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Constraint Programming Solver
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lib/examples/queens.ex
defmodule CPSolver.Examples.Queens do
alias CPSolver.Constraint.NotEqual
alias CPSolver.IntVariable
alias CPSolver.Examples.Utils, as: ExamplesUtils
require Logger
@queen_symbol "\u2655"
def solve(n, solver_opts \\ []) when is_integer(n) do
{:ok, _solver} =
CPSolver.solve(model(n), solver_opts)
end
def model(n) do
range = 1..n
## Queen positions
q = Enum.map(range, fn _ -> IntVariable.new(range) end)
constraints =
for i <- 0..(n - 2) do
for j <- (i + 1)..(n - 1) do
# queens q[i] and q[i] not on ...
[
## ... the same line
NotEqual.new(Enum.at(q, i), Enum.at(q, j), 0),
## ... the same left diagonal
NotEqual.new(Enum.at(q, i), Enum.at(q, j), i - j),
## ... the same right diagonal
NotEqual.new(Enum.at(q, i), Enum.at(q, j), j - i)
]
end
end
|> List.flatten()
%{
variables: q,
constraints: constraints
}
end
def solve_and_print(nqueens, opts \\ [timeout: 1000]) do
Logger.configure(level: :info)
timeout = Keyword.get(opts, :timeout)
ExamplesUtils.flush_solutions()
solve(nqueens,
solution_handler: ExamplesUtils.notify_client_handler(),
stop_on: {:max_solutions, 1}
)
|> tap(fn {:ok, _solver} ->
ExamplesUtils.wait_for_solution(
timeout,
fn solution ->
check_solution(solution)
|> tap(fn _ -> IO.puts(print_board(solution)) end)
end
)
end)
end
def print_board(queens) do
n = length(queens)
"\n" <>
Enum.join(
for i <- 1..n do
Enum.join(
for j <- 1..n do
if Enum.at(queens, i - 1) == j,
do: IO.ANSI.red() <> @queen_symbol,
else: IO.ANSI.light_blue() <> "."
end,
" "
)
end,
"\n"
) <> "\n"
end
def check_solution(queens) do
n = length(queens)
Enum.all?(0..(n - 2), fn i ->
Enum.all?((i + 1)..(n - 1), fn j ->
# queens q[i] and q[i] not on ...
## ... the same line
## ... the same left or right diagonal
(Enum.at(queens, i) != Enum.at(queens, j))
|> tap(fn res ->
!res && Logger.error("Queens #{i + 1} and #{j + 1} : same-line violation")
end) &&
(abs(Enum.at(queens, i) - Enum.at(queens, j)) != j - i)
|> tap(fn res ->
!res && Logger.error("Queens #{i + 1} and #{j + 1} : same-diagonal violation")
end)
end)
end)
end
end