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CSE 310 — Data Structures and Algorithms Project #1

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CSE 310 — Data Structures and Algorithms
Project #1

Encoding and decoding schemes are used in a wide variety of applications, such as in music or video streaming,
data communications, storage systems (e.g., on CDs, DVDs, RAID arrays), among many others. In a fixedlength encoding each character is assigned a bit string of the same length. An example is the standard
ASCII code. One way of getting an encoding scheme that yields a shorter bit string on the average is to
assign shorter codewords to more frequent characters and longer ones to less frequent characters. Such a
variable-length encoding scheme was used in the telegraph code invented by Samuel Morse. In that code,
frequent letters such a e (·) and a (· -) are assigned short sequences of dots and dashes while infrequent
letters such as q (- – · -) and z (- – ··) have longer ones.
In this project you will implement a variable-length encoding and decoding scheme, and run experiments
to evaluate the effectiveness of the the scheme, in addition to the efficiency of your algorithms.
Note: This project is to be completed individually. Your implementation must use C/C++ and ultimately
your code must run on the Linux machine general.asu.edu.
You may not use any external libraries to implement any part of this project, aside from the standard
libraries for I/O and string functions (stdio.h, string.h, and their equivalents in C++). If you are in
doubt about what you may use, ask.
You must use a version control system as you develop your solution to this project, e.g., GitHub or
similar. Your code repository must be private to prevent anyone from plagiarizing your work.
The rest of this project description is organized as follows. §1 gives the requirements for Project #1
including a description of the encoding and decoding schemes to implement in §1.1 and §1.2, respectively.
§2 gives the experiments to design to evaluate the effectiveness and efficiency of the encoding and decoding
schemes. Finally, §3 describes the submission requirements for the milestone and full project deadlines.
1 Program Requirements for Project #1
1. Write a C/C++ program that implements the encoding scheme described in §1.1 on plain text. The
program must be compiled into an executable named encode and it must take one command line
parameter. The parameter is one of the keywords insertion or merge. In all cases, you must read
input from stdin, allowing redirection from a text file. You must write the encoded plain text to
stdout, allowing redirection to a text file. See §1.1 for detailed instructions.
2. Write a C/C++ program that implements the decoding scheme described in §1.2 on input in the format
produced by encoding scheme as prescribed in §1.1. The program must be compiled into an executable
named decode. In all cases, you must read input from stdin allowing redirection from an encoded
text file. You must write the decoded input to stdout, allowing redirection to a text file. The decoded
input will be compared to the original input, i.e., the input prior to encoding. See §1.2 for detailed
instructions.
3. Design experiments to evaluate your programs as described in §2. A brief report with figures plotting
the data you collect, and interpretation of your results is expected.
Sample text input will be provided on Canvas; use them to test the correctness of your programs. Scripts
will be used to check the correctness of your program. Therefore, absolutely no changes to these project
requirements are permitted.
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1.1 The Encoding Algorithm
Given a normal English text file, for each line of the file:
1. Transform the line into a form that is more amenable to compression. The transformation rearranges
the characters in the input into many clusters of repeated characters, in a way that it is possible to
recover the original input.
2. Output the compressed form of the transformed line.
To transform a line of text, treat the line as a string of length N. First, compute (and store) every cyclic
shift of the string, shifting to the left by one character. Then sort the N cyclic shifts in lexicographic order
according to the ASCII code. Note the ordering of characters in the ASCII code.
Table 1 shows the transformation step for the example string Mississippi, of length N = 11. Under
Original, rows with index 0, . . . , 10 show the cyclic shift of the string to the left by as many characters, e.g.,
at index 5 is the string shifted cyclically to the left by 5 characters. Under Sorted, all N cyclic shifts of the
string are sorted. (The next column is used in decoding, so it is discussed in §1.2.)
