# 算法代写 | COSC 1285 / COSC 2123 Assignment 2: Solving Sudoku

Algorithms and Analysis COSC 1285 / COSC 2123
Assignment 2: Solving Sudoku
Assessment Type Group assignment. Submit online via Canvas → Assignments
→ Assignment Task 3: Assignment 2 → Assignment 2:
Solving Sudoku. Marks awarded for meeting requirements
via announcements/relevant discussion forums.
Due Date Week 13, Friday 5th June 2020, 11:59pm
Marks 50
1 Objectives
There are three key objectives for this assignment:
• Apply transform-and-conquer strategies to to solve a real application.
• Study Sudoku and develop algorithms and data structures to solve Sudoku puzzles.
• Research and extend algorithmic solutions to Sudoku variants.
2 Learning Outcomes
This assignment assesses learning outcomes CLO 1, 2, 3 and 5 of the course. Please
refer to the course guide for the relevant learning outcomes: http://www1.rmit.edu.
au/courses/004302
3 Introduction and Background
Sudoku was a game first popularised in Japan in the 80s but dates back to the 18th
century and the “Latin Square” game. The aim of Sudoku is to place numbers from 1
to 9 in cells of a 9 by 9 grid, such that in each row, column and 3 by 3 block/box all
9 digits are present. Typical Sudoku puzzle will have some of the cells initially filled in
with digits and a well designed game will have one unique solution. In this assignment
you will implement algorithms that can solve puzzles of Sudoku and its variants.
Sudoku
Sudoku puzzles are typically played on a 9 by 9 grid, where each cell can be filled in
with discrete values from 1-9. Sudoku puzzles have some of these cells pre-filled with
values, and the aim is to fill in all the remaining cells with values that would form a valid
solution. A valid solution (for a 9 by 9 grid with values 1-9) needs to satisfy a number of
constraints:
1. Every cell is assigned a value between 1 to 9.
2. Every row contains 9 unique values from 1 to 9.
3. Every column contains 9 unique values from 1 to 9.
4. Every 3 by 3 block (called a box) contains 9 unique values from 1 to 9.
As an example, consider Figure 1. Figure 1a shows the initial Sudoku grid, with
some values pre-filled in. After filling in all the remaining cells with values that satisfy
the constraints, we obtain the solution illustrated in Figure 1b. As an exercise, check
that every row, column and 3 by 3 block/box (delimited by bold black lines) satisfy the
respective constraints.
(a) Puzzle. (b) Solved.
Figure 1: Example of a Sudoku puzzle from Wikipedia.
Sudoku.
Killer Sudoku
Killer Sudoku puzzles are typically played on 9 by 9 grids also and have many elements
of Sudoku puzzles, including all of its constraints. It additionally has cages, which are
subset of cells that have a total assigned to them. A valid Killer Sudoku must also satisfy
the constraint that the values assigned to a cage are unique and add up to the total.
Formally, a valid solution for a Killer Sudoku of 9 by 9 grid and 1-9 as values needs
to satisfy all of the following constraints (the first 4 are the same as standard Sudoku):
1. Every cell is assigned a value between 1 to 9.
2. Every row contains 9 unique values from 1 to 9.
3. Every column contains 9 unique values from 1 to 9.
4. Every 3 by 3 block/box contains 9 unique values from 1 to 9.
5. The sum of values in the cells of each cage must be equal to the cage target total
and all the values of in a cage must be unique.
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As an example, consider Figure 2. Figure 2a shows the initial puzzle. Note the cages
are in different colours, and in the corner of each cage is the target total. Figure 2b is the
solution. Note all rows, columns and 3 by 3 blocks/boxes satisfy the Sudoku constraints,
as well as the values in each cage add up to the target totals.
(a) Puzzle. (b) Solved.
Figure 2: Example of a Killer Sudoku puzzle. Example comes from Wikipedia.
Sudoku Solvers
In this assignment, we will implement two families of algorithms to solve Sudoku, namely
backtracking and exact cover approaches. We describe these algorithms here.
