CMPSC 465, Spring 2008, Homework 3
Due: Friday,February 6, in class or before noon on the following Saturday.
Problem 1.
Youare givenpoints p0,p1,...,pn,and pihas coordinates x[i], y[i]. Assume that
x[0] =y[0] =0.
a. Assume that all points other than point 0 are in quadrant I (x[i]>0 and y[i]>0)or
in quadrant III (x[i]<0 and y[i]<0). Describe howtotest if p0is extreme in this
set using O(n)steps.
b. Modify your test so it still uses O(n)steps, but it does a bit more: if p0is extreme, it
finds neighbors of p0on the polyline of the convex hull of our point set (see Figure
3.5, where p1has neighbors: p3and p6.
Problem 2.
Youhav e array of numbers A[0], ...,A[n−1], and target number t.Check if for
some i<n/2 and j≥n/2 wehav e A[i]+A[j]=t.
a. Describe areasonable brute force algorithm. What is the running time?
b. Using sorting and binary search, describe howtofind the answer in time O(nlog n).
Problem 6 on page 119.
Idonot knowhow one can reduce the number of sets to consider in brute force
approach. Instead, explain howproblem 2 can be used to reduce the time needed to
O(2n/2)(or O(n2n/2).
Problem 7 on page 119.
Additionally,explain whythe clique problem has an algorithm that runs in time
O(2n/2).