Table 1: Transformation Step of the Encoding Algorithm
Index Original Index Sorted next
0 M i s s i s s i p p i 0 M i s s i s s i p p i 4
1 i s s i s s i p p i M 1 i M i s s i s s i p p 0
2 s s i s s i p p i M i 2 i p p i M i s s i s s 6
3 s i s s i p p i M i s 3 i s s i p p i M i s s 9
4 i s s i p p i M i s s 4 i s s i s s i p p i M 10
5 s s i p p i M i s s i 5 p i M i s s i s s i p 1
6 s i p p i M i s s i s 6 p p i M i s s i s s i 5
7 i p p i M i s s i s s 7 s i p p i M i s s i s 2
8 p p i M i s s i s s i 8 s i s s i p p i M i s 3
9 p i M i s s i s s i p 9 s s i p p i M i s s i 7
10 i M i s s i s s i p p 10 s s i s s i p p i M i 8
The compressed output for a string consists of two lines:
1. The index of the row in which the original string appears in the Sorted column.
2. Form a string last consisting of the last character of each Sorted string. In this string, which is some
permutation of the original string, characters form clusters of characters of size one or more. To encode
last step through the string from left to right processing the clusters: For each cluster, output the
cluster size, followed by the character in the cluster.
For the example string, the original string appears at index position zero in the Sorted column. The
last character of each Sorted string is a new string last=ipssMpissii. The first two characters are each
in a cluster of size one character. This is followed by a cluster of size two of the character s, and so on.
Therefore, the encoding of the string ipssMpissii is:
0
1 i 1 p 2 s 1 M 1 p 1 i 2 s 2 i
1.1.1 Input to the Encoding Algorithm
The encoding algorithm has one input parameter taken from the command line: It is a keyword indicating
the sorting algorithm to use. The text to encode must be read from stdin, which may be redirected from
a file in Unix/Linux format. (Recall, that in Window files the end of line is signified by two characters,
Carriage Return (CR) followed by Line Feed (LF). Unix files, on the other hand, only LF is used.) Similarly,
your output must be written to stdout and can be redirected to a text file.
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Some examples of input to your encode program:
encode insertion <ex1.txt >enex1.txt
encode merge <ex2.txt >enex2.txt
You must implement both the Insertion Sort algorithm and the Merge Sort algorithms. If the keyword
is equal to insertion then use Insertion Sort to sort the strings in Original. Likewise, if the keyword is
merge then the sorting algorithm used is Merge Sort.
Do not sort the strings directly because it will result in too much data movement. To be
efficient, sort pointers to the strings instead.
1.1.2 Output of the Encoding Algorithm
The output of your encoding scheme is text in which each line of the input is compressed as described in
§1.1. In principle, if there are k lines in the file, then 2k lines of output are produced.
1.2 The Decoding Algorithm
Now we describe how to decode, i.e., recover the original string. There are three steps in the recovery:
1. Read the integer giving the index of the row in which the original string appears in the Sorted column.
2. Recover the string last.
3. Using the index, last, and knowledge of the next column, recover the original string.
Recall that the encoded output of the string Mississippi is:
0
1 i 1 p 2 s 1 M 1 p 1 i 2 s 2 i
In this case, the index is zero. Recovering the string last=ipssMpissii from the encoded string is straightforward. Using index, last, and knowing the next column in Table 1, makes decoding easy, as given by
the following pseudocode (which, of course, should be generalized):
int index = 0;
int next[11] = { 4, 0, 6, 9, 10, 1, 5, 2, 3, 7, 8 };
char last[11] = “ipssMpissii”;
x = next[index];
for (i = 0; i < 11; i++)
putchar( last[x] );
x = next[x];
This results in the output Mississippi, i.e., the original string is successfully recovered.
From the Sorted strings, here is how the next column is computed. For i = 0, . . . N − 1, next[i] is
the index of the row containing the cyclic shift of Sorted[i] to left by one character. For the example in
Table 1, Sorted[0] is Mississippi. Shifting this string to left by one character gives ississippiM, and
this string can be found at Sorted[4]. Hence next[0] is 4. Sorted[1] is iMississipp. Shifting this string
to left by one character gives Mississippi, and this string can be found at Sorted[0]. Hence next[1] is 0.
Sorted[2] is ippiMississ. Shifting this string to left by one character gives ppiMississi, and this string
can be found at Sorted[6]. Hence next[2] is 6. Continuing in this way for i = 3 . . . 10 gives the values in
the column next in the table. Indeed, next is a permutation of the indices 0, . . . , N − 1.