Backtracking
The backtracking algorithm is an improvement on blind brute force generation of solutions. It essentially makes a preliminary guess of the value of an empty cell, then try
to assign values to other unassigned cell. If at any stage we find an empty cell where it
is not possible to assign any values without breaking one or more of the constraints, we
backtrack to the previous cell and try another value. This is similar to a DFS when it
hits a deadend, if a certain branch of search tree results in an invalid (partial) Sudoku
grid, then we backtrack and another value is tried.
Exact Cover
To describe this, we first explain what is the exact cover problem.
Given a universe of items (values) and a set of item subsets, an exact cover is to select
some of the subsets such that the union of these subsets equals the universal of items (or
they cover all the items) and the subsets cannot have any overlapping items.
For example, if we had a universe of items {i1, i2, i3, i4, i5, i6}, and the following subsets
of items: {i1, i3}, {i2, i3, i4}, {i1, i5, i6}, {i2, i5} and {i6}, a possible set cover is to select
{i2, i3, i4} and {i1, i5, i6}, whose union includes all 6 possible items and they contain no
overlapping items.
The exact cover can be represented as a binary matrix, where we have columns (representing the items) and rows, representing the subsets.
For example, using the example above, we can represent the exact cover problem as
follows:
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i1 i2 i3 i4 i5 i6
{i1, i3} 1 0 1 0 0 0
{i2, i3, i4} 0 1 1 1 0 0
{i1, i5, i6} 1 0 0 0 1 1
{i2, i5} 0 1 0 0 1 0
{i6} 0 0 0 0 0 1
Using the above matrix representation, an exact cover is a selected subset of rows,
such that if we constructed a sub-matrix by taking all the selected rows and columns,
each column must contain a 1 in exactly one selected row.
For example, if we selected {i2, i3, i4} and {i1, i5, i6}, we have the resulting submatrix:
i1 i2 i3 i4 i5 i6
{i2, i3, i4} 0 1 1 1 0 0
{i1, i5, i6} 1 0 0 0 1 1
Note each column in this sub-matrix have a single 1, which corresponds to the requirements of every item been covered and the subsets do not have overlapping items.
How does this relate to solving Sudoku puzzles? An example of transform and conquer, a Sudoku puzzle can be transformed into an exact cover problem and we can use
two exact cover algorithms to generally solve Sudoku faster than the basic backtracking
approach. We first describe the two algorithms to find exact cover, then explain how the
transformation works.
Algorithm X Algorithm X is Donald Knuth’s basic solution to the exact cover problem.
He devised Algorithm X to motivate the Dancing Links approach (we will discuss this
next). Algorithm X works on the binary matrix representation introduced previously.
Essentially it is a backtracking algorithm and works on the columns and rows of the
binary matrix. Recall that each column represents an item, and each row represents a
subset. What we want is to select some rows (subsets) such that across the selected rows,
there is exactly a single ’1’ in each of the columns – this condition means that all items are
covered and covered exactly once by the selected rows/subsets. We try different columns
and rows, and backtrack if there is an assignment that lead to an invalid (partial) grid.
After backtracking, another column/row will be selected.
Keeping this in mind, the algorithm goes through a number of steps, but aims to
essentially do what we have described above. See https://en.wikipedia.org/wiki/
Knuth%27s_Algorithm_X for further details.
Dancing Links Approach One of the issues with Algorithm X is the need to scan
through the (partial) matrices every time it seeks to select a column with smallest number
of 1’s, which row intersects with a column, and which column intersects with a row. Also
when backtracking it can be costly to reinsert rows and columns.
To address these challenges, Donald Knuth proposed a new approach, Dancing Links,
which is both a data structure and set of operations to speed up above.
The binary matrix for any exact cover problem is typically sparse (i.e., most entries
are 0). Recall our discussions about using linked list to represent graphs that are sparse,
i.e., few edges? We can do the same thing here, but instead use 2D doubly linked lists.
To best explain this, lets consider the structure from the exact cover example first:
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Figure 3: Example of dancing links data structure. Note columns header nodes have
number of 1s in its column represented as [Y], where Y is the number of 1s. The structure
looks back on itself, in both columns and rows.
As we can see, there is a node for each ’1’ entry in the binary matrix. Each column
is a vertical (doubly) linked list, each row is a horizontal (doubly) linked list, and they
wrap around in both directions. In addition, each column has a header node, that also
lists the number of ’1’ entries, so we can quickly find the column with smallest number
of ’1’s.
To solve the exact cover problem, we would use the same approach as Algorithm X,
but now we can scan quickly and also backtrack more easily. The data structure only
has entries for ’1’s, so we can quickly scan through the doubly linked data structure
to analyse these. In addition, a linked list allows quick (re)insertion and deletion from
backtracking, which is one issue with the standard Algorithm X formulation. See https:
//arxiv.org/abs/cs/0011047 for further details.
Sudoku Transformation To represent Sudoku as an exact cover problem, we only
need to construct a relevant binary matrix representation whose exact cover solution
corresponds to a valid Sudoku assignment. At a high level, we want to represent the
constraints of Sudoku as the columns, and possible value assignments (the ‘subsets’) as
the rows. Let’s discuss the construction of the binary matrix first before explaining why
it works.
Rows:
We specify a possible value assignment to each cell as the rows. For a 9 by 9 Sudoku
puzzle, there are 9 by 9 cells, of which each can take 9 values, giving us 9 * 9 * 9 = 729
rows. E.g., (r = 0, c = 2, v = 3) is a row in the matrix, means assign value 3 to the cell
in row 0 column 2.
Columns: The columns represents the constraints. There are four kinds of constraints:
One value per cell constraint (Row-Column): Each each cell must contain exactly
one value. For a 9 by 9 Sudoku puzzle, we have 9 * 9 = 81 cells, and therefore,
we have 81 row-column constraints, one for each cell. If a cell contains a value
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(regardless of what it is), we assign it a value of ’1’. This means for rows (r=0,
c=0, v=1), (r=0, c=0, v=2), … (r=0, c=0, v=9) in the matrix, they will all have
’1’ in the column corresponding to the row-column constraint (r=0, c=0). This
construction will mean only one of the above is selected for (r=0, c=0), satisfying
this constraint. Same applies for the other cells.
Row constraint (Row-Value): Each row must contain each number exactly once. For
a 9 by 9 Sudoku puzzle, we have 9 rows and 9 possible values that can be assigned to
each row, i.e., 9*9=81 row-value pairs. Therefore, we have 81 row-value constraints,
one for each row-value pair. If a row contains a value (regardless in which column),
we assign it a value of ’1’. This means for rows (r=0, c=0, v=1), (r=0, c=1, v=1),
… (r=0, c=8, v=1) in the matrix, they will all have ’1’ in the matrix column
corresponding to the row-value constraint (r=0, v=1). This construction will mean
only one of the above matrix rows is selected in order to satisfy the row-value
constraint (r=0, v=1). Same applies for the other rows.
Column constraint (Column-Value): Each column must contain each number exactly once. For a 9 by 9 Sudoku puzzle, we have 9 columns and 9 possible values
that can be assigned to each column, i.e., 9*9=81 column-value pairs. Therefore,
we have 81 column-value constraints, one for each column-value pair. If a column
contains a value (regardless in which row), we assign it a value of ’1’. This means
for rows (r=0, c=0, v=1), (r=1, c=0, v=1), … (r=8, c=0, v=1) in the matrix, they
will all have ’1’ in the matrix column corresponding to the column-value constraint
(c=0, v=1). This construction will mean only one of the above rows is selected in
order to satisfy the column-value constraint (c=0, v=1). Same applies for the other
columns.
Box Constraint (Box-Value): Each box must contain each value exactly once. For a
9 by 9 Sudoku puzzle, we have 9 boxes and 9 possible values that can be assigned to
each box, i.e., 9*9=81 box-value pairs. Therefore, we have 81 box-value constraints,
one for each box-value pair. If a box contains a value (regardless in which cell of
the box), we assign it a value of ’1’. This means for rows (r=0, c=0, v=1), (r=0,
c=1, v=1), … (r=2, c=2, v=1) in the matrix, they will all have ’1’ in the matrix
column corresponding to the box-value constraint (b=0, v=1). This construction
will mean only one of the above rows is selected in order to satisfy the box-value
constraint (b=0, v=1). Same applies for the other boxes.
Why this works? For exact cover, we select rows such that there is a single ’1’ in
all subsequent columns. The way we constructed the constraints, this is equivalent to
selecting value assignments (the rows) such that only value per cell, that each row and
column cannot have duplicate values, and each box also cannot have duplicate values. If
there are duplicates, then there will be more than a ’1’ in one of the column constraints.
By forcing to select a ’1’ in each column, we also ensure we a value is selected for every
cell, and all rows, columns and boxes have all values present.
This concludes the background. In the following, we will describe the tasks of this
assignment.
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The assignment is broken up into a number of tasks. Apart from Task A that should be
completed initially, all other tasks can be completed in an order you are more comfortable
with, but we have ordered them according to what we perceive to be their difficulty. Task
E is considered a high distinction task and hence we suggest to tackle this after you have
Task A: Implement Sudoku Grid (4 marks)
Implement the grid representation, including reading in from file and outputting a solved
grid to an output file. Note we will use the output file to evaluate the correctness of your
implementations and algorithms.
A typically Sudoku puzzle is played on a 9 by 9 grid, but there are 4 by 4, 16 by 16,
able to represent and solve Sudoku and variants of any valid sizes, e.g., 4 by 4 and above.
You won’t get a grid size that isn’t a perfect square, e.g., 7 by 7 is not a valid grid size,
and all puzzles will be square in shape.
In addition, the values/symbols of the puzzles may not be sequential digits, e.g., 1-9
for a 9 by 9 grid, but could be any set of 9 unique non-negative integer digits. The
same Sudoku rules and constraints still hold for non-standard set of values/symbols.
Your implementation should be able to read this in and handle any set of valid integer
values/symbols.
Task B: Implement Backtracking Solver for Sudoku (9 marks)
To help to understand the problem and the challenges involved, the first task is to develop
a backtracking approach to solve Sudoku puzzles.
Task C: Exact Cover Solver – Algorithm X (7 marks)
In this task, you will implement the first approaches to solve Sudoku as an exact cover
problem – Algorithm X.
In this task, you will implement the second of two approaches to solve Sudoku as an exact
cover problem – the Dancing Links algorithm. We suggest to attempt to understand and
implement Algorithm X first, then the Dancing Links approach.
Task E: Killer Sudoku Solver (16 marks)
In this task, you will take what you have learnt from the first two tasks and devise
and implement 2 solvers for Killer Sudoku puzzles. One will be based on backtracking
and the other should be more efficient (in running time) than the backtracking one.
Your implementation will be assessed for its ability to solve Killer Sudoku puzzles of
various difficulties within reasonable time, as well as your proposed approach, which will
be detailed in a short (1-2 pages) report. We are as interested in your approach and
rationale behind it as much as the correctness and efficiency of your approach.
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To help you get started and to provide a framework for testing, you are provided with
skeleton code that implements some of the mechanics of the Sudoku program. The main
class (RmitSudokuTester.java) implements functionality of Sudoku solving and parsing
parameters. The list of main java files provided are listed in Table 1.
file description
RmitSudokuTester.java Class implementing basic IO and processing code. Suggest
to not modify.
grid/SudokuGrid.java Abstract class for Sudoku grids Can add to, but don’t modify existing method interfaces.
grid/StdSudokuGrid.java Class for standard Sudoku grids. Please complete the implementation.
grid/KillerSudokuGrid.java Class for Killer Sudoku grids. Please complete the implementation.
