Zero Matrix Problem Statement

You are given a matrix MATRIX of dimension N x M. Your task is to make all the elements of row i and column j equal to 0 if any element in the i^th row or j^th column of the matrix is 0.

Input:

The first line of the input contains an integer 'T' denoting the number of test cases. The first line of each test case contains two space-separated integers, 'N' and 'M', as described in the problem statement. The next 'N' lines of each test case contain 'M' integers separated by spaces describing rows of the matrix.

Output:

For each test case, return 'N' rows consisting of 'M' integers representing the matrix.

Example:

Example: Consider the MATRIX below:

Input: MATRIX = [[1, 2, 3], [4, 0, 6], [7, 8, 9]]

Output: [[1, 0, 3], [0, 0, 0], [7, 0, 9]]

Constraints:

1 ≤ T ≤ 50

1 ≤ N ≤ 100

1 ≤ M ≤ 100

-10⁹ ≤ MATRIX[i][j] ≤ 10⁹ - where MATRIX[i][j] denotes the matrix element.

Note:

You don\'t need to print anything, it has already been taken care of. Just implement the given function.

Follow-Up:

Can you solve it with a space complexity of O(1)? Time limit: 1 sec.

Question

Zero Matrix Problem Statement

You are given a matrix MATRIX of dimension N x M. Your task is to make all the elements of row i and column j equal to 0 if any element in the i^th row or j^th column of the matrix is 0.

Input:

The first line of the input contains an integer 'T' denoting the number of test cases.

The first line of each test case contains two space-separated integers, 'N' and 'M', as described in the problem statement.

The next 'N' lines of each test case contain 'M' integers separated by spaces describing rows of the matrix.

Output:

For each test case, return 'N' rows consisting of 'M' integers representing the matrix.

Example:

Example: Consider the MATRIX below:

Input: MATRIX = [[1, 2, 3], [4, 0, 6], [7, 8, 9]]

Output: [[1, 0, 3], [0, 0, 0], [7, 0, 9]]

Constraints:

1 ≤ T ≤ 50
1 ≤ N ≤ 100
1 ≤ M ≤ 100
-10⁹ ≤ MATRIX[i][j] ≤ 10⁹ - where MATRIX[i][j] denotes the matrix element.

Note:

You don\'t need to print anything, it has already been taken care of. Just implement the given function.

Follow-Up:

Can you solve it with a space complexity of O(1)? Time limit: 1 sec.

Accepted Answer

The task is to modify a given matrix such that if any element in a row or column is 0, then make all elements in that row and column 0.

Iterate through the matrix and keep track of rows and columns that contain 0s
After the first iteration, iterate through the tracked rows and columns and set all elements to 0
Handle the case where the first row or column contains 0 separately
To solve with O(1) space complexity, use the first row and first column of the matrix to track the rows and columns that need to be set to 0