import structure FD from "x-alice:/lib/gecode/FD"
import structure Modeling from "x-alice:/lib/gecode/Modeling"
import structure Explorer from "x-alice:/lib/tools/Explorer"
import structure Space from "x-alice:/lib/gecode/Space";

open Modeling

(* agelist ensures the constraint a > b > c *)
fun age_list space =
    let
    	val ages as #[a,b,c] = FD.intvarVec(space,3,#[(0,9)])
    in 
    	FD.rel(space,a,FD.GR,b);
    	FD.rel(space,b,FD.GR,c);
    	ages
    end


fun makefamily space =
    let
    	val boysages  = age_list space
    	val girlsages = age_list space
    	val tmp1 = FD.range(space,(0,243))
    	val tmp2 = FD.range(space,(0,243))
    	val ages as #[a,b,c,d,e,f] = 
    		Vector.concat([boysages,girlsages])
    	fun squares_sum(#[x,y,z],res)= 
            post(space,FD(x)`* FD(x)`+ 
                       FD(y)`* FD(y)`+
                       FD(z)`* FD(z) `= FD(res),FD.DOM)
    in
    	FD.distinct(space,ages,FD.DOM);
    	post(space,FD(a) `+ FD(b) `+ FD(c) 
    	        `= FD(d) `+ FD(e) `+ FD(f),FD.DOM);
    	squares_sum(boysages,tmp1);
    	squares_sum(girlsages,tmp2);
    	FD.rel(space,tmp1,FD.EQ,tmp2);
    	{boys= #[Vector.sub(ages,0),Vector.sub(ages,1),
                 Vector.sub(ages,2)],
    	 girls = #[Vector.sub(ages,3),Vector.sub(ages,4),
    	           Vector.sub(ages,5)]}
    end
    	
    	
fun family space = 
    let
    	val maria = makefamily space
    	val clara = makefamily space
    	val ageofmariasyoungestgirl = Vector.sub(#girls maria,2)
    	val ageofclarasyoungestgirl = Vector.sub(#girls clara,2)
    	val ages = Vector.concat([#boys (maria),#girls (maria),
    	                          #boys(clara),#girls(clara)])
    in
    	Vector.app(fn x => 
    	      FD.rel(space,x,FD.GR,ageofmariasyoungestgirl))
    	          (#boys maria);
    	FD.relI(space,ageofclarasyoungestgirl,FD.EQ,0);
    	post(space,SUMV(ages) `= `60,FD.DOM);
    	FD.branch(space,ages,FD.B_SIZE_MIN,FD.B_MIN);
    	{maria,clara}
    end	  	
 
(* Explorer.exploreAll family *)