solver/SudokuSolver.java Abstract class for Sudoku solver algorithms. Can add to,
but don’t modify existing method interfaces.
solver/StdSudokuSolver.java Abstract class for standard Sudoku solver algorithms, extends SudokuSolver class. This has empty implementation
and added in case you wanted to add some common methods/attributes for solving standard Sudoku puzzles, but
you don’t have to touch this if you don’t have these. Can
solver/KillerSudokuSolver.java Abstract class for Killer Sudoku solver algorithms, extends
SudokuSolver class. This has empty implementation and
added in case you wanted to add some common methods/attributes for solving Killer Sudoku puzzles, but you
don’t have to touch this if you don’t have these. Can add
to.
solver/BackTrackingSolver.java Class for solving standard Sudoku with backtracking.
solver/AlgorXSolver.java Class for solving standard Sudoku with Algorithm X algorithm. Please complete implementation.
solver/KillerBackTrackingSolver.java Class for solving Killer Sudoku with backtracking. Please
complete the implementation.
Table 1: Table of supplied Java files.
We also strongly suggest to avoid modifying RmitSudokuTester.java, as they form
the IO code, and any of the interfaces for the abstract classes. If you wish, you may
add java classes/files and methods, but it should be within the structure of the skeleton
code, i.e., keep the same directory structure. Similar to assignment 1, this is to minimise
compiling and running issues. Please ensure there are no compilation errors because of
any modifications. You should implement all the missing functionality in *.java files.
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Ensure your structure compiles and runs on the core teaching servers. Note that the
onus is on you to ensure correct compilation and behaviour on the core teaching servers
before submission, please heed this warning.
As a friendly reminder, remember how packages work and IDE like Eclipse will automatically add the package qualifiers to files created in their environments. This is a large
source of compile errors on the core teaching servers, so remove these package qualifiers
when testing on the core teaching servers.
Compiling and Executing
To compile the files, run the following command from the root directory (the directory
that RmitSudokuTester.java is in):
javac *.java grid/*.java solver/*.java
Note that for Windows machine, remember to replace ‘/’ with ‘\’.
To run the framework:
java RmitSudokuTester [puzzle fileName] [game type] [solver type]
[visualisation]
where
• puzzle fileName: name of file containing the input puzzle/grid to solve.
• game type: type of sudoku game, one of {sudoku, killer}.
• solver type: Type of solver to use, depends on the game type.
– If (standard) Sudoku is specified (sudoku), then solver should be one of {backtracking,
algorx, dancing}, where backtracking is the backtracking algorithm for standard Sudoku, algorx and dancing are the exact cover approaches for standard
Sudoku.
– If Killer Sudoku is specified (killer), then solver should be one of
{ backtracking, advanced } where backtracking is the backtracking algorithm
for Killer Sudoku and advanced is the most efficient algorithm you can devise
for solving Killer Sudoku.
• visualisation: whether to output grid before and another solving, one of {n , y}.
• output fileName: (optional) If specified, the solved grid will be outputted to this
file. Ensure your implementation implements this as it will be used for testing (see
the outputBoard() methods for the classes in grid directory).
5.1 Details of Files
In this section we describe the format of the input and output files.
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Puzzle file (input)
This specifies the puzzle and includes information:
• size of puzzle
• location of the cells with initial values
• (for Killer Sudoku, location of cages and their totals).
Standard Sudoku (input) The exact format for standard Sudoku is as follows:
[ s i z e / dimen sion s of p u z zl e ]
[ l i s t of v a l i d symbols ]
[ t u p l e s of row , column value , one t u pl e pe r l i n e ]
For instance, for the tuple
0,0 1
means there is a value 1 in cell (r = 0, c = 0).
Using the example from Figure 1a, the first few lines of the input file corresponding
to this example would be:
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1 2 3 4 5 6 7 8 9
0 ,0 5
0 ,1 3
0 ,4 7
1 ,0 6
1 ,3 1
. . .
