Chapter 11: Q5E (page 755)
Is the rooted tree in Exercise \(3\) a full \({\bf{m}}\)-ary tree for some positive integer \({\bf{m}}\)?
Rooted tree is not a m-ary tree
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How many weighing’s of a balance scale are needed tofind a counterfeit coin among four coins if the counterfeit coin may be either heavier or lighter than the others?
Describe an algorithm to find the counterfeit coin using this number of weighing.
Draw the first seven rooted Fibonacci trees.
Give six examples of well-formed formulae with three or more operators in postfix notation over the set of symbols \(\left\{ {{\bf{x,y,z}}} \right\}\) and the set of operators \(\left\{ {{\bf{ + , \ast ,}} \circ } \right\}\).
a. Explain how to use preorder, in-order, and post-order traversals to find the pre-fix, in-fix, and post-fix forms of an arithmetic expression.
b. Draw the ordered rooted tree that represents \({\bf{((x - 3) + ((x/4) + (x - y)}} \uparrow {\bf{3))}}\)
c. Find the pre-fix and post-fix forms of the expression in part \(\left( {\bf{b}} \right)\).
Show that a tree with n vertices that has \({\bf{n - 1}}\) pendant vertices must be isomorphic to \({{\bf{K}}_{{\bf{1,n - 1}}}}\).
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