What is amazing is that the information in the encoding is enough to reconstruct next, and therefore
the original message! From last, we know all of the characters in the original string, they’re just permuted.
We can reconstruct the first column in Sorted by sorting the characters in last; see Table 2.
Because M only occurs once in the string and the array is formed using cyclic shifts, we can deduce that
next[0] = 4 because M is in the last column of row with index 4. However all the other characters are in
clusters of size larger than one, so how can we tell how to compute next? For character p, it may seem
ambiguous whether next[5] = 1 and next[6] = 5, or whether next[5] = 5 and next[6] = 1.
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Table 2: Reconstructing next from the Encoding
Index Sorted next
0 M ? ? ? ? ? ? ? ? ? i 4
1 i ? ? ? ? ? ? ? ? ? p
2 i ? ? ? ? ? ? ? ? ? s
3 i ? ? ? ? ? ? ? ? ? s
4 i ? ? ? ? ? ? ? ? ? M
5 p ? ? ? ? ? ? ? ? ? p 1
6 p ? ? ? ? ? ? ? ? ? i 5
7 s ? ? ? ? ? ? ? ? ? s
8 s ? ? ? ? ? ? ? ? ? s
9 s ? ? ? ? ? ? ? ? ? i
10 s ? ? ? ? ? ? ? ? ? i
As it turns out, there is a rule that resolves the ambiguity. It is:
If row index i and j both start with the same letter and i < j, then next[i] < next[j].
This rule implies that next[5] = 1 and next[6] = 5.
Why is this rule valid? The rows are sorted, so row 5 is lexicographically less than row 6. This means
that the nine unknown characters in row 5 must be less than the nine unknown characters in row 6 (since
both rows start with the letter p). We also know that between the two rows that end with p, row 1 is less
than row 5. But, the nine unknown characters in row 5 and 6 are precisely the first nine characters in rows
1 and 5. Thus, next[5] = 1 and next[6] = 5 or this would contradict the fact that the strings are sorted.
Using the rule allows all remaining ambiguities to be resolved and all entries of next to be computed.
1.2.1 Input to the Decoding Algorithm
The input to the decoding scheme is text in the form generated by the encoding scheme. As with the encoding
scheme, the text to decode must be read from stdin, which may be redirected from a file in Unix/Linux
format. Similarly, your output must be written to stdout and can be redirected to a text file.
If the input to the encoding scheme consists of k lines, then its output has 2k lines. Thus the decoding
scheme iterates k times in order to decode the encoded input.
1.2.2 Output of the Decoding Algorithm
The output of the decoding scheme should equal the input to the encoding scheme. Note that some care
will be needed to take care of the LF characters so that the lines match.
2 Experimentation
A standard measure of the “goodness” of a compression algorithm’s effectiveness is the compression ratio.
This is the ratio t−c
t × 100%, where t is the total number of characters in the input, and c is the number of
clusters in the encoding.
For example, the encoding of Mississippi is 1 i 1 p 2 s 1 M 1 p 1 i 2 s 2 i. In this example, the
total number of characters is t = 11, the number of clusters is c = 8, and so the compression ratio is 3
11 ×100
or 27%. (Here, we are ignoring the fact we used integers to code the cluster sizes; this can be done more
intelligently but this project is already enough work, right? ,)
4
Design a set of experiments to study:
1. The average compression ratio; in addition to the average, compute the minimum, maximum, and
standard deviation of the compression ratio. You might consider using a box and whiskers plot for this
metric.
2. The time to encode each input for each type of sort, i.e., for Insertion and for Merge Sort. Plot the
run time as a function of input size.
3. The time to decode each encoded input. Plot the run time as a function of input size.
4. The compression ratio as a function of number of lines encoded. The encoding algorithm has been
described as encoding one line at a time. If you instead encode 2, 3, . . . lines at a time, does the
compression ratio improve? What do you expect to happen?
3 Submission Instructions
Submissions are always due before 11:59pm on the deadline date.
1. For SLN 83657 (TTh) the milestone is due on Thursday, 09/19/2019. For SLN 84794 (MW) the
milestone is due on Wednesday, 09/18/2019. See §3.1 for requirements.
