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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.
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.
Addition and Subtraction of numbers in binary and round to the nearest decimal number with three significant decimal digits
Give an example of a graph in which every node is pivotal for at least two different pairs of nodes. Explain your answer.
Solve the following recurrence relations by the method of your choiceT(n) = 1 for n = 4 and T(n) =pnT(pn) + n for n > 4. Argue that the solution to the recurrence T(n) = T(n=3) + T(2n=3) + cn is (n lg n) by appealing to the recursion tree.
Find the Minimum Cost Path from a designated start node to a designated destination node in a graph.
Describe sorting algorithms and how they work
The recent discovery of the following fragment of uncommented procedural C code in the Sunlab has caused a big scandal. What is the worst-case time complexity of foo(a,1,N,k), and for which inputsdoes it occur?
Give an algorithm to decide whether the language recognized by a DFA is empty. Given two DFAs M1 and M2, give an algorithm to decide whether L(M1)subset or equal to L(M2).
Devise an algorithm that generates an access control matrix A for any given history matrix H of the Chinese Wall model. A significant portion of the grade for this problem involves your justification of your algorithm.
Write down the sample code to create a Linked List and allocate storage space for a node Write down the algorithm to insert an item At the beginning of a linked list
Design an algorithm that will receive two integer items from a terminal operator, and display to the screen their sum, difference, product and quotient.
Write a C++ program to find the intersection, A set is a collection of distinct entities regarded as a unit, being either individually specified or (more usually) satisfying specified conditions.
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