Problem description:

There are N rooms and you start in room 0. Each room has a distinct number in 0, 1, 2, ..., N-1, and each room may have some keys to access the next room.

Formally, each room i has a list of keys rooms[i], and each key rooms[i][j] is an integer in [0, 1, ..., N-1] where N = rooms.length. A key rooms[i][j] = v opens the room with number v.

Initially, all the rooms start locked (except for room 0).

You can walk back and forth between rooms freely.

Return true if and only if you can enter every room.

Example 1:

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Input:[[1],[2],[3],[]]
Output:true
Explanation:
We start in room 0, and pick up key 1.
We then go to room 1, and pick up key 2.
We then go to room 2, and pick up key 3.
We then go to room 3.  Since we were able to go to every room, we return true.

Example 2:

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Input:[[1,3],[3,0,1],[2],[0]]
Output:false
Explanation:We can't enter the room with number 2.

Note:

  1. 1 <= rooms.length <= 1000
  2. 0 <= rooms[i].length <= 1000
  3. The number of keys in all rooms combined is at most 3000.

Solution:

Original thought is to log status of each room. Then do bfs search

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0: not visited
1: could visited
2: visited
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class Solution:
    def canVisitAllRooms(self, rooms: List[List[int]]) -> bool:
        visited = [0]* len(rooms)
        visited[0] = 2
        q = deque()
        for i in range(len(rooms[0])):
            visited[rooms[0][i]] = 1
            q.append(rooms[0][i])
        
        while q:
            front = q.popleft()
            if visited[front] == 2:
                continue
            keys = rooms[front]
            for key in keys:
                if visited[key] == 0:
                    # next room need to visit
                    q.append(key)
                    visited[key] = 1
            visited[front] = 2
        
        for i in range(len(visited)):
            if visited[i] == 0:
                return False
        return True

More clean code to use set to check if every node is seen.

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class Solution:
    def canVisitAllRooms(self, rooms: List[List[int]]) -> bool:
        q = [0]
        seen = set(q)
        while q:
            i = q.pop()
            for j in rooms[i]:
                if j not in seen:
                    q.append(j)
                    seen.add(j)
                    if len(seen) == len(rooms): return True
        return len(seen) == len(rooms)

time complexity: $O()$
space complexity: $O()$
reference:
related problem: