Beginner to Mastery series: Graphs, Day 7/30 , Leetcode 417, Pacific Atlantic Water Flow using bfs.

Welcome back to the channel for Day 7 of our 30-Day Data Structures and Algorithms Challenge. We are keeping the momentum going strong after returning from my end semester exams. Yesterday we tackled a hard graph problem, and today we are continuing with another essential graph question that frequently appears in technical interviews: Leetcode 417 Pacific Atlantic Water Flow. This is a classic problem involving matrix traversal and graph theory, and it is a perfect follow-up to solidify your understanding of graph algorithms.

In this video, we provide a complete tutorial and solution for Leetcode 417 Pacific Atlantic Water Flow. This problem is often classified as a medium-level Leetcode question, but it requires a solid grasp of traversal techniques like Breadth First Search or BFS and Depth First Search or DFS. While many tutorials and solutions online might use DFS to solve this, in this specific video, I have chosen to solve Leetcode 417 Pacific Atlantic Water Flow using the Breadth First Search or BFS approach explicitly. I believe using BFS provides a very clear and iterative way to visualize how the water flows from the ocean borders back into the continent, and it is a great way to practice using queues in graph problems.

The problem statement for Leetcode 417 Pacific Atlantic Water Flow gives us an m x n rectangular island that borders both the Pacific Ocean and the Atlantic Ocean. The Pacific Ocean touches the island's left and top edges, while the Atlantic Ocean touches the right and bottom edges. The grid represents the heights of the land cells. Rainwater can flow from a cell to a neighboring cell directly north, south, east, or west if the neighbor's height is less than or equal to the current cell's height. Our goal is to find all the grid coordinates where rainwater can flow from that cell to both the Pacific Ocean and the Atlantic Ocean. This premise makes Leetcode 417 Pacific Atlantic Water Flow an excellent problem for understanding grid-based graph traversal.

In this tutorial, I walk you through the implementation of this multi-source Breadth First Search. We utilize two separate queues: one for the Pacific Ocean BFS and one for the Atlantic Ocean BFS. We also maintain two separate boolean matrices to keep track of visited cells—one to mark cells that can reach the Pacific and another for cells that can reach the Atlantic. By using Breadth First Search, we explore the grid layer by layer. We add the border cells to our queues initially and then process them. For every cell we pop from the queue, we look at its neighbors. If a neighbor has a height greater than or equal to the current cell, it means water could flow down from that neighbor to the current cell, or conversely, we can climb up from the ocean to that neighbor. This condition is crucial for the correctness of our LeetCode 417 Pacific Atlantic Water Flow solution.

I explain explicitly why we use BFS over DFS in this video. While DFS is a recursive approach that goes deep into one path, BFS explores neighbors level by level using a queue. For students who struggle with recursion depth limits or stack overflow issues, seeing the iterative Breadth First Search solution for LeetCode 417 Pacific Atlantic Water Flow can be incredibly helpful.

The space complexity is also determined by our visited matrices and the queue size, which is also O(M times N). Understanding this complexity analysis is vital for interview preparation, and LeetCode 417 Pacific Atlantic Water Flow serves as a great example to discuss these constraints.

Finally, after running both Breadth First Search traversals, we perform a simple intersection step. We iterate through the grid one last time and check which cells are marked as visited in both the Pacific matrix and the Atlantic matrix. If a cell is reachable from both oceans, it is part of our answer. I show you exactly how to code this intersection logic in C++. This step completes the solution for LeetCode 417 Pacific Atlantic Water Flow.

If you enjoyed this deep dive into LeetCode 417 Pacific Atlantic Water Flow using Breadth First Search, please stick around for the rest of the series. We have many more patterns to cover. Thank you for your support as I resume daily uploads following my exams. Let's master graphs together.

Problem Link: https://leetcode.com/problems/pacific...

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