# Assignment No. 6 EECS 210 Discrete Structures

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Assignment No. 6
EECS 210
Discrete Structures

Submit deliverables in a single zip file to Canvas
Name of the zip file: FirstnameLastname_Assignment6 (with your first and last name)
Name of the Assignment folder within the zip file: FirstnameLastname_Assignment6
Deliverables:
1. Copy of Rubric6.docx with your name and ID filled out (do not submit a PDF).
2. Source code.
3. Screen print showing the successful execution of your code or copy and paste the
output from a console screen to a Word document and PDF it.
Assignment:
• You may use any language you want, but if you want help from me or one of the
SIs, you should probably use C++, Python, or Haskell.
• Topic: Recursion
• Sudoku is a number puzzle in which a 9×9 grid is subdivided into 9 3×3 sub-grids,
or blocks.
• A typical puzzle is shown here (image credit: Wikimedia Commons):
• Each of the cells in the puzzle must be filled in with a single digit 1-9, subject to
the following constraints:
1. Each digit from 1 to 9 must appear exactly once in each row.
2. Each digit from 1 to 9 must appear exactly once in each column.
3. Each digit from 1 to 9 must appear exactly once in each block.
• Published puzzles are usually constructed to have a unique solution. This requires
that at least 17 cells be filled in (and may require more; depending on the puzzle
and which cells are empty, as many as 78 filled cells can be required to guarantee
uniqueness). In general, the number of cells that are already filled in is not a
particularly good indicator of how difficult a Sudoku puzzle is to solve.
• The Sudoku problem, then, is this: Given a partially completed Sudoku puzzle,
find the (or at least a) solution; if no solution exists, prove that.
• It is possible to solve a Sudoku puzzle entirely through logic. For example, in the
above puzzle, consider the bottom right block, top right cell. Because of other
numbers in the same row, column, or grid, that number cannot be 1, 2, 3, 5, 6, 7,
8, or 9, and so must be 4. By proceeding in this fashion, using these and more
advanced deduction rules, it’s possible to gradually fill in the entire grid.
• That is not the approach we’re going to use. Instead, we’re going to implement a
brute-force search, in which we exhaustively try possibilities until we find a
solution. This will be slower to run but is easier to solve. (And by “slower to run,”
we mean it’ll finish in a few tenths of a second rather than a few milliseconds.)
• Here’s the idea: Suppose we have a Sudoku puzzle of which k of the 81 cells are
unfilled. We identify an empty cell and deduce a list of candidates for what might
go into that cell. If there are no such values (all digits are accounted for elsewhere
in the same row, column, or grid), then we must have made a mistake in filling in
the k cells and return a no-solution-found result. Otherwise, we try putting the
first candidate value into the empty cell, and see if we can find a solution with the
k+1 cells filled (i.e. a recursive call). If we get a no-solution-found to the first
candidate, then we try the next, and so on, until we either find a solution (k == 81)
or determine that no solution exists (all candidates report no solution, which again
implies we took a wrong path somewhere earlier).
• This approach, by the way, is called depth-first search with backtracking. For
each empty cell we make an attempt and see how far we can get with it. If we fail
to find a solution, we back up until we find something else to try, and so on. If a
solution exists, we are guaranteed to find it, because we exhaustively try all
possibilities.
• You are given five files (puzzle1.txt through puzzle5.txt), each containing a
Sudoku puzzle. Digits already filled in have been placed, and an underscore
character (_) is used to indicate a blank square.
• You may read the files in or just hard-code them in the program.
• Write a recursive program to find the solution to the five puzzle files.
• The output for each solution, should include:
1. The puzzle file name (e.g., puzzle1.txt)
2. The puzzle from the file printed out.
3. The solution to the puzzle printed out or if no solution is found, “No
solution found” printed out.
• The solution may not be unique; if there is more than one solution to the puzzle,
any valid solution is acceptable.
• Provide comments that explain what each line of code is doing. See rubric below.
Exceeds Expectations
(90-100%)
Meets Expectations
(80-89%)
Unsatisfactory
(0-79%)
commented with prologue
summarizing major blocks of
line.
but missing some items or some
major blocks of code are not
commented or there are
line.
all together or there are no
code or there are very few
• Name of program contained in the file (e.g., EECS 210 Assignment 3)
• Brief description of the program, e.g.:
o Python code for demonstrating operations on relations and properties of
relations.
• Inputs (e.g., none, for a function, it would be the parameters passed to it)
• Output, e.g.,
o Print out of the name of each exercise, followed by the exercise’s output.
• Author’s full name
• Creation date: The date you first create the file, i.e., the date you write this
comment