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1. Hillary claims that a postorder traversal of a heap will list its keys in nonincreasing order. Draw an example of a heap that proves her wrong.2. Illustrate all the steps of the adaptable...

Draw an example of a heap whose keys are all the odd numbers from 1 to 59 (with no repeats), such that the insertion of an entry with key 32 would cause up-heap bubbling to proceed all the way up to...

Give an alternative analysis of bottom-up heap construction by showing the following summation is O(1), for any positive integer h:

1. Write a program that takes as input a general tree T and a position p of T and converts T to another tree with the same set of position adjacencies, but now with p as its root.2. Write a program...

We can define a binary tree representation T′ for an ordered general tree T as follows (see Figure 8.21):• For each position p of T, there is an associated position p′ of T′ . • If p is a leaf of T,...

1. Write a program that can input and display a person’s family tree.2. Write a program that visualizes an Euler tour traversal of a proper binary tree, including the movements from node to node and...