2. For SLN 83657 (TTh) the complete project is due on Thursday, 10/03/2019. For SLN 84794 (MW)
the complete project is due on Wednesday, 10/02/2019. See §3.2 for requirements.
It is your responsibility to submit your project well before the time deadline!!! Late projects
are not accepted. Do not expect the clock on your machine to be synchronized with the one on Canvas!
An unlimited number of submissions are allowed. The last submission will be graded.
3.1 Requirements for Milestone Deadline
For the milestone deadline you must implement the encoding scheme described in §1.1. Using the submission
link on Canvas for the Project #1 milestone, submit a zip1 file named yourFirstName-yourLastName.zip
that unzips into the following:
Project State (5%): In a folder (directory) named State provide a brief report (.pdf preferred) that
addresses the following:
1. Describe any problems encountered in your implementation for this project milestone.
2. Describe any known bugs and/or incomplete implementation in the project milestone.
3. While this project is to be completed individually, describe any significant interactions with anyone
(peers or otherwise) that may have occurred.
4. Cite any external books, and/or websites used or referenced.
Implementation (25%): In a folder (directory) named Code provide:
1. In one or more files, your well documented C/C++ source code implementing the encoding scheme
required for this project milestone.
2. A makefile that compiles your program and produces an executable named encode on general.asu.edu.
Our TA will write a script to compile and run all student submissions on general.asu.edu; therefore executing the command make encode in the Code directory must produce the executable
encode also located in the Code directory.
Correctness (70%): The correctness of your program will be evaluated by running a series of tests on a
text files, some of which will be provided to you on Canvas prior to the deadline for testing purposes.
For the milestone deadline, the script will only test your encode program. As stated several times, your
program must read input from standard input. Do not use file operations to read the input!
The milestone is worth 30% of the total project grade.
1Do not use any other archiving program except zip.
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3.2 Requirements for Complete Project Deadline
For the full project deadline, you must implement both the encoding and decoding schemes, as well as
conduct experiments with each program summarized in a report. Using the submission link on Canvas for
the complete Project #1, submit a zip2 file named yourFirstName-yourLastName.zip that unzips into the
following:
Project State (5%): Follow the same instructions for Project State as in §3.1.
Experimentation and Report (15%): In a folder (directory) named Report provide a brief report (.pdf
preferred) that addresses the following:
1. Describe the experiments you ran, i.e., the characteristics of the input data you used, such the
input sizes in lines and characters, among others.
2. Present figures/tables plotting the results of your experimentation as requested in §2. Use the
data you collected to interpret your results. Can you draw any general conclusions about the compression ratio, about the impact of the sorting algorithm on the run time of the encoding scheme,
about the impact of input size on the decoding scheme, about the impact on the compression
ratio as a function of the number of lines encoded?
Implementation (20%): Follow the same instructions for Implementation as in §3.1, except that the TA
should be able to make both the encode and decode programs on general.asu.edu in your Code
directory.
Correctness (60%): The same instructions for Correctness as in §3.1 apply except that the input will test
both the encoding and decoding schemes.
4 Marking Guide
The project milestone is out of 100 marks.
Project State (5%): Summary of project state, use of a zip file, and directory structure required (i.e., a
folder/directory named State and Code is provided).
Implementation (25%): 15% for the quality of implementation in your encoding scheme; 5% for reading
from stdin and writing to stdout; 5% for a working makefile.
Correctness (70%): For correct output at least 7 tests of sample input.
The full project is out of 100 marks.
Project State (5%): Summary of project state, use of a zip file, and directory structure required (i.e., a
folder/directory named State, Report, and Code is provided).
Experimentation and Report (15%): Experiment design, results (plots/tables) of results gathered, and
interpretation of results.
Implementation (20%): 15% for the quality of implementation in your code; 5% for reading from stdin
and writing to stdout, and for a working makefile.
Correctness (60%): 60% for correct output on at least 10 tests of sample input.
Comments will be provided to you when your graded project is returned.
2Do not use any other archiving program except zip.
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PlaceholderCSE 310 — Data Structures and Algorithms Project #1
$30.00
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