A.55.4.3 Example 3

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.