Medium
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
这道题看起来就知道要用BFS,但是写起来还是卡住了，不知道该怎么像number of islands那样一个一个吃掉岛，一层一层蔓延来计算到gate的最短距离。看了答案还是觉得写得比较巧妙，把关注点放在了gate身上而不是一个一个INFI也就是empty space. 再次重复一下最基本的东西：BFS用Queue, BFS用Queue, BFS用Queue.
我们先把所有的gate offer到queue里，然后开始poll. 我们每次poll()的时候，要观察上下左右四个方向的元素（BFS里常见的步骤），如果元素为INFI,也就是empty rooms,那么我们就知道了该点到gate的最短距离肯定是1（因为我们从gate出发，向上下左右四个方向只走了1步）。那么我们更新该点的值为rooms[i][j] + 1.其实这时候就是更新为1， 但为什么我们不直接写1呢？后面即将揭晓。更新完之后，我们要把该点offer到queue里。实际上，该点就构成了其他点通向gate的一条path。
当我们把gate都poll完之后，继续poll出来的点就是刚才我们遇到的INFI更新后的点。当我们poll他们时，同样也继续访问他们周围的四个点，如果遇到INFI也就是empty space, 我们继续更新周围这些点到gate的距离。这时候就应该更新为rooms[i][j] + 1而不是1. 因为现在的中心点并不是gate,也是可以通往gate的empty space.这个周围的点要通往gate,就需要先到这个中心点，再走到gate,所以是rooms[i][j] + 1.
class Solution {
//shortest path
public void wallsAndGates(int[][] rooms) {
if (rooms == null || rooms.length == 0){
return;
}
int n = rooms.length;
int m = rooms[0].length;
Queue<int[]> queue = new LinkedList<>();
//first offer all gates to the queue
for (int i = 0; i < n; i++){
for (int j = 0; j < m; j++){
if (rooms[i][j] == 0){
queue.offer(new int[] {i, j});
}
}
}
while (!queue.isEmpty()){
int[] curt = queue.poll();
int row = curt[0];
int col = curt[1];
//first, check the up, down, left, right of the gate, if the value of that grid is INF, we know now the closest
//path to a gate is 1, or in general rooms[i][j] + 1. Then we add this grid to the queue, it's not IFNI anymore.
//When we poll out this grid to the queue, we will check its up, down, left, right, and if the value of these
//grid is IFNI, we know we can get to the gate from this spot through what we polled out from the queue, and the
//total path is just 1 more.
if (row > 0 && rooms[row - 1][col] == Integer.MAX_VALUE){
rooms[row - 1][col] = rooms[row][col] + 1;
queue.offer(new int[]{row - 1, col});
}
if (row < n - 1 && rooms[row + 1][col] == Integer.MAX_VALUE){
rooms[row + 1][col] = rooms[row][col] + 1;
queue.offer(new int[]{row + 1, col});
}
if (col > 0 && rooms[row][col - 1] == Integer.MAX_VALUE){
rooms[row][col - 1] = rooms[row][col] + 1;
queue.offer(new int[]{row, col - 1});
}
if (col < m - 1 && rooms[row][col + 1] == Integer.MAX_VALUE){
rooms[row][col + 1] = rooms[row][col] + 1;
queue.offer(new int[]{row, col + 1});
}
}
}
}
这道题还可以用DFS做，先遍历整个rooms, 找到所有的gate进行DFS搜索。搜索前进行边界判断（DFS常用），注意一下这里的d值
