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Question 1. Present a formal mathematical proof that an even split of an array into two subarrays results in the best performance of the quicksort algorithm (evaluated with respect to the running time). (No coding or empirical investigation required. Theoretical analysis only.)
Question 2. You have received a program implementing a pseudocode of the quicksort algorithm given on page 171 of the 3rd edition of the textbook. You can run this program but you don't have access to its code and you are not allowed to modify it. You only have access to an array to be sorted. The objective is to sort a set of numbers given in this array by applying the program you have received. Can you optimize time needed for this sorting process? If so, when and how? If your answer is positive, theoretically justify it, and support your solution with empirical results. Collect and analyze them. Report your observations and conclusions. In your report include listings of source codes of all the programs you need to produce your empirical results.
A facility consisting of eight departments has the activity relationship chart pictured in Figure. Compute the TCR for each department.
Write an algorithm that checks if an essentially complete binary tree is a heap. Analyze your algorithm and show the results using order notation.
An initial layout for five departments and a from-to flow data chart are given in Figure. Assuming that departments A and D are in fixed locations.
Is a flowchart more valuable in documenting the logic of a program than just the coded instructions in the programming language
If an arbitrary item is added to the end of an already sorted list, how much time will it take to sort the array again using insertion sort?
Assume Alice wishes to send an e-mail to Bob. Bob has a public private key pair, Alice has Bob's certificate. But Alice does not have a public, private key pair.
You need to write a program which uses binary search to search a sorted array of floating point numbers - Create an array of doubles, using the following statement. Notice that the array is sorted.
Create an algorithm or program to implement the following function: insert_in_array (element,position). The element parameter is a data item to be added.
There is no predefined limitation on the number of records (linked list needed)
Generalize the 2-3 algorithms for INSERT and DELETE to K-J trees, where non-leaf vertices have between K and J children for fixed integers K >=2, and J>= 2K-1.
Construct the project activity network using AON methodology and label each node. Identify the critical path and other paths through the network.
Give an algorithm that performs a three-way in-place partition of an N element subarray using only N- I three-way comparisons.
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