Consider the following undirected binary tree T with 17 vertices. Starting with the root vertex a, we can use Breadth-First Search (BFS) or Depth-First Sea (DFS) to pass through all of the vertices in this tree. Whenever we have more than one option, we always pick the vertex that appears earlier in alphabet. For example, from vertex a, we go to b instead of c. Clearly explain the difference between Breadth-First Search and Depth-First Search, and det mine the order in which the 17 vertices are reached using each algorithm.

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).

Proper Answer

Consider the following graph. If we run breadth first search on this graph starting at any vertex, which one of the following is a possible order for visiting the nodes?    NQMPOR QMNPOR MNOPQR QMNPRO   Assume the following adjacency list for a graph. After you draw the graph, what is the path to reach D from A. Vertex          Edges A      --------> B, C B      --------> C C      --------> B, E D      --------> B E      --------> B, D   Both (B) and (C) A->B->C->E->D A->B->C->D A->C->E->D