# Keys and Rooms

## Problem Highlights

Understand what the interviewer is asking for by using test cases and questions about the problem.

• Established a set (2-3) of test cases to verify their own solution later.
• Established a set (1-2) of edge cases to verify their solution handles complexities.
• Have fully understood the problem and have no clarifying questions.
• Have you verified any Time/Space Constraints for this problem?

## 1: U-nderstand

• How do we keep track of the rooms? Does the set begin at room 0? If so, should I add 0 to the visited set?
• What if the room has not been visited yet? "If the key is not visited yet, add the key to visited and recursively visit keys in that room, otherwise do not visit the room again."
• When do we know all rooms are visited? "We can visit all rooms only when the size of visited set equals to the size of the rooms."
• What if inputs are too large? "If input is too large, DFS might cause stack overflow."
• How would you use DFS to see which rooms can be reached from room 0?
``````  HAPPY CASE
Input: [[1],[2],[3],[]]
Output:	true

EDGE CASE
Input: [[2], [], [1]]
Output: false``````

## 2: M-atch

Match what this problem looks like to known categories of problems, e.g. Linked List or Dynamic Programming, and strategies or patterns in those categories.

``````To apply a graph algorithm for this problem, here are things we want to consider are:
``````
• BFS/DFS: Think about a BFS queue or a DFS stack approach, or even a DFS recursion approach here. The DFS can be implemented in Recursion or the classic iterative approach with the help of a stack. We would need a hash set e.g. unordered_set to remember the rooms that we have been to. Then, as long as we are in the room, we can depth first search the rooms whose keys are in the room. Once the search is finished, we can count the number of the keys in the set, and compare to the number of the rooms.
• Adjacency List: We can use an adjacency list to store the graph, especially when the graph is sparse.
• Adjacency Matrix: We can use an adjacency matrix to store the graph, but a sparse graph will cause an unneeded worst-case runtime.
• Topological Sort: We can use topological sort when a directed graph is used and returns an array of the nodes where each node appears before all the nodes it points to. In order to have a topological sorting, the graph must not contain any cycles.
• Union Find: Are there find and union operations here? Can you perform a find operation where you can determine which subset a particular element is in? This can be used for determining if two elements are in the same subset. Can you perform a union operation where you join two subsets into a single subset? Can you check if the two subsets belong to same set? If no, then we cannot perform union.

## 3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea: Use a stack to store previous operator/operand combinations and compute the answer as we go.

1. create a hashmap to hold graph that it will be a map of Integer: [], because we will insert room: [list of keys]
2. build the map from the given list of lists
3. create a boolean array to say whether a room is visited
4. iterate over each room, perform DFS.
5. for each room, push it onto stack
6. while we still have rooms on stack (current room or rooms we could go to using the keys that we will find.
7. finally, we iterate over all the rooms and see if we have any unvisited rooms

⚠️ Common Mistakes

• What if we start at the beginning and push the values into some array, then visit the cells of those inner values and push their values into the array, as well. We should end up with an array of length rooms.length if we get all the keys.
• Once DFS has completed (it will stop running once it can't find any more unvisited rooms), we check to see if its size is equal to the length of the rooms array.

## 4: I-mplement

Implement the code to solve the algorithm.

``````class Solution(object):
def canVisitAllRooms(self, rooms):
seen = [False] * len(rooms)
seen[0] = True
stack = [0]
#At the beginning, we have a todo list "stack" of keys to use.
#'seen' represents at some point we have entered this room.
while stack:  #While we have keys...
node = stack.pop() # get the next key 'node'
for nei in rooms[node]: # For every key in room # 'node'...
if not seen[nei]: # ... that hasn't been used yet
seen[nei] = True # mark that we've entered the room
stack.append(nei) # add the key to the todo list
return all(seen) # Return true iff we've visited every room``````
``````class Solution {
public boolean canVisitAllRooms(List<List<Integer>> rooms) {
boolean[] seen = new boolean[rooms.size()];
seen[0] = true;
Stack<Integer> stack = new Stack();
stack.push(0);

// at the beginning, we have a todo list "stack" of keys to use.
while (!stack.isEmpty()) { // While we have keys...
int node = stack.pop(); // Get the next key 'node'
for (int nei: rooms.get(node)) // For every key in room # 'node'...
if (!seen[nei]) { // ...that hasn't been used yet
seen[nei] = true; // mark that we've entered the room
stack.push(nei); // add the key to the todo list
}
}

for (boolean v: seen)  // if any room hasn't been visited, return false
if (!v) return false;
return true;
}
}``````

## 5: R-eview

Review the code by running specific example(s) and recording values (watchlist) of your code's variables along the way.

• Trace through your code with an input to check for the expected output
• Catch possible edge cases and off-by-one errors and verify the code works for the happy and edge cases you created in the “Understand” section

## 6: E-valuate

Evaluate the performance of your algorithm and state any strong/weak or future potential work.

• Time Complexity: The time complexity for this algorithm is `O(N + K)`, where `N` is the number of rooms and `K` is the number of Keys.
• Space Complexity: The space complexity is `O(N)` since we are using a list to store the visited rooms list.