CS 241 Data Organization using C
Project 1: Magic Squares
Fall 2013
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Magic Squares
A magic square is an arrangement of numbers in a square grid, where the numbers in each
row, in each column, and each major diagonal is a constant. For project, we will be dealing
with a Magic Square of Order 3, that is, a 3x3 matrix of unique positive integers such that
the sum of each row, column, and major diagonal is a constant.
We will restrict the values in the 3x3 matrix to two digits (adding a leading zero for single
digit values). We’ll call the 18 digits from the rows of the matrix a magic number.
12 27 6 → 45
9 15 21 → 45
24 3 18 → 45
. ↓ ↓ ↓ &
45
45 45 45
45
Nonconsecutive Magic Square of Order 3
18 digit Magic Number: 122706091521240318
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Requirements
Write a C program that reads from the standard input stream a list of 18 digit numbers
with ‘?’ characters replacing some of the digits.
• If an 18-digit Magic Number exists that uses the given digits in the given order, then
find it, and print it. Specifically, echo the input, print “->”, and print the number
found.
• If not, echo the input and print “No Solution”.
• If the input does not follow the specified format, then echo the input record and print
“Error”.
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2.1
Input format
• A record is a sequence of characters followed by the newline character: ‘\n’.
• The input will consist of some number of records (lines).
• Each valid record will consist of 18 characters.
• The only valid characters in a record are the ten digits (0-9) and ‘?’.
• Either a full two-digit pair will be missing “??” or fully given. For example, “?2270609??212403??”
is an error because part of one pair is given.
2.1.1
Example Error Cases
Example
?2270609??212403?? Error
1122334455667?8899 Error
0409020307?????? Error
??270609??212403??24 Error
??270609??212403??2 Error
??270609x3212403?? Error
12??????????????12 Error
??270609??210303?? Error
2.1.2
Comment
Unmatched ?
Unmatched ?
< 18 characters
> 18 characters
> 18 characters
bad char ‘x’
12 not unique
03 not unique
Example Non-Error Cases
Example
060702010509??0304 -> 060702010509080304
06??02010509??0304 -> 060702010509080304
0409020305???????? -> 040902030507080106
??270609??212403?? -> 122706091521240318
15??09??182427???? -> 153009121824270621
54??364563????2772 -> 549936456381902772
??23????111720??14 No Solution
??331215??273009?? -> 183312152127300924
??50??32??44??26?? -> 355029323844472641
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Comment
very easy
easy
easy
No sum given
No sum given with 4 unknowns
No sum given
5 unknowns; can take up to 5 minutes
Turning in your assignment
Attach your program file to the Magic Square assignment in UNM Learn.
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Grading Rubric
20 Points:
Adheres to CS-241 coding standard. This includes indenting, comments, dead code elimination, not using goto, . . .
54 Points: Three points for each passed test record of: magicNumber.in using:
./yourprogram < magicNumber.in > youroutputfile
/usr/bin/diff youroutputfile magicNumber.out
28 Points:
+30 Points extra credit
two points for each passed test record of an unknown set. No valid
record will have more than 5 unknowns.
if you can find magic numbers with 5 unknowns in less than 30 seconds
(when run on moons.cs.unm.edu)
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