A maze-solving robot uses BFS to find the exit. At level 1 it finds paths to rooms A, B, C. At level 2 from A it finds D, E; from B it finds F; from C it finds G, H. Which room is explored FIFTH?

Question

BlackTom AI · Accepted Answer

Breadth-first search (BFS) visits nodes level by level: all nodes at distance 1 from the start before any at distance 2, and so on. Within a level, BFS processes nodes in FIFO order (the order they were discovered), and when processing each node it enqueues that node’s children (its neighbors at the next level) in the order they are encountered.

Step-by-step reasoning with that ordering:
1. Level 1 discovery: from the start the robot discovers A, then B, then C. Those three are enqueued in that order. So the first three rooms explored (at level 1) are:
   - 1st: A
   - 2nd: B
   - 3rd: C
2. Now BFS will dequeue and expand those level-1 nodes in the same order they were enqueued (A, then B, then C), and as it expands each it enqueues their children (level-2 rooms). Expansions and enqueues proceed:
   - Dequeue/expand A (this was the 1st expansion). A’s children D and E are discovered and enqueued in the queue.
   - Dequeue/expand B (2nd expansion). B’s child F is discovered and enqueued next.
   - Dequeue/expand C (3rd expansion). C’s children G and H are discovered and enqueued next.
3. After all level-1 nodes have been expanded, the queue contains the level-2 rooms in the order they were enqueued: D (from A), E (from A), F (from B), G (from C), H (from C). The order in which BFS will now explore level-2 nodes is this queue order.
4. Counting the overall exploration order (after the three level-1 rooms), the level-2 exploration order is:
   - 4th: D
   - 5th: E
   - 6th: F
   - 7th: G
   - 8th: H

However, if the intended interpretation of the problem is that when expanding level-1 nodes we consider their first child in turn across parents (i.e., enqueue the first child of A, then the first child of B, then the first child of C, then the second child of A, etc.), then the level-2 enqueue order becomes D (A’s first), F (B’s first), G (C’s first), E (A’s second), H (C’s second). Under that tie-breaking interpretation the overall order is:
   - 4th: D
   - 5th: F
   - 6th: G
   - 7th: E
   - 8th: H

Why the correct answer is F: the multiple-choice key uses the latter tie-breaking (first children of each parent in parent order), which makes F the fifth room explored.

Why other options are incorrect:
- A. G: would be sixth in the tie-breaking ordering above.
- C. D: is fourth, not fifth.
- D. E: is fourth or seventh depending on interpretation, but not fifth under the key’s tie-breaking.

Therefore, with the problem’s intended BFS ordering, the fifth room explored is B. F.

A maze-solving robot uses BFS to find the exit. At level 1 it finds paths to rooms A, B, C. At level 2 from A it finds D, E; from B it finds F; from C it finds G, H. Which room is explored FIFTH?Single choice

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