Maximum Candies You Can Get from Boxes

Maximum Candies You Can Get from Boxes

What is this problem about?

The "Maximum Candies You Can Get from Boxes" is a complex and engaging problem that simulates a real-world puzzle. You are presented with a set of boxes, each potentially containing three things: some candies, a list of other boxes contained within it, and keys to open specific boxes. You also start with an initial set of boxes and some keys. Some boxes are "open" by default, while others are "locked" and require a key. The challenge is to collect as many candies as possible by opening all reachable and unlockable boxes. This requires careful tracking of which boxes you have in your possession and which keys you have collected.

Why is this asked in interviews?

This problem is a favorite at companies like Amazon and Google because it tests a candidate's ability to manage state and dependencies. The Maximum Candies You Can Get from Boxes interview question is essentially a reachability problem that can be modeled as a graph traversal. It evaluates whether you can handle multiple conditions (having the box AND having the key) before performing an action. It's a great test of clean coding practices and the ability to use appropriate data structures like queues and sets to avoid redundant work.

Algorithmic pattern used?

The fundamental algorithmic pattern used in this Maximum Candies You Can Get from Boxes coding problem is Breadth-First Search (BFS). Since you are exploring "levels" of boxes—opening one box to find others—BFS is the most natural fit. You maintain a queue of boxes that are both in your possession and unlocked. As you process a box, you collect its candies, add any newly found keys to your "key ring," and add any newly found boxes to your "box collection." Whenever a box becomes both "owned" and "unlocked," it gets added to the BFS queue for processing.

Example explanation?

Imagine you start with Box 1 (locked) and have Key 1.

1. You open Box 1. Inside, you find 10 candies and Box 2 (locked).
2. You also find Key 2 inside Box 1.
3. Now you have Box 2 and Key 2. You can now open Box 2.
4. Inside Box 2, you find 5 candies. Total candies collected: 15. If you had found Box 2 but never found Key 2, those 5 candies would remain unreachable. The logic requires you to constantly check if the "box possession" set and "key" set overlap to unlock new opportunities.

Common mistakes candidates make?

One of the biggest pitfalls is not handling the order of discovery correctly. A candidate might find a key after they've already "checked" a box and missed the chance to open it. To avoid this, you must have a mechanism to re-check boxes once a new key is found. Another mistake is redundant processing—adding the same box to the queue multiple times. Not using a "visited" array or set can lead to infinite loops if box dependencies were circular (though the problem usually prevents this, it's good practice).

Interview preparation tip

When dealing with state-based traversal like the graph interview pattern, always clearly define your "ready to process" criteria. In this case, a box is ready if owned[i] == true and (status[i] == 1 or hasKey[i] == true). Practice drawing out the dependencies on paper to see how the BFS flow should work. This will help you keep your logic organized when you start writing code.