Pacific Atlantic Water Flow

Pacific Atlantic Water Flow

Question:

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).

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 the 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.

How to Solve:

We start by creating two hash sets that will respectively hold coordinate pairs that are reachable by Pacific or Atlantic ocean. In the end, we'd take the intersection of these two sets as our returned result.

The key to solving this problem is, instead of starting at each cell and checking if it can reach an ocean, we start at the ocean and perform depth-first search, marking every cell along the way (by storing it to the correct hash set), and stopping when the height progression is no longer valid. Naturally, we should start the borders and DFS inwards. In order for the DFS traversal to continue, the heights must be "weakly ascending" -- we perform this by passing an extra variable, prevHeight, into the deeper recursive call.

My C++ Solution:

struct PairHash {
  template <typename T1, typename T2>
  auto operator()(const pair<T1, T2> &pair_) const -> size_t {
    return hash<T1>{}(pair_.first) ^ hash<T2>{}(pair_.second);
  }
};

class Solution {
 public:
  auto pacificAtlantic(const vector<vector<int>> &heights_) -> vector<vector<int>> {
    heights = heights_;
    ROWS = static_cast<int>(heights.size());
    COLS = static_cast<int>(heights[0].size());
    unordered_set<pair<int, int>, PairHash> pacific;
    unordered_set<pair<int, int>, PairHash> atlantic;

    for (int col = 0; col < COLS; ++col) {
      dfs(0, col, pacific, numeric_limits<int>::min());
      dfs(ROWS - 1, col, atlantic, numeric_limits<int>::min());
    }

    for (int row = 0; row < ROWS; ++row) {
      dfs(row, 0, pacific, numeric_limits<int>::min());
      dfs(row, COLS - 1, atlantic, numeric_limits<int>::min());
    }

    vector<vector<int>> res;
    for (const auto &coordinate : pacific) {
      if (atlantic.find(coordinate) != atlantic.end()) {
        res.push_back({coordinate.first, coordinate.second});
      }
    }

    return res;
  }

 private:
  int ROWS;
  int COLS;
  vector<vector<int>> heights;

  void dfs(int row, int col, unordered_set<pair<int, int>, PairHash> &ocean, int prevHeight) {
    if (ocean.find({row, col}) != ocean.end() || row < 0 || row >= ROWS || col < 0 || col >= COLS ||
        heights[row][col] < prevHeight) {
      return;
    }
    ocean.insert({row, col});
    dfs(row + 1, col, ocean, heights[row][col]);
    dfs(row - 1, col, ocean, heights[row][col]);
    dfs(row, col + 1, ocean, heights[row][col]);
    dfs(row, col - 1, ocean, heights[row][col]);
  }
};