= Tangram =

<<TableOfContents>>

== Problem Description ==

Tangram is an ancient Chinese game of Shapes. The goal is to form a particular shape from a set of seven pieces consisting of 5 triangles (of three different sizes), a square, and a parallelogram.

The number of sides, the sizes and basic orientations of the seven blocks is defined below. The 1st argument is the block number, the 2nd is the number of sides, then there is the  sequence of coordinates of successive vertexes:
{{{
size_block(1,3, 0,0, 4,0, 2,2). %%% Large triangle 
size_block(2,3, 0,0, 4,0, 2,2). %%% Large triangle 
size_block(3,3, 0,0, 2,0, 0,2). %%% Medium triangle
size_block(4,3, 0,0, 2,0, 1,1). %%% Small triangle 
size_block(5,3, 0,0, 2,0, 1,1). %%% Small triangle 
size_block(6,4, 0,0, 1,-1, 2,0, 1,1). %%% Square 
size_block(7,4, 0,0, 1,1,  1,3, 0,2).   %%% parallelogram 
}}}
Allowed angles are represented by the number 0..7 in parenthesis.
You can assume MAXX=8 and MAXY=6.

Your program needs to compute a predicate put/4 that associates to each block i in {1,...,7} one pair (X,Y) and one angle A. With that association the entire surface of the instance figure must be covered (and without overlapping, but this is a consequence for the chosen figures).

== Predicates ==

 * '''Input''': {{{sides/1, coord/3}}}

 * '''Output''': {{{put/4}}}

== Input format ==

Any input instance is defined using two predicates: {{{sides(n)}}}.

that fixes the number of sides of the figure and
{{{
coord(1,X1,Y1). 
coord(2,X2,Y2). 
...             
coord(n,Xn,Yn). 
}}}
that are the coordinates of the consecutive vertexes 1,2, ..., n of the figure. No need to say that the perimeter of the figure is the set of segments { (X1,Y1)-(X2,Y2), (X2,Y2)-(X3,Y3), ..., (Xn-1,Yn-1)-(Xn,Yn), (Xn-Yn)-(X1,Y1) }.

Although is clear that some of the sides of the 7 blocks have an irrational length, their orientation (above) as well as the orientations of the instances are chosen so as to work with integer numbers only.

The allowed action is to "put" the vertex corresponding to (0,0) in the above "size_block" definition in a point (X,Y) with X in {0,1,...,MAXX} and Y in {0,1,...,MAXY} rotated wrt its
basic orientation by 0 (0), 45 (1), 90 (2), 135 (3), 180 (4), 225 (5), 270 (6), 315 (7) degrees.

== Output format ==

A possible output should be of the form
{{{
put(1,4,0,0). put(2,4,4,6). put(3,4,0,2). put(4,0,0,0). 
put(5,3,1,2). put(6,1,1,0). put(7,3,1,0). 
}}}
that  is also a correct solution of the instance
{{{
sides(3). 
coord(1,0,0). 
coord(2,8,0). 
coord(3,4,4). 
}}}
== Example(s) ==

== Author(s) ==
 * Author:  Agostino Dovier 	
   * Affiliation: University of Udine, Italy
 * Author: Andrea Formisano 	
   * Affiliation: University of Perugia, Italy
 * Author: Enrico Pontelli	
   * Affiliation: New Mexico State University, USA