#eight-queen problem in #Lua

8queen.lua

--[[
PiL Exercise 10.2: An alternative implementation for the eight-queen problem
would be to generate all possible permutations of 1 to 8 and, for each
permutation, to check whether it is valid.
--]]

local _ENV,M = require 'pl.import_into' ()

local N = 8

-- 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   -- samn diagonal?
            (a[i] + i == c + n) then -- same diagonal?
            return false
        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
            io.write(a[i] == j and "X" or "-", " ")
        end
        io.write("\n")
    end
end

for a in list(permute.table{1, 2, 3, 4, 5, 6, 7, 8}) do
  for n,c in a do
    if not isplaceok(a, n, c) then
      break
    end
    printsolution(a)
  end
end