Efficient In-Place Matrix Zeroing in Python

Setting all elements in a row and column to zero when an element is zero can be a classic interview problem, especially when the matrix must be modified in place without using additional space. Today, we'll explore a solution that achieves this requirement by cleverly using the matrix itself as a storage mechanism for "flags."

Problem Statement

Given an m×n times m×n integer matrix, if any element is 0, set its entire row and column to 0. The solution must be in place and ideally, use constant space.

Approach and Solution

The naive solution would be to create a new matrix to store information about which rows and columns should be zeroed out, which would require O(m+n)O(m + n)O(m+n) additional space. However, our goal is a more efficient approach that only uses constant extra space.

Key Insight: Use the First Row and Column as Flags

The key insight here is to use the first row and column of the matrix itself as storage for flags. This allows us to keep track of which rows and columns need to be zeroed out without needing extra memory.

Here’s how this approach works:

1. Identify Zero Flags for the First Row and Column
2. Mark the Zeroed Rows and Columns
3. Use the Flags to Zero Out Rows and Columns
4. Zero Out the First Row and Column (if needed)

Python Code Implementation

Here’s the Python code implementing this approach:

Complexity Analysis

• Time Complexity: O(m×n)
• Space Complexity: O(1)

Why This Solution Works

This approach leverages the fact that we can use the input matrix as our storage, avoiding additional memory usage. By restricting our modifications to just the first row and column, we manage to keep track of which rows and columns need to be zeroed while leaving the rest of the matrix free for other calculations.