Pacific Atlantic Water Flow - Leetcode 417 - Python

Solving Pacific Atlantic Water Flow

In this video, the presenter solves the Pacific Atlantic Water Flow problem from the Blind 75 list. The problem involves determining whether a cell in a two-dimensional grid can reach either the Pacific or Atlantic Ocean based on its height and neighboring cells.

Understanding the Problem

• The problem involves a two-dimensional grid of values where each value represents a height.

• The top and left borders of the grid are considered to be the Pacific Ocean, while everything to the right and bottom is considered to be the Atlantic Ocean.

• A cell can reach either ocean if water can flow from it to that ocean through adjacent cells with lower or equal heights.

• Water can only flow in four directions: up, down, left, or right.

Naive Solution

• A brute force solution would involve checking every position in the grid using DFS or BFS to determine if it can reach both oceans.

• This approach would have a time complexity of O(n*m^2), where n and m are dimensions of the grid.

Clever Solution

• A more efficient solution involves starting at all positions bordering the Pacific Ocean and finding all cells that can reach it.

• Similarly, we start at all positions bordering the Atlantic Ocean and find all cells that can reach it.

• Finally, we return all cells that were found by both traversals as they are able to reach both oceans.

Efficient Algorithm for Water Flow

In this section, the speaker explains an efficient algorithm for water flow. The algorithm involves starting at each node and doing a depth-first search to see which nodes can reach the Pacific or Atlantic Ocean.

Algorithm Explanation

• The algorithm is more efficient because it only visits each node once.

• Starting at a node, a depth-first search is done to see which other nodes can reach the Pacific Ocean.

• Water can flow from a cell with higher value to one with lower value until it reaches the ocean.

• If going in the opposite direction (from Atlantic to Pacific), water can only flow from cells of equal or increasing height.

Implementation Details

• Two hash sets are used to maintain positions that can reach the Pacific and Atlantic oceans respectively.

• The first row (Pacific Ocean values) is traversed, and then every position in the last row (Atlantic Ocean values).

• A DFS function is called on each position in these rows, passing in either the Pacific or Atlantic set depending on which row is being traversed.

• The DFS function checks if a position has already been visited before continuing.

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