Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 33.3, Problem 5E
Program Plan Intro
To calculate the on-line convex-hull problem in the
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Let P be a set of n points in the plane. The points of P are given one point at a time. After receiving eachpoint, we compute the convex hull of the points seen so far.
(a) As a naive approach, we could run Graham’s scan once after receiving each point, with a total runningtime of O(n2log n). Write down the psuedo-code for this algorithm
Let f(x) = x¹ Hx-x¹b, where H and b are constant, independent of x, and H is
symmetric positive definite. Given vectors x0) and p0), find the value of the scalar a that
minimizes f(x0) + ap0)). This is the formula for the stepsize ak in the linear conjugate
gradient algorithm.
Determine φ (m), for m=12,15, 26, according to the definition: Check for each positive integer n smaller m whether gcd(n,m) = 1. (You do not have to apply Euclid’s algorithm.)
Chapter 33 Solutions
Introduction to Algorithms
Ch. 33.1 - Prob. 1ECh. 33.1 - Prob. 2ECh. 33.1 - Prob. 3ECh. 33.1 - Prob. 4ECh. 33.1 - Prob. 5ECh. 33.1 - Prob. 6ECh. 33.1 - Prob. 7ECh. 33.1 - Prob. 8ECh. 33.2 - Prob. 1ECh. 33.2 - Prob. 2E
Ch. 33.2 - Prob. 3ECh. 33.2 - Prob. 4ECh. 33.2 - Prob. 5ECh. 33.2 - Prob. 6ECh. 33.2 - Prob. 7ECh. 33.2 - Prob. 8ECh. 33.2 - Prob. 9ECh. 33.3 - Prob. 1ECh. 33.3 - Prob. 2ECh. 33.3 - Prob. 3ECh. 33.3 - Prob. 4ECh. 33.3 - Prob. 5ECh. 33.3 - Prob. 6ECh. 33.4 - Prob. 1ECh. 33.4 - Prob. 2ECh. 33.4 - Prob. 3ECh. 33.4 - Prob. 4ECh. 33.4 - Prob. 5ECh. 33.4 - Prob. 6ECh. 33 - Prob. 1PCh. 33 - Prob. 2PCh. 33 - Prob. 3PCh. 33 - Prob. 4PCh. 33 - Prob. 5P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Similar questions
- USING PYTHON A tridiagonal matrix is one where the only nonzero elements are the ones on the main diagonal (i.e., ai,j where j = i) and the ones immediately above and belowit(i.e.,ai,j wherej=i+1orj=i−1). Write a function that solves a linear system whose coefficient matrix is tridiag- onal. In this case, Gauss elimination can be made much more efficient because most elements are already zero and don’t need to be modified or added. Please show steps and explain.arrow_forwardsuppose a computer solves a 100x100 matrix using Gauss elimination with partial pivoting in 1 second, how long will it take to solve a 300x300 matrix using Gauss elimination with partial pivoting on the same computer? and if you have a limit of 100 seconds to solve a matrix of size (N x N) using Gauss elimination with partial pivoting, what is the largest N can you do? show all the steps of the solutionarrow_forwardMinimize the function using Karnaugh map method. F(A, B, C, D) = E(1, 2, 3, 8, 9, 10, 11, 14) + Ed(7, 15).arrow_forward
- Analyze the running time (i.e. T(n)) of these functions. You should be able to find some simple function f(n) such that T(n) O(f(n)). You should show your work and rigorously justify your an- 1. swer.arrow_forwardProve that f(n)= {floor function of sqrt(n)} - { floor function of sqrt(n-1)} is a multiplicative function, but it is not completely multiplicative.arrow_forwardThere are n ≥ 2 married couples who need to cross a river. They have a boat that can hold no more than two people at a time. To complicate matters, all the husbands are jealous and will not agree on any crossing procedure that would put a wife on the same bank of the river with another woman's husband without the wife's husband being there too, even if there are other people on the same bank. Can they cross the river under such constraints? Solve the problem for n = 2.arrow_forward
- Lets say you need to arrange seating in a club. There is a finite amount of seating, that is close to VIP seating,L. Therefore, there is a fixed amount of people you can seat near VIP. The goal is to choose a set of L seats so that the max distance between VIP seating and the partyer is minimized. Write a poly-time approximation algorithm for this problem, prove it has a specific approximation ratio.arrow_forwardAnalyze the running time (i.e. T(n)) of these functions. You should be able to find some simple function f(n) such that T(n) = Θ(f(n)). Can you find the anwer using summation and show the work for the given image please, im confused how to use summations to Analyze the running time and get Θ(f(n)). Thank you step by steparrow_forwardAbout a set X of numbers we say that it is almost sum-free if the sum of two different elements of X never belongs to X. For instance, the set {1, 2, 4} is almost sum-free. Almost-Schur number A(k) is the largest integer n for which the interval {1, . . . , n} can be partitioned into k almost sum-free sets. Use clingo to find the exact values of A(1), A(2), A(3) and try to find the largest lower bound for A(4), i.e., the largest number l such that A(4) ≥ l. Hint: you do not need to find all partitions to find the values of A(k). PLEASE USE CLINGO.arrow_forward
- Let f(n) and g(n) be asymptotically nonnegative increasing functions. Prove: (f(n) + g(n))/2 = ⇥(max{f(n), g(n)}), using the definition of ⇥ .arrow_forwardImagine a 3D plane P in your 3D scene. An infinite number of lines can lie on that plane. Consider one set of parallel lines on this 3D plane. This set will produce one vanishing point when projected on the image plane. Consider now all possible sets of parallel line on the plane P. What is the locus of all vanishing points produced by all sets of parallel lines? [Note that you do not have to right down a formula in order to solve this. You need to use a geometric argument.]arrow_forwardDraw convex hull for the following set of 10 points such as (1,1), (2,3), (2,5), (3,2), (3,5), (3,7), (3,9), (4,4), (5,2) and (6,7) using Graham Scan algorithm and explain how it overcomes the limitation found in Jarvis's March algorithm. Analyse its time complexity.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole