/*

  Simple money change problem in Picat.

 

  Model created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import cp.

main => go.

go =>
   problem(1,Value, Coins),
   solveit(Value,Coins).

go2 =>
   problem(2,Value, Coins),
   solveit(Value,Coins).

solveit(Value,Coins) =>
   L = findall(X, $money(Value, Coins, X)),
   writeln(L),
   writeln(len=L.length),
   nl.

scalar_product(A, X, Product) => 
   Product #= sum([S : I in 1..A.length, S #= A[I]*X[I]]).


money(Value, Coins, X) =>
   
   N = length(Coins),
   X = new_list(N),
   X :: 0..Value,
   scalar_product(Coins, X, Value),
   solve(X).


% problem(Problem, Value, Coins).
problem(1, Value, Coins) => Value = 100, Coins = [100,50,25,10,5,1].
problem(2, Value, Coins) => Value = 100, Coins = [100,50,25,10,5,2,1].