Pens/pencils and a math calculator along with this exampaper are only 
allowed on the table.  No scratch paper; use the rear of an 
exam page that is blank and mark it properly. 
Do not detach pages of this exampaper.

ALERT: Mobile phones, devices, including wearables
connected to phones (e.g. iwatch, hearing aids or attachments) 
SHOULD NOT BE ON YOU. 
They must be powered down (equivalent to removing the battery) 
and put securely in a backpack or bag that should be 
closed/zippered. Read the Syllabus clause on devices. 
 FOOD/DRINKS are not allowed per NJIT regulations.

NOTE: Give an algorithm means, 
present the algorithm (pseudocode or english), 
show that it works as claimed, and analyze its 
running time by providing an asymptotically tight bound or
as instructed.  
In some cases, you may be asked explicitly to provide a 
tight exact answer in terms of a fundamental operation.

Efficient means an algorithm whose performance 
(space or time or both) cannot be improved upon 
asymptotically.
Time efficient means asymptotic time efficiency 
cannot be improved upon.
Space efficiency is to be interpreted likewise.
Comparison efficient means the number of comparisons cannot 
be improved upon and thus constants are important for 
higher-order terms: thus $\Theta (n)$ is worse than $3n$,  
and $3n$ is worse than say $2n+o(n)$.

Use T(.) for running time, S(.) for space resources, 
and C(.) for comparison counts with the choice of 
parameter(s) as needed.
}
$INCR = \langle 1, 2, ... , n-1, n \rangle$ is the sorted 
sequence of the first n positive integers starting with 1.


$DECR = \langle n, n-1, ... , 2, 1 \rangle$ is the reverse 
sorted sequence of the first n positive integers starting with n.


CLASS RESUMES FIVE MINUTES after EXAM PICK-UP