We are given:
- 3 coins each worth 1 unit
- 20 coins each worth 5 units and
- 10 coins each worth 20 units.
The task is to find a minimal number of these coins that
amount to 111 units in total. We introduce variables c(1), c(5)
and c(20) denoting how many coins to take of the respective
type:
:- use_module(library(simplex)).
coins(S) :-
gen_state(S0),
coins(S0, S).
coins -->
constraint([c(1), 5*c(5), 20*c(20)] = 111),
constraint([c(1)] =< 3),
constraint([c(5)] =< 20),
constraint([c(20)] =< 10),
constraint([c(1)] >= 0),
constraint([c(5)] >= 0),
constraint([c(20)] >= 0),
constraint(integral(c(1))),
constraint(integral(c(5))),
constraint(integral(c(20))),
minimize([c(1), c(5), c(20)]).
An example query:
?- coins(S), variable_value(S, c(1), C1),
variable_value(S, c(5), C5),
variable_value(S, c(20), C20).
C1 = 1,
C5 = 2,
C20 = 5.
