#
# Least diff problem in Elixir.
#
# What is the smallest difference between two numbers X - Y
# if you must use all the digits (0..9) exactly once, i.e.
# Minimize the difference
#   ABCDE - FGHIJ
#
# Solution: 50123 - 49876 = 247
#
# This program was created by Hakan Kjellerstrand, hakank@gmail.com
# See also my Elixir page: http://www.hakank.org/elxir/
#
defmodule LeastDiff do
  # import CPUtils

  alias CPSolver.IntVariable
  alias CPSolver.Constraint.Sum
  # alias CPSolver.Constraint.Equal
  alias CPSolver.Constraint.AllDifferent.FWC, as: AllDifferent
  alias CPSolver.Constraint.LessOrEqual
  alias CPSolver.Model
  alias CPSolver.Objective

  import CPSolver.Constraint.Factory
  import CPSolver.Variable.View.Factory

  alias CPSolver.Variable.Interface

  def main() do
    n = 10

    xs =
      for i <- 0..(n - 1) do
        IntVariable.new(0..9, name: "x[#{i}]")
      end

    [a, b, c, d, e, f, g, h, i, j] = xs

    # To minimize
    z = IntVariable.new(0..(10 ** 6), name: "z")

    # This is slower: 0.45s
    # x = IntVariable.new(0..10**6, name: "x")
    # y = IntVariable.new(0..10**6, name: "y")
    # x_constraint = Sum.new(x, [mul(a,10_000),mul(b,1000),mul(c,100),mul(d,10),e])
    # y_constraint = Sum.new(y, [mul(f,10_000),mul(g,1000),mul(h,100),mul(i,10),j])

    # A little faster: 0.2s
    {x, x_constraint} = sum([mul(a, 10_000), mul(b, 1000), mul(c, 100), mul(d, 10), e])
    {y, y_constraint} = sum([mul(f, 10_000), mul(g, 1000), mul(h, 100), mul(i, 10), j])

    IO.inspect(Interface.size(x), label: :size_x)
    IO.inspect(Interface.size(y), label: :size_y)

    model =
      Model.new(
        xs ++ [x, y, z],
        [
          x_constraint,
          y_constraint,
          AllDifferent.new(xs),
          LessOrEqual.new(y, x),
          # calculate z
          Sum.new(z, [x, mul(y, -1)])
        ],
        objective: Objective.minimize(z)
      )

    Logger.configure(level: :info)

    opts = [
      # search: {:first_fail, :indomain_min},
      search: {:input_order, :indomain_min},
      # search: {:first_fail, :indomain_random},
      space_threads: 12,
      timeout: :infinity
      # stop_on: {:max_solutions, 2},
    ]

    {:ok, res} =
      CPSolver.solve_sync(
        model,
        opts
      )

    IO.inspect(res.statistics)
    sols = res.solutions |> List.last()
    diff_val = Enum.at(sols, 10)
    x_val = Enum.at(sols, 11)
    y_val = Enum.at(sols, 12)
    :io.format("~w - ~w = ~w~n", [x_val, y_val, diff_val])
  end
end