[LeetCode] 286. Walls and Gates 墙和门

You are given a m x n 2D grid initialized with these three possible values.

-1 - A wall or an obstacle.
0 - A gate.
INF - Infinity means an empty room. We use the value 2³¹ - 1 = 2147483647 to represent INF as you may assume that the distance to a gate is less than 2147483647.

Fill each empty room with the distance to its nearest gate. If it is impossible to reach a gate, it should be filled with INF.

For example, given the 2D grid:

INF  -1  0  INF
INF INF INF  -1
INF  -1 INF  -1
  0  -1 INF INF

After running your function, the 2D grid should be:

  3  -1   0   1
  2   2   1  -1
  1  -1   2  -1
  0  -1   3   4

这道题类似一种迷宫问题，规定了 -1 表示墙，0表示门，让求每个点到门的最近的曼哈顿距离，这其实类似于求距离场 Distance Map 的问题，那么先考虑用 DFS 来解，思路是，搜索0的位置，每找到一个0，以其周围四个相邻点为起点，开始 DFS 遍历，并带入深度值1，如果遇到的值大于当前深度值，将位置值赋为当前深度值，并对当前点的四个相邻点开始DFS遍历，注意此时深度值需要加1，这样遍历完成后，所有的位置就被正确地更新了，参见代码如下：

解法一：

class Solution {
public:
    void wallsAndGates(vector<vector<int>>& rooms) {
        for (int i = 0; i < rooms.size(); ++i) {
            for (int j = 0; j < rooms[i].size(); ++j) {
                if (rooms[i][j] == 0) dfs(rooms, i, j, 0);
            }
        }
    }
    void dfs(vector<vector<int>>& rooms, int i, int j, int val) {
        if (i < 0 || i >= rooms.size() || j < 0 || j >= rooms[i].size() || rooms[i][j] < val) return;
        rooms[i][j] = val;
        dfs(rooms, i + 1, j, val + 1);
        dfs(rooms, i - 1, j, val + 1);
        dfs(rooms, i, j + 1, val + 1);
        dfs(rooms, i, j - 1, val + 1);
    }
};

那么下面再来看 BFS 的解法，需要借助 queue，首先把门的位置都排入 queue 中，然后开始循环，对于门位置的四个相邻点，判断其是否在矩阵范围内，并且位置值是否大于上一位置的值加1，如果满足这些条件，将当前位置赋为上一位置加1，并将次位置排入 queue 中，这样等 queue 中的元素遍历完了，所有位置的值就被正确地更新了，参见代码如下：

解法二：

class Solution {
public:
    void wallsAndGates(vector<vector<int>>& rooms) {
        queue<pair<int, int>> q;
        vector<vector<int>> dirs{{0, -1}, {-1, 0}, {0, 1}, {1, 0}};
        for (int i = 0; i < rooms.size(); ++i) {
            for (int j = 0; j < rooms[i].size(); ++j) {
                if (rooms[i][j] == 0) q.push({i, j});   
            }
        }
        while (!q.empty()) {
            int i = q.front().first, j = q.front().second; q.pop();
            for (int k = 0; k < dirs.size(); ++k) {
                int x = i + dirs[k][0], y = j + dirs[k][1];
                if (x < 0 || x >= rooms.size() || y < 0 || y >= rooms[0].size() || rooms[x][y] < rooms[i][j] + 1) continue;
                rooms[x][y] = rooms[i][j] + 1;
                q.push({x, y});
            }
        }
    }
};