Chapter 11: Q45E (page 757)
Draw the first seven rooted Fibonacci trees.
Short Answer
\({T_1}\)is 0 .
\({T_2}\)is0 .
Chapter 11: Q45E (page 757)
Draw the first seven rooted Fibonacci trees.
\({T_1}\)is 0 .
\({T_2}\)is0 .
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Get started for freeIn Exercises 2โ6 find a spanning tree for the graph shown byremoving edges in simple circuits.
a) How many edges does a tree with \({\bf{n}}\) vertices have?
b) What do you need to know to determine the number of edges in a forest with \({\bf{n}}\) vertices?
How many comparisons are needed to locate or to addeach of these wordsin the search tree for Exercise 1, starting fresh each time?
a) pear
b) banana
c) kumquat
d) orange
What is wrong with the following โproofโ using mathematical induction of the statement that every tree with \({\bf{n}}\) vertices has a path of length \({\bf{n - 1}}\). Basis step: Every tree with one vertex clearly has a path of length \(0\). Inductive step: Assume that a tree with \({\bf{n}}\) vertices has a path of length \({\bf{n - 1}}\), which has \({\bf{u}}\) as its terminal vertex. Add a vertex \({\bf{v}}\) and the edge from \({\bf{u}}\)to \({\bf{v}}\). The resulting tree has \({\bf{n + 1}}\) vertices and has a path of length \({\bf{n}}\). This completes the inductive step.
Explain how to use breadth-first search to find the length of a shortest path between two vertices in an undirected graph.
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