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Magazine Problem 1
Build a binary search tree for the words banana, peach, apple, pear, coconut, mango, and papaya using alphabetical order.
Problem 2
Build a binary search tree for the words oenology, phrenology, campanology, ornithology, ichthyology, linology, alchemy, and astrology using alphabetical order.
Problem 6
Can the leaves of an ordered rooted tree have the following list of universal addresses? If so, construct such an ordered rooted tree. a) \(1.1 .1,1.1 .2,1.2,2.1 .1 .1,2.1 .2,2.1 .3,2.2,3.1 .1\) \(3.1 .2 .1,3.1 .2 .2,3.2\) b) \(1.1,1.2 .1,1.2 .2,1.2 .3,2.1,2.2 .1,2.3 .1,2.3 .2\) 2.4.2.1, \(2.4 .2 .2,3.1,3.2 .1,3.2 .2\) c) \(1.1,1.2 .1,1.2 .2,1.2 .2 .1,1.3,1.4,2,3.1,3.2,4.1 .1 .1\)
Problem 6
Using alphabetical order, construct a binary search tree for the words in the sentence 鈥淭he quick brown fox jumps over the lazy dog.鈥�
Problem 8
How many weighings of a balance scale are needed to find a counterfeit coin among eight coins if the counterfeit coin is either heavier or lighter than the others? Describe an algorithm to find the counterfeit coin using this number of weighings.
Problem 9
How many weighings of a balance scale are needed to find a counterfeit coin among 12 coins if the counterfeit coin is lighter than the others? Describe an algorithm to find the lighter coin using this number of weighings.
Problem 10
One of four coins may be counterfeit. If it is counterfeit, it may be lighter or heavier than the others. How many weighings are needed, using a balance scale, to determine whether there is a counterfeit coin, and if there is, whether it is lighter or heavier than the others? Describe an algorithm to find the counterfeit coin and determine whether it is lighter or heavier using this number of weighings.
Problem 11
Devise an algorithm similar to Prim鈥檚 algorithm for constructing a maximum spanning tree of a connected weighted graph.
Problem 13
a) How many nonisomorphic unrooted trees are there with five vertices? b) How many nonisomorphic rooted trees are there with five vertices (using isomorphism for directed graphs)?
Problem 14
In Exercises \(13-15\) use depth-first search to produce a spanning tree for the given simple graph. Choose \(a\) as the root of this spanning tree and assume that the vertices are ordered alphabetically.
