midterm1-solutions.pdf - CIS 320 – Spring 2018 02/26/18 1...

CIS 320 – Spring 2018 (02/26/18) 1
Midterm Exam 1 Solutions
Important Note: Do not distribute or share these solutions. They are strictly
for the personal use of students registered in the Spring 2018 edition of CIS
320 at University of Pennsylvania. Any violations will be referred to the Office
of Student Conduct.
Problem 1.
For each of the four subproblems problem below, a clear description of
your solution, an analysis of its time complexity, and a brief justification of your approach
is sufficient. No detailed proof of correctness is needed for problems 1a – 1d .
(a) You are given an unsorted array A that contains n positive integers. Design an O ( n )
expected time algorithm to determine whether or not all values in A are distinct.
( 10 points )
(b) You are given a sorted array A containing n distinct positive integers from the set
{ 1 , 2 , 3 , . . . , n, n + 1 } . Design an O (log n ) time algorithm that outputs the unique
value from the set which is not present in the array A . You may assume that n = 2
k
for some positive integer k . ( 10 points )

Strictly for the personal use of students registered in CIS 320, Spring 2018 at University of Pennsylvania.