8 queens problem solution in Lua

queens.lua

#!/usr/bin/env lua

--
-- Copyright (c) 2023 Gabriel G. de Brito
--
-- Permission is hereby granted, free of charge, to any person obtaining a copy
-- of this software and associated documentation files (the "Software"), to deal
-- in the Software without restriction, including without limitation the rights
-- to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
-- copies of the Software, and to permit persons to whom the Software is
-- furnished to do so, subject to the following conditions:
--
-- The above copyright notice and this permission notice shall be included in
-- all copies or substantial portions of the Software.
--
-- THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
-- IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
-- FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
-- AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
-- LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
-- OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
-- SOFTWARE.
--

print_coord = function(c)
    io.write(string.format("(%d,%d)", c.x, c.y))
end

print_queens = function(q)
    io.write("[")
    for i = 1, #q do
        print_coord(q[i])
    end
    io.write("]")
end

coord = function(x, y)
    return { x = x, y = y }
end

transp = function(c, size)
    return coord(c.y, size + 1 - c.x)
end

nextp = function(c, size)
    if not c then
        return nil
    end
    if c.y < size then
        return coord(c.x, c.y + 1)
    elseif c.x < size then
        return coord(c.x + 1, 1)
    end

    return nil
end

sameax = function(p1, p2)
    return p1.x == p2.x or p1.y == p2.y
end

samediag = function(p1, p2, size)
    local pt1 = transp(p1, size)
    local pt2 = transp(p2, size)
    return p1.x - p1.y == p2.x - p2.y or pt1.x - pt1.y == pt2.x - pt2.y
end

kills = function(p1, p2, size)
    return sameax(p1, p2) or samediag(p1, p2, size)
end

killsl = function(p1, l, size)
    for i = 1,#l do
        if kills(p1, l[i], size) then
            return true
        end
    end

    return false
end

queens8 = function(queens, size, n)
    if n > size then
        return queens
    end

    local np = nextp(queens[#queens], size) or coord(1, 1)
    while np do
        io.write("trying ")
        print_queens(queens)
        io.write(" + ")
        print_coord(np)
        print ""

        if not killsl(np, queens, size) then
            table.insert(queens, np)
            if queens8(queens, size, n + 1) then
                return queens
            end
            queens[#queens] = nil
        end
        np = nextp(np, size)
    end

    return nil
end

queens = {}
size = 8

q = queens8(queens, size, 1)
if q then
    print "solution found!!"
    print_queens(queens)
    print ""
else
    print "no solution found"
end