Killer Sudoku (input) The exact format for Killer Sudoku is as follows:
[ s i z e / dimen sion s of p u z zl e ]
[ l i s t of v a l i d symbols ]
[ number of cag e s ]
[ To tal of cage , l i s t of row , column f o r each cage , one pe r l i n e ]
Using the example from Figure 2a, the first few lines of file corresponding to this
example would be:
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1 2 3 4 5 6 7 8 9
28
3 0 ,0 0 ,1
15 0 ,2 0 ,3 0 ,4
. . .
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Solved/filled in grid output file (output)
After a puzzle is solved, the output format of a filled in grid should be a comma separate
file. For a n by n grid, with the cells referenced by (row, column) and the top left corner
is (0,0) (row =0, column = 0), should have the following output (we included the first
row and column for indexing purposes but they shouldn’t be in your output file):
c = 0 c = 1 c = 2 . . . c = n − 1
r = 0 v0,0, v0,1, v0,2, . . . , v0,n−1
r = 1 v1,0, v1,1, v − 1, 2, . . . , v − 1, n − 1
.
.
.
.
.
.
.
.
.
.
.
.
r = n − 1 vn−1,0, vn−1,1, vn−1,2, . . . , vn−1,n−1
where vr,c is the value of cell (r,c). More concretely, for a 4 by 4 puzzle using 1-4 values/symbols, a sample valid filled grid could be:
2,1,4,3
4,3,2,1
3,2,1,4
1,4,3,2
5.2 Clarification to Specifications
Please periodically check the assignment FAQ for further clarifications about specifications. In addition, the lecturer and course coordinator will go through different aspects
of the assignment each week, so be sure to check the course material page on Canvas to
see if there are additional notes posted.
6 Submission
The final submission will consist of:
• The Java source code of your implementations, including the ones we provided.
Keep the same folder structure as provided in skeleton (otherwise the packages
won’t work). Maintaining the folder structure, ensure all the java source files
are within the folder tree structure. Rename the root folder as Assign2-. Specifically, if your student number is s12345, then all the
source code files should be within the root folder Assign2-s12345 and its children
folders.
• All folder (and files within) should be zipped up and named as Assign2-.zip. E.g., if your student number is s12345, then your submission file should be called
Assign2-s12345.zip, and when we unzip that zip file, then all the submission files
should be in the folder Assign2-s12345.
• Your report of your approach, called “assign2Report.pdf”. Place this pdf within
the Java source file root directory/folder, e.g., Assign2-s12345.
Note: submission of the zip file will be done via Canvas.
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Late Submission Penalty Late submissions will incur a 10% penalty on the total
marks of the corresponding assessment task per day or part of day late. Submissions
that are late by 5 days or more are not accepted and will be awarded zero, unless special
consideration has been granted. Granted Special Considerations with new due date set
after the results have been released (typically 2 weeks after the deadline) will automatically result in an equivalent assessment in the form of a practical test, assessing the
same knowledge and skills of the assignment (location and time to be arranged by the
instructor). Please ensure your submission is correct (all files are there, compiles etc),
re-submissions after the due date and time will be considered as late submissions. The
core teaching servers and Canvas can be slow, so please ensure you have your assignments
are done and submitted a little before the submission deadline to avoid submitting late.
7 Academic integrity and plagiarism (standard warning)
You should take extreme care that you have:
• Acknowledged words, data, diagrams, models, frameworks and/or ideas of others
you have quoted (i.e. directly copied), summarised, paraphrased, discussed or mentioned in your assessment through the appropriate referencing methods
• Provided a reference list of the publication details so your reader can locate the
source if necessary. This includes material taken from Internet sites. If you do not
acknowledge the sources of your material, you may be accused of plagiarism because
you have passed off the work and ideas of another person without appropriate
referencing, as if they were your own.
RMIT University treats plagiarism as a very serious offence constituting misconduct.
