Given a sorted array of n comparable items A, and a search value key, return the position (array index) of key in A if it is present, or -1 if it is not present. If key is present in A, your algorithm must run in order O(log k) time, where k is the location of key in A. Otherwise, if key is not present, your algorithm must run in O(log n) time.

Consider the following algorithm that uses a sorted list of n elements (alist). What is the worst case runtime of this algorithm? for each element in alist    1. ask the user for an input, call it value    2. search value in alist using the binary search algorithm    3. if value exists in alist, print "successful"       otherwise print "unsuccessful"      Question 10 options:   O(2^n)   O(n log n)   O(log n)   O(n^2)   O(n)   O(1)

You are given k > 2 linked lists, each containing n > k natural numbers sorted in increasing order. All n · k numbers in these lists are distinct. Describe an algorithm that finds the k-th smallest element among all n k numbers. Your algorithm should run in O(k log k) time. Analyze the running time of your algorithm and prove its correctness.

For each question, an algorithm will be described that operates on N elements, and your answer should include: (a) a big-O expression that describes the total number of operations in the worst case (for ex- ample, O(N³)) (b) a description of how to achieve the same effect as the algorithm described, but achieved with a better big-O time bound (for example, "use mergesort instead of insertion sort") (c) the big-O time bound for your improved approach. Your improved algorithm does not need to be provably the best possible, but it should have a different and better big-O bound. (It may not be as simple as substituting one named algorithm for another; consider what is redundant about the work done by the existing algorithm.) You don't need to use pseudocode to describe your algorithms - the style used in the problem descriptions is also sufficient for your solutions. You can use pseudocode if you like. Do not write real code. If you wish to use an algorithm described in class, you can name…