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Chapter 11: Q19E (page 756)

How many edges does a full binary tree with \({\bf{1000}}\) internal vertices have?

Short Answer

Expert verified

A full binary tree with internal 1000 vertices has 2000 edges.

Step by step solution

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01

Finding \({\bf{m,i}}\)

A full m-ary tree with i internal vertices has\({\bf{e = m i}}\)edges.

For the given information, \(m = 2\) and \(i = 1000\)

02

Finding the edges

So, \(e = 2 \times 1000 = 2000\)

So, a full binary tree with 1000 internal vertices have 2000 edges.

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Most popular questions from this chapter

Find the height of \({{\bf{B}}_{\bf{k}}}\). Prove that your answer is correct.

In this exercise we will develop an algorithm to find the strong components of a directed graph \({\bf{G = }}\left( {{\bf{V,E}}} \right)\). Recall that a vertex \({\bf{w}} \in {\bf{V}}\) is reachable from a vertex \({\bf{v}} \in {\bf{V}}\) if there is a directed path from v to w.

  1. Explain how to use breadth-first search in the directed graph G to find all the vertices reachable from a vertex \({\bf{v}} \in {\bf{G}}\).
  2. Explain how to use breadth-first search in \({{\bf{G}}^{{\bf{conv}}}}\) to find all the vertices from which a vertex \({\bf{v}} \in {\bf{G}}\) is reachable. (Recall that \({{\bf{G}}^{{\bf{conv}}}}\) is the directed graph obtained from G by reversing the direction of all its edges.)
  3. Explain how to use part (a) and (b) to construct an algorithm that finds the strong components of a directed graph G, and explain why your algorithm is correct.

Prove that Kruskal’s algorithm produces minimum spanning trees.

Devise an algorithm based on breadth-first search for finding the connected components of a graph.

Devise an algorithm for constructing the spanning forest of a graph based on depth-first searching.
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