Chapter 3: Q66E (page 204)
Show that the problem of deciding whether a specific program with a specific input halts is solvable.
We can decide whether a program with a specific input halts is solvable by running the two programs and the one which halts is solvable.
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a.) Explain the concept of a greedy algorithm.
b.) Prove the example of a greedy algorithm that produces an optimal solution and explain why it produces an optimal solution.
c.) Provide an example of a greedy algorithm that does not always produce an optimal solution and explain why it fails to do so.
a) Describe an algorithm for finding the first and second largest elements in a list of integers.
b) Estimate the number of comparisons used.
Define the statement
A palindrome is a string that reads the same forward and backward. Describe an algorithm for determining whether a string of n characters is a palindrome.
a) Describe in detail (and in English) the steps of an algorithm that finds the maximum and minimum of a sequence of elements by examining pairs of successive elements, keeping track of a temporary maximum and a temporary minimum. Ifn is odd, both the temporary maximum and temporary minimum should initially equal the first term, and ifn is even, the temporary minimum and temporary maximum should be found by comparing the initial two elements. The temporary maximum and temporary minimum should be updated by comparing them with the maximum and minimum of the pair of elements being examined.
b) Express the algorithm described in part (a) in pseudocode.
c) How many comparisons of elements of the sequence are carried out by this algorithm? (Do not count comparisons used to determine whether the end of the sequence has been reached.) How does this compare to the number of comparisons used by the algorithm in Exercise 5?
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