Count Nodes in a Distributed Tree via Async Messages

Count Nodes in a Distributed Tree (Async Messaging) You are given a directed tree rooted at root. Each node represents an independent machine: You cannot directly access node.children or any global graph structure. The only way to communicate is via asynchronous messages. A primitive API is provided: sendAsyncMessage(nodeId, message): asynchronously send a message to the node with id nodeId. You must implement the following callback on every node: receiveMessage(fromNodeId, message): invoked when this node receives a message from fromNodeId. Goal Design a message protocol and node-side logic so that when a counting request is initiated from root, the root outputs the total number of nodes in the entire tree. Requirements All traversal and aggregation must be done through sendAsyncMessage/receiveMessage. You must define the message format to distinguish requests vs responses. Each node maintains per-request intermediate state (e.g., pending children, partial aggregates). The root prints/returns the final answer after it has collected all subtree results. I/O (per counting run) Input: rootId; and all nodes have receiveMessage registered. Output: root prints/returns an integer total node count. Assumptions Number of nodes N up to 1e5. Depth can be large. Messages may arrive concurrently. Example topology 1 -> {2,3}, 2 -> {4,5}, 3 -> {6} Expected output: 6 Example Input root=1, edges: 1->[] Output 1