Consider a sequence of real numbers (assume is even). We are interested in partitioning the numbers into pairs (that is, each of the numbers appears in exactly one of the pairs) in the following way. For each pair in the partition, compute the sum of its numbers. Denote by the sums. The goal is to find the partition that minimizes the maximum sum. (a) Describe concisely in English the idea of a brute-force algorithm for solving this problem, and provide, using big- notation, the worst-case running time of your algorithm. (b) Establish a mathematical result that will allow you to design a worst-case polynomial-time algorithm for the problem, and prove the result. (c) Describe the polynomial-time algorithm and provide, using big- notation, its worst-case running time.

Write a grading program for a class with the following grading policies: a. there are two quizzes, each graded on the basis of 10 points. b. there is one midterm exam and one final exam, each graded on the basis of 100 points. c. the final exam counts for 50% of the grade, the midterm counts for 25%, and the two quizzes together count for a total of 25%. (do not forget to normalize the quiz scores. they should be converted to a percentage before they are averaged in.) any grade of 90 or more is an a, any grade of 80 or more (but less than 90) is a b, any grade of 70 or more (but less than 80) is a c, any grade of 60 or more (but less than 70) is a d, and any grade below 60 is an f. the program will read in the student’s scores and output the student’s record, which consists of two quiz and two exam scores as well as the student’s average numeric score for the entire course and final letter grade. define and use a structure for the student reco

Atype of researcher who uses computers to make sense of complex digital data

Your mom wants to purchase a laptop computer. she said she wants her new computer to be able to play her dvds so she can listen to music and wants to know what type of optical drives will play her disk. which type of drive should she look for?