10/4/2018 COMP9024 18s2 - Assignment 2
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COMP9024 18s2 Assignment 2
Partial Order Graphs
Data Structures andAlgorithms
Change Log
We may make minor changes to the spec to address/clarify some outstanding issues. These mayrequire minimal changes in your design/code, if at all. Students are strongly encouraged to check the
change log regularly.
18 September
Linked list ADT added to admissible ADTs.
16 September
Images modified to make clear which edges are included in a partial order graph.Requirements for stages 1 2 clarified.
Version 1: Released on 14 September 2018
Objectives
The assignment aims to give you more independent, self-directed practice with
advanced data structures, especially graphsgraph algorithms
asymptotic runtime analysis
Admin
Marks 2 marks for stage 1 (correctness) 3 marks for stage 2 (correctness)
3 marks for stage 3 (correctness) 4 marks for stage 4 (correctness)
2 marks for complexity analysis 1 mark for style.
——————— Total: 15 marks
Due 23:59 on Monday 8 October (week 11)
Late 2.25 marks (15%) off the ceiling per day late
(e.g. if you are 25 hours late, your maximum possible mark is 10.5)
Background
A partially ordered set ("poset") is a set S together with a partial order ≼ on the elements from S.
A partial order graph for a finite poset (S,≼) is a directed graph ("digraph") with
the elements in S as verticesa directional edge from s to t if, and only if, s ≼ t and s ≠ t
Example:
10/4/2018 COMP9024 18s2 - Assignment 2
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where
S = {1, 11, 13, 143}s ≼ t iff s is a divisor of t
A monotonically increasing sequence of length k over a poset (S,≼) is a sequence of elements from
S,
s1 ≺ s2 ≺ … sk-1 ≺ sk
such that si ≼ si+1 and si ≠ si+1, for all i=1…k-1. Examples:
1 ≺ 11 ≺ 143 and 1 ≺ 13 ≺ 143 are monotonically increasing sequences of length 3 over the
poset from above.1 ≺ 143 121 is a monotonically increasing sequence of length 2 over this poset.
Aim
Your task is to write a program poG.c for computing a partial order graph from a given specification andthen find and output all longest monotonically increasing sequences that can be constructed over this
poset.
Your program should:
accept a single positive number p on the command line;compute the set S
p of all (positive) divisors of p;Task A:
build and output the partial order graph over Sp corresponding to a specific partial order
(see below);Task B:
output all longest monotonically increasing sequences over this partial order.
Your program should include a time complexity analysis, in Big-Oh notation, for
1. your implementation for Task A, depending on the number n of divisors of p and the length m ofthe decimal p;
2. your implementation for Task B, depending on the number n of divisors of p.
Hints
You may assume that
the command line argument is correct (a number p ≥1);
p is at most 2,147,483,647 (the maximum 4-byte int);p will have no more than 1000 divisors.
If you find any of the following ADTs from the lectures useful, then you can, and indeed are encouragedto, use them with your program:
stack ADT : stack.h, stack.c
queue ADT : queue.h, queue.c
list ADT : list.h, list.c
10/4/2018 COMP9024 18s2 - Assignment 2
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prompt$ ./poG 121 Partial order:
1: 11 121 11: 121
121:
Longest monotonically increasing sequences: 1 < 11 < 121
prompt$ ./poG 9481 Partial order:
1: 19 9481 19: 9481
499: 9481 9481:
Longest monotonically increasing sequences:
1 < 19 < 9481
graph ADT : Graph.h, Graph.c
weighted graph ADT : WGraph.h, WGraph.c
You are free to modify any of the four ADTs for the purpose of the assignment (but without changing thefile names). If your program is using one or more of these ADTs, you should submit both the header and
implementation file, even if you have not changed them.
Your main program file should start with a comment: /* … */ that contains the time complexity of yoursolutions for Task A and Task B, together with an explanation.
Stage 1 (2 marks)
For stage 1, you should demonstrate that you can build the underlying graph correctly from all divisorsof input p and the following partial order:
x ≼ y iff x is a divisor of y
All you need to do for Task B at this stage is to output all nodes of the graph in ascending order.
