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Pacific Atlantic Water Flow

The key idea

Don't flood forward from each cell to an ocean (that re-runs a search per cell). Instead start from the ocean borders and flood INWARD against the flow: a cell is ocean-reachable if you can climb to it from the border moving only to equal-or-higher neighbors. Run that reverse search once per ocean, then intersect the two reachable sets.

Problem

There is 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, 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] is the height above sea level of the cell at coordinate (r, c).

The island receives a lot of rain, and the 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 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.

Constraints

Examples

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]]
Input: heights = [[1]] Output: [[0,0]]

Complexity

Time: O(m*n) Space: O(m*n)

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