kaplan MM250 Unit 8 assignment

kaplan MM250 Unit 8 assignment

Question
	
Unit 8: Algorithms - Assignment



Total
points for Assignment: 35 points. Assignments must be submitted as a Microsoft
Word document and uploaded to the Dropbox for Unit 8.
 All Assignments are due by
Tuesday at 11:59 PM ET of the assigned Unit.

NOTE: Assignment problems should not be
posted to the Discussion threads. Questions on the Assignment problems should
be addressed to the instructor by sending an email or by attending office
hours.



You must show your
work on all problems. If a problem is
worth 2 points and you only show the answer, then you will receive only 1 point
credit. If you use a calculator or online website,
give the source and tell me exactly what you provided as input. For example, if you used Excel to compute 16
* 16, state “I typed =16*16 into Excel and got 256. You may type your answer right into this
document. 









Part I. Basic Computations

1. (5 points) Consider
the following pseudo code for determining any sum in this form: 

ComputeSum:

INPUT m

sum = 0

for k = 6 to m do

 sum = sum + 5*k^2 + 2*k -10

next k

OUTPUT
sum

a. Are the inputs and
outputs for this algorithm well defined?
Explain.

b. Identify an
iterative operation in this algorithm.









2. (
5 points) Consider this algorithm used
to sort an array in this form:


 

 

 
5
 
 

 
8
 
 

 
6
 
 

 
3
 
 

 
5
 
 

 
1
 
 

 
6
 
 

 
19
 
 

 
7
 
 

 
4
 





S(n) = 



BUBBLESORT:

INPUT S, n (an array called S, with n
elements)

FOR i = 1 to n – 1

 FOR j = 1 to n – 1

 if S(j) > S(J+1) then

 exchange the contents of
S(j) with S(j+1)

 NEXT

NEXT

OUTPUT S 

Using the following grid, show a trace for
this algorithm using the following values:









Part II.
Case Study Season
Finale: Unlocking the Treasure



The directors and producers of the “Patty
Madeye Mysteries” have decided that the
season finale for the show will be filmed in a secret location. They have identifed a remote island and
visited it to determine what facilities and features are available on the
island. The interns that were sent to
scout out the island only had time to draw this map of the island and collect
some other information. 









In order to open the lock to the treasure
chest, you will need to solve a puzzle using discrete math. Shown below are the paths and distances
that connect the 7 locations on the map. 


 

 

 
From
 
 

 
To
 
 

 
Distance

 (in meters)
 

 

 

 
C
 
 

 
D
 
 

 
80
 

 

 

 
D
 
 

 
E
 
 

 
25
 

 

 

 
E
 
 

 
G
 
 

 
80
 

 

 

 
D
 
 

 
G
 
 

 
80
 

 

 

 
D
 
 

 
A
 
 

 
100
 

 

 

 
A
 
 

 
F
 
 

 
80
 

 

 

 
A
 
 

 
G
 
 

 
80
 

 

 

 
B
 
 

 
A
 
 

 
25
 

 

 

 
C
 
 

 
B
 
 

 
25
 

 

 

 
C
 
 

 
E
 
 

 
100
 

 

 

 
B
 
 

 
E
 
 

 
100
 

 

 

 
G
 
 

 
F
 
 

 
25
 

 

 

 
B
 
 

 
F
 
 

 
80
 

 

 

 
A
 
 

 
C
 
 

 
80
 











Clue #1: (3 points)
One of the things that the film crew will need to know about is the
condition of light during the day at the island. The only marking on the island was this
binary representation of the longitude.
Convert this longitude to decimal so that the crew can estimate time of
sunrise and sunset. Show your work.



Longitude: 



Answer: 



Clue #2.
(3 points) The cast and crew will be staying in
the 8 tents shown in the Tent Village. Two
of the tents will be set aside for to be used for “Hair and Makeup” (one for
the males, one for the females). How
many different ways can you select these special tents out of the 8 available? 



Answer: 



Clue #3.
(3 points) Since the natives on
this remote island only speak Spanish, it is important to know how many people
in the cast & crew of 56 people.
The producers have provided the following information and asked you to
prepare a Venn Diagram depicting the various sets and subsets of this
group. 



F = {members of
the film crew}

S = {members of
the cast & crew who speak Spanish}

M = {male
members of the cast & crew}



n(F) = 10 

n(S) = 14

n(M) = 15

n(F and S) = 4

n(F and M) = 5

n(M and S and F)
= 3

n(M or S or F) =
28



How many members of the cast & crew are male and speak
Spanish, but are NOT on the Film Crew?

Answer:













Clue #4.
(3 points) A strange children’s
game was found on the island with the following markings: 




 

 

 
53
 
 

 
56
 
 

 
59
 
 

 
62
 
 

 
…
 





Determine the 20th element of the sequence using the general term
for the sequence.



Answer





Clue #5. (3 points)
This clue requires solving a logic problem:



p: cast member is male

q: cast member speaks Spanish

r: cast member has short hair

s: it is NOT
raining



If a cast member is male and has short hair, does not speak
Spanish, and it is raining, determine the truth value for the following
expression:









Answer: 











Answer: 







Clue #7. (2 points)
Determine a Minimum Spanning Tree for the graph described by the paths
on the island, using the distances between the locations as weights. 



What is the weight of the resulting
spanning tree? 



Answer: 





Clue #8. (5 points)
Record your clues here, then use the following algorithm to determine
the 5 digit combination to unlock the treasure. 






 

 

 
Clue #1:

 Longitude expressed in decimal:

 

 

 
 
 

 
Clue #2:
 
Number of combinations:
 


 

 
 
 

 
Clue #3:

 n(M + S +~F) 

 

 

 
 

 
 

 
Clue #4:
 


 

 

 

 
 
 

 
Clue #5:
 
Truth Value

 

 

 

 
 
 

 
Clue #6: 

 Path, Circuit, or None?

 

 

 
 
 

 
Clue #7:

 Weight of spanning tree:

 

 
 








 

 

 
DIGIT1

 

 
 
 

 
DIGIT2
 

 
 

 
DIGIT3

 

 
 
 

 
DIGIT4
 
 

 
DIGIT5