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: =Bin2Dec(10010100) the answer is 148 Clue #2. (3 ...

1. 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.

2. 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:

8. 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

9. 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

10. 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: =Bin2Dec(10010100) the answer is 148
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: =COMBIN(8,2) the answer is 28

11. 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}
X - n(F) = 10
ok - n(S) = 14
X - n(M) = 15
X - n(F and S) = 4
X - 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: 7
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.

12. Answer 3*16 the number of boxes needed to be determined
added to the 62 the last number determined 62. The answer (
110 )
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:
Clue #6. (3 points) To solve this clue, you must determine if
there exists an Euler path or Euler circuit between the 7
locations on the island. If so, describe it. If not, explain how
you know that such a path or circuit does not exist.
Answer: The image drawn around the map shows this island to
be a ( euler circuit ) because every locations could be visited
exactly once
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.

13. 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: 148
Clue #2:
Number of combinations:28
Clue #3:
n(M + S +~F)
7
Clue #4:
110
Clue #5:
Truth Value
Clue #6:

14. Path, Circuit, or None?
Clue #7:
Weight of spanning tree:
DIGIT1
DIGIT2
DIGIT3
DIGIT4
DIGIT5
148
28
7
110
To unlock the treasure, you must determine the combination for
the lock:
DIGIT1 = 2
FOR i = 1 to Clue#3
DIGIT1 = DIGIT1 + 2
NEXT
DIGIT2 = (Clue#1 / 4) – Clue#2
IF Clue#4 = 71
THEN DIGIT3 = 4
ELSE DIGIT3 = 7

15. IF Clue#5 = True AND Clue #7 < 275
THEN DIGIT4 = 2
ELSE DIGIT4 = 1
IF Path exists in Clue #6
THEN DIGIT5 = 0
ELSE
IF Circuit exists in Clue #6
THEN DIGIT5 = 2
ELSE DIGIT5 = 8
Copyright 2010 – Kaplan University – All Rights Reserved
1 | Page
10010100
(~)(~)(~)
pqrssq
ÙÚÙÅÙ
20
a
=
2
6
(5210)
m
k
kk
=
+-
å
{25,1,26,9,2)
5

16. S
n
=
=