Problem 1
According to the loop, we can get such table:
i
n
j
[1,n]
n log 2 n
k2k
n
2
n
n
4
n
[1, 2 ]
[1 , 4 ]
n
log 2 n
2 *
n
log 2 n
4
From the table, we know that the cycles of k2k equal to i* log 2 n .
i
f (n)
Set cycles of i 2 is f(n). It stops for n

Samuel Boakye (skb3bb)
Required Reading: 43/36
Catherine Crump: The small and surprisingly dangerous detail the police track about you
Police are utilizing military style weapons, and gathering NSA style information. Programmed
tag perusers mounted on squ

Samuel Boakye (skb3bb)
Required Reading: 48/36
Danny Hillis: The Internet Could Crash. We need a Plan B
Danny proposes we require a different framework autonomous of the web as a "reinforcement" if
the web is brought around an assault. It needn't be as la

Samuel Boakye (skb3bb)
Required Reading: 47/36
Ben Saunders: Why bother leaving the House?
Ben was offered the conversation starter: with steady data supply these days why try going
out? He utilizes a quote from George Mallory perhaps the principal man to

Samuel Boakye (skb3bb)
Required Reading: 46/36
Margaret Heffernan: Dare to Disagree
Margaret says that pHd understudies at a few colleges are compelled to submit 5 proclamations
that they will guard they should do this to show they can manage being tested

Samuel Boakye (skb3bb)
Required Reading: 40/36
Seth Godin: How to Get Your Ideas to Spread
For the initial couple of years, cut bread was a total tumble noone needed it, and noone knew it
was accessible. The first concentration was on licenses and plants

Samuel Boakye (skb3bb)
Required Reading: 44/36
Catherine Crump: The small and surprisingly dangerous detail the police track about you
Police are utilizing military style weapons, and gathering NSA style information. Programmed
tag perusers mounted on squ

Samuel Boakye (skb3bb)
Required Reading: 38/36
Are You Smart Enough to Work at Google?
In the wake of understanding this, you ponder something else: do I give it a second thought?
Silicon Valley may well have the most discussed HR offices on the planet, y

Samuel Boakye (skb3bb)
Required Reading: 39/36
Algorithms- Wikipedia
Regularly, when a calculation is connected with handling data, information are perused from an
info source, kept in touch with a yield gadget, as well as put away for further preparing.

Samuel Boakye (skb3bb)
Required Reading: 50/36
Tom Wujec: Got a wicked Idea?
Directors can utilize this straightforward procedure to delineate their association or system to
break an exceptionally entangled element into the working parts. They just draw t

Required:
1. The Last Lecture, by Randy Pausch, its Oprah Show Reprise, and its related media
coverage, 2007.
2. Time Management by Randy Pausch and its Powerpoint slides, 2007.
3. You and Your Research by Richard Hamming (or PDF version
4. Powers of Ten,

DeMorgans Laws complementation
Download the Logisim file called DeMorgan from collab and open it using Logisim. You will
see four simple circuits representing algebraic functions of two variables X and Y. In the table
below, enumerate all the possible Boo

Mystery Circuits
Download the Logisim file called mystery circuits which contains several similar circuits. In
this exploration you will investigate each of these circuits to discover the function they are
performing. The similarities and differences are

Fun with T Flip Flops
Download and open the Logisim file called simple counter T flip-flop. This file is very similar to
the one you looked at recently (which was called simple counter) with one major difference:
the D flip-flops have been replaced with a

CS3102 Theory of Computation
Problem Set 1
Department of Computer Science, University of Virginia
Gabriel Robins
Please start solving these problems immediately, and work in study groups. Please prove all your
answers; informal arguments are acceptable, b

Fun with Flip Flops
Download and open the Logisim file called fun with FF. Begin with the circuit called flip flop
demo
1. Toggle the input a few times and see that nothing happens. Notice that the clock input
shows that the clock is low. Set the input to

CS3102 Theory of Computation
Midterm Examination Fall 2016
University of Virginia
Gabriel Robins
This is a 6-hour take-home open-book, open notes, pledged exam.
Note: while for your convenience the possession time of this exam is up to 24 hours,
the act

Samuel Boakye (skb3bb)
Required Reading: 45/36
Heather White: Its not about Working the Room
Heather's organizing has got her private voyages through Buckingham Palace and 10 Downing
St. While not each discussion will end so especially, it is still useful

Samuel Boakye (skb3bb)
Required Reading: 49/36
Naomi Klein: Addicted To Risk
Right now, environmental change is the greatest hazard amusement we are playing. There is a
considerable measure of uncertainty about the models which indicate warming of 2-4 deg

Problem 1
Consider the recurrence
T ( n ) =4 T ( n ) +log 2 n
This equation is unfortunately not in a form that allows us to use the master method. So we can
put it into such a form, however, by introducing the variable
k =log n , which let us write
k
( )

Problem 1
It not works.
Consider such sample:
We know the optimal solution is (1,2,3,4). But if we use such algorithm we will get (1,6,4).
Because, each of 1,4,6 has two overlaps, and each of 2,3,5,7,8,9 has three overlaps. So we will
choose 1,4,6 instead

Problem 1
When divide the input in groups of 7, it will still work in linear time.
4
There are
( 12 7n 2) 27n 8
elements are median (or < median)
5n
+8 elements in big section of the problem
7
So worst split has
T (n)=
From what learned in course, we can

Problem 1
Base case: for k=0, its obvious that we have 2 k=1 node.
Induction hypothesis: its true for rank k-1, which means we have 2 k-1 nodes.
Induction: as we know, a node gets rank k only if the merged two roots has rank k 1(each has
2k-1 nodes). So,

Problem 1
1. According to the basic Karatsubas algorithm we can divide n-bit integrity into several m3
n
log
r=
+1
bit. Set
. Time of each part is O(m 2 ) . So we know
m
3
2
n
T ( n ) =rO (m )=( +1)m
m
log
log
3
2
=O(n m
T ( n ) =4 T
2. From the question

CS203 F16
Lab 1
1. Objectve
The goal of project 1 is to extend a simple pipeline simulator to support forwarding. For
this lab, we will build off Pipesim, a timing simulator for 5-stage pipeline processor.
If you have any questions, please post to Piazza

Problem 1
From the question, we can use P(v, w, k) denotes the possibility that from s to v that has total
weight w and uses exactly k edges.
First, K=0 and w=0, which means, there exists a path.
Second, k=0 and 0<w W, which means, there is not such path.

1A) Byte stuffing is the process of adding 1 extra byte whenever there is aflag or escape character in the
text while bit stuffing is the process of adding oneextra 0 whenever five consecutive 1s follow a 0 in the
data, so that the receiverdoes not mistak