/*

Fractions problem in AMPL+CP.

Prolog benchmark problem (BProlog)
"""
Find distinct non-zero digits such that the following equation holds:
A        D        G
------  + ----- + ------  = 1
B*C      E*F      H*I
"""

This AMPL model was created by Hakan Kjellerstrand, hakank@gmail.com

*/

# Licenced under CC-BY-4.0 : http://creativecommons.org/licenses/by/4.0/

param n;

# decision variables
var A >= 1 <= n integer;
var B >= 1 <= n integer;
var C >= 1 <= n integer;
var D >= 1 <= n integer;
var E >= 1 <= n integer;
var F >= 1 <= n integer;
var G >= 1 <= n integer;
var H >= 1 <= n integer;
var I >= 1 <= n integer;

var x{1..n} >= 1 <= n integer;

var D1 >= 1 <= 81 integer;
var D2 >= 1 <= 81 integer;
var D3 >= 1 <= 81 integer;

#
# constraints
#
s.t. c0:
x[1] = A and
x[2] = B and
x[3] = C and
x[4] = D and
x[5] = E and
x[6] = F and
x[7] = G and
x[8] = H and
x[9] = I
;
s.t. c1: alldiff{i in 1..n}  x[i];

s.t. c2:

D1 = 10*B+C and
D2 = 10*E+F and
D3 = 10*H+I and
A*D2*D3 + D*D1*D3 + G*D1*D2 = D1*D2*D3 and
# symmetry breaking
A*D2 >= D*D1 and
D*D3 >= G*D2 and
# redundant constraints
3*A >= D1 and
3*G <= D2
;

data;

param n := 9;

# option presolve 0;
option show_stats 2;

option solver gecode;
option gecode_options "var_branching=degree_max val_branching=max outlev=1 outfreq=1";

# option solver ilogcp;
# option ilogcp_options "optimizer=auto alldiffinferencelevel=4 debugexpr=0 logperiod=10 logverbosity=0";

solve;

display x;