Distance of nearest cell having 1 | DSA Problem

Explore the problem of finding the distance to the nearest cell containing '1' in a binary matrix with our comprehensive tutorial. This guide is perfect for computer science students, programmers, and anyone interested in mastering algorithms for matrix manipulation and shortest path problems.

In this tutorial, you'll learn:

• Understanding the Problem: Gain a foundational understanding of the task, which involves calculating the minimum distance from each cell in a binary matrix to the nearest cell containing '1'. This distance is measured in terms of the number of cell moves horizontally or vertically.
• Breadth-First Search (BFS) Approach: Learn why BFS is the most suitable approach for this problem, given its ability to explore all nodes at the present depth level before moving on to nodes at the next depth level, ensuring the shortest path is found.
• Using a Queue for BFS: Explore how to use a queue to facilitate BFS in the matrix, where each cell containing '1' is initially enqueued, and distances are propagated from these cells.
• Algorithm Steps:
  1. Initialization: Initialize a distance matrix of the same dimensions as the input matrix, with all values set to infinity (or a large number) except for cells containing '1', which are set to zero.
  2. Enqueue All '1's: Push all cells containing '1' into the queue, as these are the starting points for BFS.
  3. BFS Traversal: Dequeue each cell, and for each of its 4 possible neighbors (up, down, left, right), update their distances if a shorter path is found and enqueue them.
• Step-by-Step Code Implementation: Detailed code examples in popular programming languages like Python, Java, and C++. These examples will demonstrate how to implement the BFS algorithm to solve the problem efficiently.
• Complexity Analysis: Discuss the time complexity of the BFS approach, which is 𝑂(𝑛×𝑚)O(n×m), where 𝑛n is the number of rows and 𝑚m is the number of columns in the matrix. The space complexity is also 𝑂(𝑛×𝑚)O(n×m) due to the additional distance matrix and the queue.
• Handling Edge Cases: Tips on managing edge cases such as a matrix with no '1's, a matrix with all '1's, and ensuring the algorithm handles large matrices efficiently.
• Practical Examples and Testing: Provide practical examples and test cases to demonstrate the function and verify its correctness across different scenarios.

By the end of this tutorial, you’ll be well-equipped to solve the problem of finding the distance to the nearest cell containing '1' in a binary matrix, enhancing your understanding of BFS and matrix manipulation techniques.

For a comprehensive guide on finding the distance to the nearest cell containing '1' in a binary matrix, including detailed explanations, code examples, and practical tips, check out our full article at https://www.geeksforgeeks.org/distance-nearest-cell-1-binary-matrix/.

This tutorial will not only improve your understanding of BFS and matrix operations but also prepare you to tackle similar challenges in your software development and algorithmic problem-solving efforts.