queen.lua

--[[
MIT License

Copyright (c) 2017 Gabriel de Quadros Ligneul

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.
]]
local function prequire(name) local success, result = pcall(require, name); return success and result end
local bench = script and require(script.Parent.bench_support) or prequire("bench_support") or require("../../bench_support")

function test()

local N = tonumber((arg and arg[1]) or 8)    -- board size


-- check whether position (n,c) is free from attacks
local function isplaceok (a, n, c)
  for i = 1, n - 1 do   -- for each queen already placed
    if (a[i] == c) or                -- same column?
       (a[i] - i == c - n) or        -- same diagonal?
       (a[i] + i == c + n) then      -- same diagonal?
      return false            -- place can be attacked
    end
  end
  return true    -- no attacks; place is OK
end


-- print a board
local function printsolution (a)
  for i = 1, N do
    for j = 1, N do
      --print(a[i] == j and "X" or "-", " ")
    end
    --print("\n")
  end
  --print("\n")
end


-- add to board 'a' all queens from 'n' to 'N'
local function addqueen (a, n)
  if n > N then    -- all queens have been placed?
    printsolution(a)
  else  -- try to place n-th queen
    for c = 1, N do
      if isplaceok(a, n, c) then
        a[n] = c    -- place n-th queen at column 'c'
        addqueen(a, n + 1)
      end
    end
  end
end


-- run the program
addqueen({}, 1)

end

bench.runCode(test, "queen")