Count Nodes in a Line Network through Neighbor Messages

Nodes form a left-to-right network. Each node can call isLeftMost() and isRightMost(), sendMessageToLeft(message), and sendMessageToRight(message), and receives messages through receiveMessageFromLeft(message) and receiveMessageFromRight(message). Design a protocol that lets any node answer a request for the total number of nodes. ### Clarifying Questions Clarify whether the topology is a finite static line, whether messages are reliable and ordered, and whether nodes or links can fail. For the baseline, choose a connected static line, reliable eventual delivery, and a single initialization epoch. No shared-memory traversal API is available. Discuss initialization separately from the latency of later cached queries. ### What a Strong Answer Covers A concrete message protocol, boundary behavior, initialization readiness, message and time complexity, and the conditions under which a cached total remains valid. ### Follow-up Questions - How would a new node or failed link invalidate the cached count? - How would query handling change before initialization finishes?