Lecture Notes: Matrix Zeros Problem

Overview

• This lecture is part of the Strippers A2Z DSA course.
• The course covers in-depth data structures and algorithms (DSA).
• By the end of the course, students will solve over 400 DSA problems.
• The lecture focuses on the "Matrix Zeros" problem.

Problem Statement

• Given an N x M binary matrix (only contains 0s and 1s)
• If an element is 0, set all elements in its row and column to 0.
• Zeros already present in the matrix should not affect marking.

Steps to Approach the Problem

1. Brute Force Solution:

   • Iterate through the matrix.
   • Upon finding a 0, traverse the respective row and column to set 1s to 0.
   • Problem: This approach can lead to incorrect results as it modifies the matrix while traversing.
   • Instead of marking as 0 immediately, mark as -1 to avoid re-marking.

2. Code for Brute Force:

   • Create functions to mark rows and columns.
   • First pass: replace 1s with -1 based on initial 0s.
   • Second pass: convert all -1s to 0s.

3. Time Complexity of Brute Force:

   • O(N^3) due to nested loops for marking and traversing.

4. Optimized Solution:

   • Use two arrays to track which rows and columns should be set to 0.
   • Traverse the matrix once to mark rows and columns based on 0s found.
   • Second pass to set the corresponding elements to 0 based on the tracking arrays.
   • Space Complexity: O(N + M) due to the two arrays.

5. Further Optimization:

   • Instead of using extra space, modify the original matrix.
   • Use the first row and first column as flags to indicate if a row or column should be set to 0.
   • Track if the first row and first column themselves need to be zeroed.

Implementation Notes

• Marking logic:
  • If a 0 is found, mark its row and column in the first row/column.
  • After marking, iterate again to set elements to 0 based on the flags.
• Be cautious about the dependency between elements when converting them to 0.

Conclusion

• The lecture covered multiple approaches to the Matrix Zeros problem - from brute force to optimized solutions using space-saving techniques.
• Reinforces the understanding of handling matrix problems efficiently in interviews.

Additional Information

• Links to coding examples in C++, Java, and Python provided in the description.
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