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[Leetcode] Walls and Gates 墻與門

Edison / 750人閱讀

摘要:廣度優先搜索復雜度時間空間思路實際上就是找每個房間到最近的門的距離,我們從每個門開始,廣度優先搜索并記錄層數就行了。這題要注意剪枝,如果下一步是門或者下一步是墻或者下一步已經訪問過了,就不要加入隊列中。

Walls and Gates

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
廣度優先搜索 復雜度

時間 O(NM) 空間 O(N)

思路

實際上就是找每個房間到最近的門的距離,我們從每個門開始,廣度優先搜索并記錄層數就行了。如果某個房間之前被標記過距離,那就選擇這個距離和當前距離中較小的那個。這題要注意剪枝,如果下一步是門或者下一步是墻或者下一步已經訪問過了,就不要加入隊列中。否則會超時。

代碼
public class Solution {
    public void wallsAndGates(int[][] rooms) {
        if(rooms.length == 0) return;
        for(int i = 0; i < rooms.length; i++){
            for(int j = 0; j < rooms[0].length; j++){
                // 如果遇到一個門,從門開始廣度優先搜索,標記連通的節點到自己的距離
                if(rooms[i][j] == 0) bfs(rooms, i, j);
            }
        }
    }
    
    public void bfs(int[][] rooms, int i, int j){
        Queue queue = new LinkedList();
        queue.offer(i * rooms[0].length + j);
        int dist = 0;
        // 用一個集合記錄已經訪問過的點
        Set visited = new HashSet();
        visited.add(i * rooms[0].length + j);
        while(!queue.isEmpty()){
            int size = queue.size();
            // 記錄深度的搜索
            for(int k = 0; k < size; k++){
                Integer curr = queue.poll();
                int row = curr / rooms[0].length;
                int col = curr % rooms[0].length;
                // 選取之前標記的值和當前的距離的較小值
                rooms[row][col] = Math.min(rooms[row][col], dist);
                int up = (row - 1) * rooms[0].length + col;
                int down = (row + 1) * rooms[0].length + col;
                int left = row * rooms[0].length + col - 1;
                int right = row * rooms[0].length + col + 1;
                if(row > 0 && rooms[row - 1][col] > 0 && !visited.contains(up)){
                    queue.offer(up);
                    visited.add(up);
                }
                if(col > 0 && rooms[row][col - 1] > 0 && !visited.contains(left)){
                    queue.offer(left);
                    visited.add(left);
                }
                if(row < rooms.length - 1 && rooms[row + 1][col] > 0 && !visited.contains(down)){
                    queue.offer(down);
                    visited.add(down);
                }
                if(col < rooms[0].length - 1 && rooms[row][col + 1] > 0 && !visited.contains(right)){
                    queue.offer(right);
                    visited.add(right);
                }
            }
            dist++;
        }
    }
}

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