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Suppose you have one machine and a set of n jobs a1 , a2 , · · · , an to process on that machine. Each job aj has a processing time tj , a pro?t pj , and a deadline dj . The machine can process only one job at a time, and job aj must run uninterruptedly for tj consecutive time units. If job aj is completed by its deadline dj , you receive a profit pj , but if it is completed after its deadline, you receive a profit of 0. Give an algorithm to find the schedule that obtains the maximum amount of profit, assuming that all processing times are integers between 1 and n.
Illustrate that if you were given a polynomial time algorithm for determining whether two rooted directed acyclic graphs are isomorphic, then polynomial time algorithm for testing.
Implement a queue as a circular array as follows: Use two index variables head and tail that contain the index of the next element to be removed and the next element to be added.
Implement the following algorithm for the evaluation of arithmetic expressions. Each operator has a precedence. The + and - operators have the lowest precedence.
Design an algorithm and souce code C++ that will read a file of employee records and produce a weekly report of gross earnings for those employees.
The problem is to assign each skier a ski to minimize the average difference between height of a skier and his/her ski. Give pseudocode and write its asymptotic running time.
Make a list of some of the common data structures provided by C#. You should have a minimum of 4 different data types.
Look up each test item in array of member items, by using sequential search. What is the worst-case running time of it. (asymptotically, in terms of n and k)?
Calculate the worst-case run-time complexity of your algorithm and prove optimality of the solution it gives. Suppose that the road is a straight line with a western end and an eastern end.
Find the Minimum Cost Path from a designated start node to a designated destination node in a graph.
A group of ten people need to decide which one flavor of ice cream they will all order, out of three options. The algorithm can question and re-question the participants, and present the answers to the participants.
Select a specific category of vertical applications to investigate. Use the Internet and any other sources of information you might have to study some of the different products that are available in that category.
Design an algorithm to solve the Spectral Assembly problem under the above conditions. Does the problem have a unique solution?
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