Problem 1: Answer TRUE or sc False. 1. The root of a binary scarch tree is the median of the elements stored in the tree. 2. An AVL tree with n elements has height O(log 3. If a directed graph G contains cycles then the DFS-based topological sort algorithm described in class (and in Section 22.4 of the book) produces a vertex ordering that minimizes the number of "bad" edges, .e. edges that are inconsistent with the ordering produced by the algorithm. in a leaf Problem 2: Consider a binary scarch tree. Assume that you scarch for value r, and you find Consider the following three sets: .A the set of nodes to the left of the path from the root to B the path from the root to a C the set of nodes to the right of the path from the root to ar Show a counterexample to the following statement: for every a E A, bE B and cE C we have a Sbsc Problem 3: The transpose of a directed graph G = (V,E) is the graph G: (V, ET) such that (u, u) e ET if and only if (v, u) E E and (, w) EE.In other words GT is G with all its edges reversed. Show how to compute GT when given G in either adjacency-list or adjacency-matrix representation