Here is an example to show the desired behaviour of your program for a stage 1 test:
Hint: The only tests for this stage will be with numbers p for which the above order is identical to the stricter partial order for stages 2–4,and such that all of the divisors of p together form. a monotonically increasing sequence.
Stage 2 (3 marks)
For stage 2, you should extend your program for stage 1 such that it puts an additional constraint on thepartial order of the divisors of p:
x ≼ y iff
x is a divisor of y, andall digits in x also occur in y
For example, 11 ≺ 143 since 1 is also contained in 143, but 16 ⊀ 128 since 6 is not a digit in 128.
All you need to do for Task B at this stage is to find and oputput the path that starts in 1 and alwaysselects the next neighbour in ascending order until you reach a node without outgoing edge.
Here is an example to show the desired behaviour of your program for a stage 2 test:
10/4/2018 COMP9024 18s2 - Assignment 2
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prompt$ ./poG 125 Partial order:
1: 125 5: 25 125
25: 125 125:
Longest monotonically increasing sequences:
5 < 25 < 125
prompt$ ./poG 143 Partial order:
1: 11 13 143 11: 143
13: 143 143:
Longest monotonically increasing sequences:
1 < 11 < 143 1 < 13 < 143
Hint: All tests for this stage will be such that the only longest monotonically increasing sequence is the unique path from 1 to p obtained byalways moving to the next neighbour in ascending order.
Stage 3 (3 marks)
For stage 3, you should demonstrate that you can find a single longest monotonically increasingsequence.
All tests for this stage will be such that there is a unique longest sequence.
Here is an example to show the desired behaviour of your program for a stage 3 test:
Stage 4 (4 marks)
For stage 4, you should extend your program for stage 3 such that it outputs, in ascending order, allmonotonically increasing sequences of maximal length.
Here is an example to show the desired behaviour of your program for a stage 4 test:
Note:
It is required that the sequences be printed in ascending order.
Testing
We have created a script. that can automatically test your program. To run this test you can execute thedryrun
program for the corresponding assignment, i.e. assn2. It expects to find, in the current
directory, the program poG.c and any of the admissible ADTs (Graph,WGraph,stack,queue,list)that your program is using, even if you use them unchanged. You can use dryrun as follows:
prompt$ ~cs9024/bin/dryrun assn2
10/4/2018 COMP9024 18s2 - Assignment 2
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Please note: Passing the dryrun tests does not guarantee that your program is correct. You shouldthoroughly test your program with your own test cases.
Submit
For this project you will need to submit a file named poG.c and, optionally, any of the ADTs namedGraph,WGraph,stack,queue,list
that your program is using, even if you have not changed them.You can either submit through WebCMS3 or use a command line. For example, if your program uses
the Graph ADT and the queue ADT, then you should submit:
prompt$ give cs9024 assn2 poG.c Graph.h Graph.c queue.h queue.c
Do not forget to add the time complexity to your main source code file poG.c.
You can submit as many times as you like — later submissions will overwrite earlier ones. You cancheck that your submission has been received on WebCMS3 or by using the following command:
prompt$ 9024 classrun -check assn2
Marking
This project will be marked on functionality in the first instance, so it is very important that the output ofyour program be exactly correct as shown in the examples above. Submissions which score very low
on the automarking will be looked at by a human and may receive a few marks, provided the code iswell-structured and commented.
Programs that generate compilation errors will receive a very low mark, no matter what other virtuesthey may have. In general, a program that attempts a substantial part of the job and does that part
correctly will receive more marks than one attempting to do the entire job but with many errors.
Style. considerations include: readability, structured programming and good commenting.
Plagiarism
Group submissions will not be allowed. Your program must be entirely your own work. Plagiarismdetection software will be used to compare all submissions pairwise (including submissions for similar
projects in previous years, if applicable) and serious penalties will be applied, particularly in the case ofrepeat offences.
Do not copy ideas or code from othersDo not use a publicly accessible repository or allow anyone to see your code, not even
after the deadline
Please refer to the on-line sources to help you understand what plagiarism is and how it is dealt with atUNSW:
Plagiarism and Academic IntegrityUNSW Plagiarism Policy Statement
UNSW Plagiarism Procedure
Help
See FAQ for some additional hints.
Finally …
Best of luck and have fun! Michael