University of Calgary

domino effect

The Domino Effect
source: ACM programming contest
A standard set of Double Six dominoes contains 28 pieces (called bones) each displaying two numbers from 0 (blank) to 6 using dicelike pips. The 28 bones, which are unique, consist of the following combinations of pips:
 
Bone# Pips  Bone# Pips  Bone# Pips  Bone# Pips
1  0 | 0   8  1 | 1   15  2 | 3   22  3 | 6
2  0 | 1   9  1 | 2   16  2 | 4   23  4 | 4
3  0 | 2  10  1 | 3   17  2 | 5   24  4 | 5
4  0 | 3  11  1 | 4   18  2 | 6   25  4 | 6
5  0 | 4  12  1 | 5   19  3 | 3   26  5 | 5
6  0 | 5  13  1 | 6   20  3 | 4   27  5 | 6
7  0 | 6  14  2 | 2   21  3 | 5   28  6 | 6
All the Double Six dominoes in a set can he laid out to display a 7 x 8 grid of pips. Each layout corresponds at least one _map_ of the dominoes. A map consists of an identical 7 x 8 grid with the appropriate bone numbers substituted for the pip numbers appearing on that bone. An example of a 7 x 8 grid display of pips and a corresponding map of bone numbers is shown below.
 7 x 8 grid of pips
6 6 2 6 5 2 4 1
1 3 2 0 1 0 3 4
1 3 2 4 6 6 5 4
1 0 4 3 2 1 1 2
5 1 3 6 0 4 5 5
5 5 4 0 2 6 0 3
6 0 5 3 4 2 0 3
 map of bone numbers
28 28 14  7 17 17 11 11
10 10 14  7  2  2 21 23
 8  4 16 25 25 13 21 23
 8  4 16 15 15 13   9 9
12 12 22 22  5  5 26 26
27 24 24  3  3 18  1 19
27  6  1 19
 
Write a program that will analyze the pattern of pips in any 7 x 8 layout of a standard set of dominoes and produce a map showing the position of all dominoes in the set. If more than one arrangement of dominoes yield the same pattern, your program should generate a map of each possible layout.
 
Input and Output
The input file will contain several of problem sets. Each set consists of seven lines of eight integers from 0 through 6, representing an observed pattern of pips. Each set is corresponds to a legitimate configuration of bones (there will be at least one map possible for each problem set). There is no intervening data separating the problem sets.
 
Correct output consists of a problem set label (beginning with Set #1) followed by an echo printing of the problem set itself. This is followed by a map label for the set and the map(s) which correspond to the problem set. (Multiple maps can be output in any order.) After all maps for a problem set have been printed, a summary line stating the number of possible maps appears. At least three lines are skipped between the output from different problem sets while at least one line separates the labels, echo printing, and maps within the same problem set. A sample input file of two problem sets along with the correct output are shown on the reverse of this page.
 Sample Input
5 4 3 6 5 3 4 6
0 6 0 1 2 3 1 1
3 2 6 5 0 4 2 0
5 3 6 2 3 2 0 6
4 0 4 1 0 0 4 1
5 2 2 4 4 1 6 5
5 5 3 6 1 2 3 1
4 2 5 2 6 3 5 4
5 0 4 3 1 4 1 1
1 2 3 0 2 2 2 2
1 4 0 1 3 5 6 5
4 0 6 0 3 6 6 5
4 0 1 6 4 0 3 0
6 5 3 6 2 1 5 3
Sample Output
Layout #1:
 
5 4 3 6 5 3 4 6
0 6 0 1 2 3 1 1
3 2 6 5 0 4 2 0
5 3 6 2 3 2 0 6
4 0 4 1 0 0 4 1
5 2 2 4 4 1 6 5
5 5 3 6 1 2 3 1
 Maps resulting from layout #1 are:
 
 6 20 20 27 27 19 25 25
 6 18  2  2  3 19  8  8
21 18 28 17  3 16 16  7
21  4 28 17 15 15 5  7
24  4 11 11 1  1  5 12
24 14 14 23 23 13 13 12
26 26 22 22  9  9 10 10
   There are 1 solution(s) for layout #1.
Layout #2:
4 2 5 2 6 3 5 4
5 0 4 3 1 4 1 1
1 2 3 0 2 2 2 2
1 4 0 1 3 5 6 5
4 0 6 0 3 6 6 5
4 0 1 6 4 0 3 0
6 5 3 6 2 1 5 3
   Maps resulting from layout #2 are:
16 16 24 18 18 20 12 11
 6  6 24 10 10 20 12 11
 8 15 15  3  3 17 14 14
 8  5  5  2 19 17 28 26
23  1 13  2 19  7 28 26
23  1 13 25 25  7  4  4
27 27 22 22  9  9 21 21
 
16 16 24 18 18 20 12 11
 6  6 24 10 10 20 12 11
 8 15 15  3  3 17 14 14
 8  5  5  2 19 17 28 26
23  1 13  2 19  7 28 26
23  1 13 25 25  7 21  4
27 27 22 22  9  9 21  4
 
There are 2 solution(s) for layout #2.



Updated: August 30, 2005 05:14 PM