Time Complexity: O(m * n * (m + n)), We iterate through every cell (m * n), and for each zero, we potentially mark its entire row (O(n)) and column (O(m)), leading to O(m * n * (m + n)) overall.

Space Complexity: O(1), We are not using any extra data structures, only modifying the matrix in place (apart from a few variables).

Better Approach

Algorithm

Instead of marking directly in the matrix, keep two extra arrays:

One to track which rows need to be zeroed.
One to track which columns need to be zeroed.

When you find a zero, mark its row index in the row array and column index in the col array. After the scan, you go back and zero out all marked rows and columns. This avoids accidental over-zeroing in the first pass.

Create a row array of size m (rows) and a col array of size n (columns) initialized to false.
First pass: Traverse the matrix, and when you find a zero:

Mark the corresponding row index in row array.
Mark the corresponding col index in col array.

Second pass: Traverse the matrix again, and if either the row or col is marked, set the cell to zero.