Misconduct and plagiarism covers a variety of inappropriate behaviours, including:
• Failure to properly document a source
• Copyright material from the internet or databases
• Collusion between students
• Submitting assignments of other students from previous semesters
For further information on our policies and procedures, please refer to the following:
https://www.rmit.edu.au/students/student-essentials/rights-and-responsibilities/
8 Getting Help
There are multiple venues to get help. There are weekly consultation hours (see Canvas
for time and location details). In addition, you are encouraged to discuss any issues you
have with your Tutor or Lab Demonstrator. We will also be posting common questions on
the assignment 2 FAQ section on Canvas and we encourage you to check and participate
in the discussion forum on Canvas. However, please refrain from posting solutions,
particularly as this assignment is focused on algorithmic and data structure design.
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9 Marking guidelines
The assignment will be marked out of 50 and a bonus of up to 3 marks.
The assessment in this assignment will be broken down into a number of components.
The following criteria will be considered when allocating marks. All evaluation will be
done on the core teaching servers.
For this task, we will evaluate whether you are able to read in puzzle input files,
represent and construct a grid and whether you can output a solved grid to output files.
For this task, we will evaluate your implementation and algorithm on whether:
1. Implementation and Approach: It implements the backtracking algorithm to solve
Sudoku puzzles.
2. Correctness: Whether it correctly solves Sudoku puzzles.
3. Efficiency: As part of correctness, your implementation should not take excessively
long to solve a puzzle. We will benchmark the running time against our nonoptimised solution and add a margin on top, and solutions taking longer than this
will be considered as inefficient.
For this task, we will evaluate your implementation and algorithm on whether:
1. Implementation and Approach: It implements AlgorithmX approach to solve Sudoku puzzles.
2. Correctness: Whether it correctly solves Sudoku puzzles.
3. Efficiency: As part of correctness, your implementation should not take excessively
long to solve a puzzle. We will benchmark the running time against our nonoptimised solution of the same algorithm and add a margin on top, and solutions
taking longer than this will be considered as inefficient.
For this task, we will evaluate your implementation and algorithm on whether:
1. Implementation and Approach: It implements the Dancing Link approach to solve
Sudoku puzzles.
2. Correctness: Whether it correctly solves Sudoku puzzles.
3. Efficiency: As part of correctness, your implementation should not take excessively
long to solve a puzzle. We will benchmark the running time against our nonoptimised solution of the same algorithm and add a margin on top, and solutions
taking longer than this will be considered as inefficient.
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For this task, we will evaluate your two implementations and algorithms on whether:
1. Implementation and Approach: It takes reasonable approaches and can solve Killer
Sudoku puzzles.
2. Correctness: Whether they correctly solves Killer Sudoku puzzles.
3. Description of Approach: In addition to the code, you will be assessed on a description of your proposed advanced approach, which will help us to understand your
approach. Include how you represented the Killer Sudoku grid, how you approached
solving Killer Sudoku puzzles with your advanced approach and your rationale behind it. You may cite other references you have researched upon and utilised the
information within. Include a comparison of the backtracking and advanced algorithms and include empirical evidence (similar to Assignment 1) to show your
should be no longer than two pages and submitted as a pdf as part of your submission. You will be assessed on the approach, its clarity and whether it reflects your
code.
Interview (5/50) We will conduct a short interview with you about the tasks above.
This is compulsory and if not completed, will lead to the assignment not being assessed
and a mark of 0 given. A schedule will be released and the time can be further negotiated.
Coding style and Commenting (2/50):
You will be evaluated on your level of commenting, readability and modularity. This
should be at least at the level expected of a first year masters student who has done some
programming courses.
Bonus (up to 3 marks extra) To encourage exploration of novel solvers to Killer
Sudoku, we will award up to 3 bonus marks to individuals who has the fatest empirical
(average) running times for the advanced solver. The student with the fastest algorithm
will receive 3 bonus marks, 2nd fastest 2 marks, and 3rd fastest will be awarded 1 bonus
marks.
the bonus your overall course total is > 100, your total will be capped at 100.
14 E-mail: vipdue@outlook.com  微信号:vipnxx 