# 286 Walls and Gates

## 286. Walls and Gates

## 1. Question

You are given am x n2D grid initialized with these three possible values.

1. `-1`- A wall or an obstacle.
2. `0`- A gate.
3. `INF`- Infinity means an empty room. We use the value`2^31- 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 itsnearestgate. 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
```

## 2. Implementation

**(1) BFS**

```java
class Solution {
    public void wallsAndGates(int[][] rooms) {
        if (rooms == null || rooms.length == 0 || rooms[0].length == 0) {
            return;
        }

        int m = rooms.length, n = rooms[0].length;
        Queue<int[]> queue = new LinkedList<>();

        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (rooms[i][j] == 0) {
                    queue.add(new int[] {i, j});
                }
            }
        }

        int[][] directions = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}};

        while (!queue.isEmpty()) {
            int[] cell = queue.remove();
            int curRow = cell[0], curCol = cell[1];

            for (int[] direction : directions) {
                int nextRow = curRow + direction[0];
                int nextCol = curCol + direction[1];

                if (isValid(rooms, nextRow, nextCol)) {
                    rooms[nextRow][nextCol] = rooms[curRow][curCol] + 1;
                    queue.add(new int[] {nextRow, nextCol});
                }
            }
        }
    }

    public boolean isValid(int[][] matrix, int nextRow, int nextCol) {
        return nextRow >= 0 && nextRow < matrix.length && nextCol >= 0 && nextCol < matrix[0].length && matrix[nextRow][nextCol] == Integer.MAX_VALUE;
    }
}
```

## 3. Time & Space Complexity

BFS: 时间复杂度O(mn), 空间复杂度O(mn)


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