What is the optimal time complexity of solving Pacific Atlantic Water Flow?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Pacific Atlantic Water Flow?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Pacific Atlantic Water Flow?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Pacific Atlantic Water Flow?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Pacific Atlantic Water Flow

Learn how to solve the 'Pacific Atlantic Water Flow' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

There is an m x n rectangular island that borders both the Pacific Ocean and Atlantic Ocean. The Pacific Ocean touches the island's left and top edges, and the Atlantic Ocean touches the island's right and bottom edges.

The island is partitioned into a grid of square cells. You are given an m x n integer matrix heights where heights[r][c] represents the height above sea level of the cell at coordinate (r, c).

Rain water can flow to neighboring cells directly north, south, east, and west if the neighboring cell's height is less than or equal to the current cell's height. Water can flow from any cell adjacent to an ocean into that ocean.

Return a 2D list of grid coordinates result where result[i] = [ri, ci] denotes that rain water can flow from cell (ri, ci) to both the Pacific and Atlantic oceans.

Write a function pacificAtlantic(heights: List[List[int]]) -> List[List[int]].

Constraints

•m == len(heights)
•n == len(heights[0])
•1 <= m, n <= 200
•0 <= heights[i][j] <= 10^5

Examples

Example 1

Input

heights = [[1,2,2,3,5],[3,2,3,4,4],[2,4,5,3,1],[6,7,1,4,5],[5,1,1,2,4]]

Output

[[0,4],[1,3],[1,4],[2,2],[3,0],[3,1],[4,0]]

Explanation

These coordinates can flow to both Pacific (via top/left) and Atlantic (via bottom/right) oceans.

Example 2

Input

heights = [[1]]

Output

[[0,0]]

Explanation

The single cell borders both oceans directly.

Need a Hint?

Represent graph node connections as an adjacency list/matrix, then use standard BFS or DFS graph traversal.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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