for each cell (i, j) such that mat[i][j] = 0, mark mat[i][0] and mat[0][j] as 0. Note: If i = 0, mark mat[0][0] as 0 and if j = 0, mark c0 as 0.
- Again traverse the matrix from (1, 1) to (n-1, m-1), and set mat[i][j] = 0 if either mat[i][0] = 0 or mat[0][j] = 0.
- Finally, update the first row and first column:
- If arr[0][0] = 0, set all elements in first row to 0.
- If c0 = 0, set all elements in the first column to 0.
Illustration:
C++
#include <iostream>
#include <vector>
using namespace std;
void setMatrixZeroes(vector<vector<int>> &mat) {
int n = mat.size(), m = mat[0].size();
int c0 = 1;
// Traverse the arr and mark first
// cell of each row and column
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
if (mat[i][j] == 0) {
// mark i-th row
mat[i][0] = 0;
// mark j-th column
if (j == 0)
c0 = 0;
else
mat[0][j] = 0;
}
}
}
// Traverse and mark the matrix from
// (1, 1) to (n - 1, m - 1)
for (int i = 1; i < n; i++) {
for (int j = 1; j < m; j++) {
// Check for col & row
if (mat[i][0] == 0 || mat[0][j] == 0) {
mat[i][j] = 0;
}
}
}
// Mark the first row
if (mat[0][0] == 0) {
for (int j = 0; j < m; j++)
mat[0][j] = 0;
}
// Mark the first column
if (c0 == 0) {
for (int i = 0; i < n; i++)
mat[i][0] = 0;
}
}
int main() {
vector<vector<int> > mat = { { 0, 1, 2, 0 },
{ 3, 4, 0, 2 },
{ 1, 3, 1, 5 } };
setMatrixZeroes(mat);
for (int i = 0; i < mat.size(); i++) {
for (int j = 0; j < mat[0].size(); j++) {
cout << mat[i][j] << " ";
}
cout << endl;
}
return 0;
}
class GfG {
static void setMatrixZeroes(int[][] mat) {
int n = mat.length, m = mat[0].length;
int c0 = 1;
// Traverse the arr and mark first
// cell of each row and column
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
if (mat[i][j] == 0) {
// mark i-th row
mat[i][0] = 0;
// mark j-th column
if (j == 0)
c0 = 0;
else
mat[0][j] = 0;
}
}
}
// Traverse and mark the matrix from
// (1, 1) to (n - 1, m - 1)
for (int i = 1; i < n; i++) {
for (int j = 1; j < m; j++) {
// Check for col & row
if (mat[i][0] == 0 || mat[0][j] == 0) {
mat[i][j] = 0;
}
}
}
// Mark the first row
if (mat[0][0] == 0) {
for (int j = 0; j < m; j++)
mat[0][j] = 0;
}
// Mark the first column
if (c0 == 0) {
for (int i = 0; i < n; i++)
mat[i][0] = 0;
}
}
public static void main(String[] args) {
int[][] mat = { { 0, 1, 2, 0 },
{ 3, 4, 0, 2 },
{ 1, 3, 1, 5 } };
setMatrixZeroes(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();
}
}
}
def setMatrixZeroes(mat):
n = len(mat)
m = len(mat[0])
c0 = 1
# Traverse the arr and mark first
# cell of each row and column
for i in range(n):
for j in range(m):
if mat[i][j] == 0:
# mark i-th row
mat[i][0] = 0
# mark j-th column
if j == 0:
c0 = 0
else:
mat[0][j] = 0
# Traverse and mark the matrix from
# (1, 1) to (n - 1, m - 1)
for i in range(1, n):
for j in range(1, m):
# Check for col & row
if mat[i][0] == 0 or mat[0][j] == 0:
mat[i][j] = 0
# Mark the first row
if mat[0][0] == 0:
for j in range(m):
mat[0][j] = 0
# Mark the first column
if c0 == 0:
for i in range(n):
mat[i][0] = 0
if __name__ == "__main__":
mat = [
[0, 1, 2, 0],
[3, 4, 0, 2],
[1, 3, 1, 5]
]
setMatrixZeroes(mat)
for row in mat:
print(" ".join(map(str, row)))
using System;
class GfG {
static void setMatrixZeroes(int[,] mat) {
int n = mat.GetLength(0), m = mat.GetLength(1);
int c0 = 1;
// Traverse the arr and mark first cell
// of each row and column
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
if (mat[i, j] == 0) {
// mark i-th row
mat[i, 0] = 0;
// mark j-th column
if (j == 0)
c0 = 0;
else
mat[0, j] = 0;
}
}
}
// Traverse and mark the matrix from
// (1, 1) to (n - 1, m - 1)
for (int i = 1; i < n; i++) {
for (int j = 1; j < m; j++) {
// Check for col & row
if (mat[i, 0] == 0 || mat[0, j] == 0) {
mat[i, j] = 0;
}
}
}
// Mark the first row
if (mat[0, 0] == 0) {
for (int j = 0; j < m; j++)
mat[0, j] = 0;
}
// Mark the first column
if (c0 == 0) {
for (int i = 0; i < n; i++)
mat[i, 0] = 0;
}
}
static void Main() {
int[,] mat = {
{ 0, 1, 2, 0 },
{ 3, 4, 0, 2 },
{ 1, 3, 1, 5 }
};
setMatrixZeroes(mat);
int n = mat.GetLength(0), m = mat.GetLength(1);
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
Console.Write(mat[i, j] + " ");
}
Console.WriteLine();
}
}
}
function setMatrixZeroes(mat) {
const n = mat.length, m = mat[0].length;
let c0 = 1;
// Traverse the array and mark
// first cell of each row and column
for (let i = 0; i < n; i++) {
for (let j = 0; j < m; j++) {
if (mat[i][j] === 0) {
// mark i-th row
mat[i][0] = 0;
// mark j-th column
if (j === 0)
c0 = 0;
else
mat[0][j] = 0;
}
}
}
// Traverse and mark the matrix
// from (1, 1) to (n - 1, m - 1)
for (let i = 1; i < n; i++) {
for (let j = 1; j < m; j++) {
// Check for col & row
if (mat[i][0] === 0 || mat[0][j] === 0) {
mat[i][j] = 0;
}
}
}
// Mark the first row
if (mat[0][0] === 0) {
for (let j = 0; j < m; j++)
mat[0][j] = 0;
}
// Mark the first column
if (c0 === 0) {
for (let i = 0; i < n; i++)
mat[i][0] = 0;
}
}
// Driver Code
let mat = [
[0, 1, 2, 0],
[3, 4, 0, 2],
[1, 3, 1, 5]
];
setMatrixZeroes(mat);
for (let row of mat) {
console.log(row.join(" "));
}
Output0 0 0 0
0 0 0 0
0 3 0 0
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