ta2_sol - COMP 271H Design and Analysis of Algorithms 2006...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
COMP 271H Design and Analysis of Algorithms 2006 Fall Semester Tutorial 2 Solution 1. You are given a set S of n points in the plane. p S , we use p x and p y to denote its x - and y -coordinates. We assume that p x = q x and p y = q y for any two points p, q S . A point p S is maximal if for any other point q S , q x < p x or q y < p y . Design a divide-and-conquer algorithm to compute the maximal points in O ( n log n ) time. Idea: We first sort S in increasing order of x-coordinates. In our divide-and-conquer algorithm, we divide these points into a left point set and a right point, solve them recursively, and combine these two partial solutions. We claim that this combined solution is the solution we want to compute. Observations: (Note: Observation is just used to guide you thinking, it won’t be included in the solution. But it may help in the correctness proof.) First, what these partial solutions look like? Since we have pre-sorted S in the very beginning, we may assume that the partial point list in increasing order of x-coordinates.
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern