Hi,

I came with this subproblem while working on something else. Can someone help me understand if it's solvable problem ?

Difficulty: Hard++

Design a data structure that maintains an directed graph. A node with node_id=0 is created by default, having no edges. The data-structure supports following queries:

Create() : Create a new node, with node_id assigned from an auto-incrementing counter. Add a directed edge from node-0 to this new node; return node_id of new node.

Add(x, y) : Add a directed edge from node-x to node-y. Ignore if there is already an edge from x to y.

Delete(x, y) : Delete the directed edge from node-x to node-y, and also delete all the nodes (and their edges) of graph which are not reachable from node-0. return the list of deleted edges and nodes.

All APIs should work in amortized complexity O(log(N)) , where N is the number of nodes in the graph at the time of query.