Keys and Rooms
Explanation & Solution
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 visit room i, return true if you can visit all the rooms, or false otherwise.
Examples
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 cannot enter room 2 since the only key that unlocks it is in room 2 itself.
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.
Approach
Graphs pattern
1. Start from Room 0
- Room 0 is always unlocked, so we begin there.
- Use a stack (DFS) or queue (BFS) to track which rooms to visit next.
- Use a Set to track which rooms we have already visited.
2. Collect Keys and Explore
- Pop a room from the stack.
- If we have already visited it, skip it.
- Otherwise, mark it as visited and add all its keys (unvisited rooms) to the stack.
3. Check if All Rooms Were Visited
- After the stack is empty, compare the size of the visited set to the total number of rooms.
- If they are equal, we visited every room — return true.
- Otherwise, return false.
Key Insight
- This problem is a graph traversal question in disguise. Each room is a node and each key represents a directed edge. Starting from node 0, we need to determine if all nodes are reachable — a classic DFS/BFS connectivity check.
Visualization
Press play to start bfs traversal