Prim's minimal spanning tree algorithm makes use of a priority queue Q of vertices with an associated value on which the queue is sorted. The value on which the priority queue is ordered is the minimum weight of any edge from the vertex to a vertex already removed from Q. O True O False

Recursively, a complete binary tree is a graph. Basis step: One vertex forms a binary tree. Inductive step: If T1 and T2 are disjoint complete binary trees with roots r1, r2, respectively, the graph produced by starting with a root r and adding an edge from r to each of the vertices r1, r2 is also complete. Recursively define a complete binary tree's leaves. Base step: The full binary tree has one root, r. Inductive step: T's leaves are the union of T1's and T2's.       Class defines binary tree height h(T). Use structural induction to prove that `(T), the number of leaves of a complete binary tree T, is less than 2 h(T).

In binary search trees, how may pre-order traversal be most efficiently utilized?

Draw the binary search tree if the pre-order and in-order traversals of that binary search tree are given as below: Pre-order traversal: 7, 4, 2, 3, 6, 5, 12, 9, 8, 11, 19, 15, 20 In-order traversal: 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 19, 20