Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 7.3, Problem 1E
Program Plan Intro
To explain the reason of analyzing the expected running time of a randomized
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Describe the worst-case running-time function of the following algorithms:
When the order of increase of an algorithm's running time is N log N, the doubling test leads to the hypothesis that the running time is a N for a constant a. Isn't that an issue?
SIMULATION AND MODELING
Using the mid- square method obtain the random variables using Z0= 1009 until the cycle degenerates to zero.
Chapter 7 Solutions
Introduction to Algorithms
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- Given a program designed to calculate rocket trajectories, the algorithm has an O(2n) complexity and takes 1 second for each iteration, and n = 15. How many hours will it take to calculate the trajectories, worst case?arrow_forwardan iterative algorithm for separating n VLSI chips into those that are good and those that are bad by testing two chips at a time and learning either that they are the same or that they are different. To help, at least half of the chips are promised to be good. Now design (much easier) a randomized algorithm for this problem. Here are some hints.Randomly select one of the chips. What is the probability that the chip is good? How can you learn whether or not the selected chip is good? If it is good, how can you easily partition the chips into good and bad chips? If the chip is not good, what should your algorithm do? When should the algorithm stop? What is the expected running time of this algorithm?arrow_forwardHow can we tweak virtually any algorithm to work well?arrow_forward
- The time complexity of an algorithm gives an indication of the amount of time the algorithm will take to run completely. (a) Is the time complexity of an algorithm based on the best-case or the worst-case scenario of the Algorithm?arrow_forwardUpdate all JAVA methods of Cohen Sutherland line clipping algorithm if region code (RLAB). (Where L=left, R=right, B=bottom, A=Above; for example: Left point = (0100), Left-above point = (0110)Jand also write JAVA method for polygon clipping. Answer:arrow_forwardFind the Worst case time Complexity of the following recursive functions T(n) = T(n/2)+n-1, T(1) = 0arrow_forward
- with n=6 and A=(3,5,4,1,3,2). Draw the corresponding walkthrough as shownarrow_forwardSuppose that I searched for a number x in a sorted list of n items by comparing against the 5th item, then the 10th, then the 15th, etc. until I found an item bigger than x, and then I searched backwards from that point. Which expression best describes the approximate running time of this algorithm:arrow_forwardWhen the order of growth of the running time of an algorithm is N log N, the doubling test will lead to the hypothesis that the running time is ~ a N for a constant a. Isn’tthat a problem?arrow_forward
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