841 Keys and Rooms 钥匙和房间
Description:
There are n rooms labeled from 0 to n - 1 and all the rooms are locked except for room 0. Your goal is to visit all the rooms. However, you cannot enter a locked room without having its key.
When you visit a room, you may find a set of distinct keys in it. Each key has a number on it, denoting which room it unlocks, and you can take all of them with you to unlock the other rooms.
Given an array rooms where rooms[i] is the set of keys that you can obtain if you visited room i, return true if you can visit all the rooms, or false otherwise.
Example:
Example 1:
Input: rooms = [[1],[2],[3],[]]
Output: true
Explanation:
We visit room 0 and pick up key 1.
We then visit room 1 and pick up key 2.
We then visit room 2 and pick up key 3.
We then visit room 3.
Since we were able to visit every room, we return true.
Example 2:
Input: rooms = [[1,3],[3,0,1],[2],[0]]
Output: false
Explanation: We can not enter room number 2 since the only key that unlocks it is in that room.
Constraints:
n == rooms.length
2 <= n <= 1000
0 <= rooms[i].length <= 1000
1 <= sum(rooms[i].length) <= 3000
0 <= rooms[i][j] < n
All the values of rooms[i] are unique.
题目描述:
有 N 个房间，开始时你位于 0 号房间。每个房间有不同的号码：0，1，2，...，N-1，并且房间里可能有一些钥匙能使你进入下一个房间。
在形式上，对于每个房间 i 都有一个钥匙列表 rooms[i]，每个钥匙 rooms[i][j] 由 [0,1，...，N-1] 中的一个整数表示，其中 N = rooms.length。 钥匙 rooms[i][j] = v 可以打开编号为 v 的房间。
最初，除 0 号房间外的其余所有房间都被锁住。
你可以自由地在房间之间来回走动。
如果能进入每个房间返回 true，否则返回 false。
示例 :
示例 1：
输入: [[1],[2],[3],[]]
输出: true
解释:
我们从 0 号房间开始，拿到钥匙 1。
之后我们去 1 号房间，拿到钥匙 2。
然后我们去 2 号房间，拿到钥匙 3。
最后我们去了 3 号房间。
由于我们能够进入每个房间，我们返回 true。
示例 2：
输入：[[1,3],[3,0,1],[2],[0]]
输出：false
解释：我们不能进入 2 号房间。
提示:
1 <= rooms.length <= 1000
0 <= rooms[i].length <= 1000
所有房间中的钥匙数量总计不超过 3000。
思路:
BFS
用一个 bool 数组 visited 记录访问过的位置
所有位置都被访问则是可以用钥匙打开
时间复杂度为 O(n), 空间复杂度为 O(n)
代码:
C++:
class Solution
{
private:
void dfs(int key, const vector<vector<int>>& rooms, vector<bool>& visited)
{
if (visited[key]) return;
visited[key] = true;
for (int key : rooms[key]) dfs(key, rooms, visited);
}
public:
bool canVisitAllRooms(vector<vector<int>>& rooms)
{
vector<bool> visited(rooms.size());
dfs(0, rooms, visited);
for (int i : visited) if (!i) return false;
return true;
}
};
Java:
class Solution {
public boolean canVisitAllRooms(List<List<Integer>> rooms) {
boolean visited[] = new boolean[rooms.size()];
dfs(0, rooms, visited);
for (boolean i : visited) if (!i) return false;
return true;
}
private void dfs(int key, List<List<Integer>> rooms, boolean[] visited) {
if (visited[key]) return;
visited[key] = true;
for (int keys : rooms.get(key)) dfs(keys, rooms, visited);
}
}
Python:
class Solution:
def canVisitAllRooms(self, rooms: List[List[int]]) -> bool:
visited = [False] * len(rooms)
def dfs(i: int) -> None:
if visited[i]:
return
visited[i] = True
for key in rooms[i]:
if not visited[key]:
dfs(key)
dfs(0)
return all(visited)
