Program | DICE.C, DICE.CPP, DICE.PAS |
InterGames is a high-tech startup company that specializes in developing technology
that allows users to play games over the Internet. A market analysis has alerted
them to the fact that games of chance are pretty popular among their potential
customers. Be it Monopoly, ludo or backgammon, most of these games involve throwing
dice at some stage of the game. Of course, it would be unreasonable if players
were allowed to throw their dice and then enter the result into the computer,
since cheating would be way to easy. So, instead, InterGames has decided to
supply their users with a camera that takes a picture of the thrown dice, analyzes
the picture and then transmits the outcome of the throw automatically. For this
they desperately need a program that, given an image containing several dice,
determines the numbers of dots on the dice.
We make the following assumptions about the input images. The images contain
only three different pixel values: for the background, the dice and the dots
on the dice. We consider two pixels connected if they share an edge -- meeting
at a corner is not enough. In the figure, pixels A and B are connected, but
B and C are not.
.... .B.. .AC. ....
A set S of pixels is connected if for every pair (a;b) of pixels in S, there
is a sequence a1, a2 , ..., ak in S such that
a = a1 and b = ak , and ai and ai+1
are connected for 1 <= i < k.
We consider all maximally connected sets consisting solely of nonbackground
pixels to be dice. ‘Maximally connected' means that you cannot add any
other nonbackground pixels to the set without making it disconnected. Likewise
we consider every maximal connected set of dot pixels to form a dot.
The input consists of pictures of several dice throws. Each picture description
starts with a line containing two numbers w and h, the width and height of the
picture, respectively. These values satisfy 5 <= w; h <= 50.
The following h lines contain w characters each. The characters can be: ``.''
for a background pixel, ``*'' for a pixel of a die, and ``X'' for a pixel of
a die's dot. Dice may have different sizes and not be entirely square due to
optical distortion. The picture will contain at least one die, and the numbers
of dots per die is between 1 and 6, inclusive. The input is terminated by a
picture starting with w = h = 0, which should not be processed.
For each throw of dice, first output its number. Then output the number of dots on the dice in the picture, sorted in increasing order. Print a blank line after each test case.
Sample input
30 15 .............................. .............................. ...............*.............. ...*****......****............ ...*X***.....**X***........... ...*****....***X**............ ...***X*.....****............. ...*****.......*.............. .............................. ........***........******..... .......**X****.....*X**X*..... ......*******......******..... .....****X**.......*X**X*..... ........***........******..... .............................. 0 0
Throw 1
1 2 2 4