【LeetCode】417. Pacific Atlantic Water Flow 解题报告（Python & C++）

作者： 负雪明烛
id： fuxuemingzhu
个人博客： http://fuxuemingzhu.cn/

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题目地址: https://leetcode.com/problems/pacific-atlantic-water-flow/description/

题目描述

Given an m x n matrix of non-negative integers representing the height of each unit cell in a continent, the "Pacific ocean" touches the left and top edges of the matrix and the ``“Atlantic ocean”```touches the right and bottom edges.

Water can only flow in four directions (up, down, left, or right) from a cell to another one with height equal or lower.

Find the list of grid coordinates where water can flow to both the Pacific and Atlantic ocean.

Note:

1. The order of returned grid coordinates does not matter.
2. Both m and n are less than 150.

Example:

Given the following 5x5 matrix:

  Pacific ~   ~   ~   ~   ~
       ~  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  *
          *   *   *   *   * Atlantic

Return:

[[0, 4], [1, 3], [1, 4], [2, 2], [3, 0], [3, 1], [4, 0]] (positions with parentheses in above matrix).

题目大意

上面一条边和左边一条边代表的是太平洋，右边一条边和下边一条边代表的是大西洋。现在告诉你水往低处流，问哪些位置的水能同时流进太平洋和大西洋？

解题方法

直接DFS求解。一般来说DFS需要有固定的起点，但是对于这个题，四条边界的每个位置都算作起点。

使用两个二维数组，分别记录每个位置的点能不能到达太平洋和大西洋。然后对4条边界进行遍历，看这些以这些边为起点能不能所有的地方。注意了，因为是从边界向中间去寻找，所以，这个时候是新的点要比当前的点海拔高才行。

最坏情况下的时间复杂度是O((M+N)*MN)，空间复杂度是O(MN)。

python代码如下：

class Solution(object):
    def pacificAtlantic(self, matrix):
        """
        :type matrix: List[List[int]]
        :rtype: List[List[int]]
        """
        if not matrix or not matrix[0]: return []
        m, n = len(matrix), len(matrix[0])
        p_visited = [[False] * n for _ in range(m)]
        a_visited = [[False] * n for _ in range(m)]
        for i in range(m):
            self.dfs(p_visited, matrix, m, n, i, 0)
            self.dfs(a_visited, matrix, m, n, i, n -1)
        for j in range(n):
            self.dfs(p_visited, matrix, m, n, 0, j)
            self.dfs(a_visited, matrix, m, n, m - 1, j)
        res = []
        for i in range(m):
            for j in range(n):
                if p_visited[i][j] and a_visited[i][j]:
                    res.append([i, j])
        return res

    def dfs(self, visited, matrix, m, n, i, j):
        visited[i][j] = True
        directions = [(-1, 0), (1, 0), (0, 1), (0, -1)]
        for dire in directions:
            x, y = i + dire[0], j + dire[1]
            if x < 0 or x >= m or y < 0 or y >= n or visited[x][y] or matrix[x][y] < matrix[i][j]:
                continue
            self.dfs(visited, matrix, m, n, x, y)

C++代码如下：

class Solution {
public:
    vector<pair<int, int>> pacificAtlantic(vector<vector<int>>& matrix) {
        if (matrix.empty() || matrix[0].empty()) return {};
        const int M = matrix.size();
        const int N = matrix[0].size();
        vector<vector<bool>> p_visited(M, vector<bool>(N));
        vector<vector<bool>> a_visited(M, vector<bool>(N));
        for (int i = 0; i < M; ++i) {
            dfs(matrix, p_visited, i, 0);
            dfs(matrix, a_visited, i, N - 1);
        }
        for (int j = 0; j < N; ++j) {
            dfs(matrix, p_visited, 0, j);
            dfs(matrix, a_visited, M - 1, j);
        }
        vector<pair<int, int>> res;
        for (int i = 0; i < M; ++i) {
            for (int j = 0; j < N; ++j) {
                if (p_visited[i][j] && a_visited[i][j]) {
                    res.push_back({i, j});
                }
            }
        }
        return res;
    }
    void dfs(vector<vector<int>>& matrix, vector<vector<bool>>& visited, int i, int j) {
        const int M = matrix.size();
        const int N = matrix[0].size();
        visited[i][j] = true;
        vector<pair<int, int>> dirs = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}};
        for (auto d : dirs) {
            int nx = i + d.first;
            int ny = j + d.second;
            if (nx >= 0 && nx < M && ny >= 0 && ny < N && !visited[nx][ny] && matrix[nx][ny] >= matrix[i][j]) {
                dfs(matrix, visited, nx, ny);
            }
        }
    }
};

参考资料：

https://leetcode.com/problems/pacific-atlantic-water-flow/discuss/90739/Python-DFS-bests-85.-Tips-for-all-DFS-in-matrix-question./181815

日期

2018 年 10 月 1 日 —— 欢度国庆！