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.

{\bf ALERT:} 
Mobile phones, mobile or not devices, including wearables
connected to phones or to networks  (e.g. iwatch) SHOULD NOT 
BE ON YOU or on the exam table.  They must be powered down
(equivalent to removing the battery) and put securely in 
a backpack or bag. The backpack/bag should be closed/zippered.
Read the Syllabus clause on devices.
This includes hearing aids or hearing attachments. 
(You should have requested  permission for their use through the Dea
n of Students.)  FOOD/DRINKS are not allowed per NJIT regulations.


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 = < 1, 2, ... , n-1, n >$ is the sorted
sequence of the first n positive integers starting with 1.

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