Assuming that quick sort algorithm presented selects the first element in the list as the pivot. (A)  Give a list of n items (for example, an array of 10 integers) representing a scenario. (B)  Give a list of n items (for example, an array of 10 integers) representing the worst-case scenario. (C)  Give a list of n items (for example, an array of 10 integers) representing the best-case scenario.

Array lists and linked lists are both examples of list implementations. Give an example of a case in which an array list might be preferable over a linked list. Justify your actions in each scenario.

A singly linked list contains n - 1 strings that are binary representations of numbers from the set {0, 1,.…, n – 1} where n is an exact power of 2. However, the string corresponding to one of the numbers is missing. For example, if n = 4, the list will contain any three strings from 00, 01,10 and 11. Note that the strings in the list may not appear in any specific order. Also note that the length of each string is lgn, hence the time to compare two strings in O(lgn). Write an algorithm that generates the missing string in O(n).

The algorithm: –In an array of n elements, go to index [n/2] –If the record there is the one you want, you are done –If the record value there is smaller than your search value, all records less than the current record can be ignored – set your search range of elements to [n/2+1…n] and return to step 1 –Otherwise, set your range of elements to [0…(n/2)-1] and return to step 1 –Repeat this loop until you have 0 elements (record is not found) or record is found Short answer Another approach to the update algorithm is to perform use the delete function for the old value and if it is successful, call the insert function using the new value. Explain in your own words if you think this approach is significantly better, worse, or in the same category as the algorithm discussed in the slides, and why.

1. Write an algorithm to determine whether a given element x belongs to a set S := {s1, . . . , sn}.

Consider a situation of a boarding gate of a plane where passengers are allowed to board on the place based on their age. All passengers are on a line (queue) to board on the place, however, the oldest one is always allowed to board first no matter when he/she got in the line (queue). In this case, you cannot sort the passengers by their age, however, you know that oldest ones are always at the top of the line. This is an example of a priority queue where data will be accessed and processed based on their level of priority. Suppose you need to organize such type of data so that the data in highest priority can be accessed in a constant time, O(1). What type of data structure would you use in such cases? Justify your answer.