Introduction to Algorithms
Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 22.1, Problem 2E
Program Plan Intro

To give an adjacency-list representation for a complete binary tree on 7 vertices and an equivalent adjacency-matrix representation.

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Let B be a binary tree. If for each of its vertices v the data item inserted in v is greater than the data item inserted in the left son of the vertex v and at the same time smaller than the data item inserted in the right son of the vertex v, then B is a search tree. Prove that if G is a tree, then its vertex with maximum eccentricity is a leaf.
A complete binary tree is a graph defined through the following recur- sive definition. Basis step: A single vertex is a complete binary tree.Inductive step: If T1 and T2 are disjoint complete binary trees with roots r1, r2, respectively, the graph formed by starting with a root r, and adding an edge from r to each of the vertices r1,r2 is also a complete binary tree.The set of leaves of a complete binary tree can also be defined recursively.Basis step: The root r is a leaf of the complete binary tree with exactly one vertex r.Inductive step: The set of leaves of the tree T built from trees T1, T2 is the union of the sets of leaves of T1 and the set of leaves of T2. The height h(T ) of a binary tree is defined in the class.Use structural induction to show that L(T), the number of leaves of a complete binary tree T , satisfies the following inequality L(T) ≤ 2^h(T).
BFS on a connected undirected graph G yields a depth-first tree T. G becomes a tree if we eliminate all edges that intersect T.
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