Suppose that you are implementing a DFS graph traversal, but the class implementing graph nodes does not support node marking. You decide to use an

AVL$-$tree to implement node marking. You start with an empty tree. To mark

a node as visited, you insert it into the tree. A node is unmarked if it is not

in the tree, and marked if it is in the tree. Assume graph is represented as an

adjacency list, you mark only nodes, not edges. Let m be the number of edges,

n the number of nodes. What is the best characterization of the worst$-$case

asymptotic complexity of DFS in this case?