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--local N = tonumber(arg[1] or 8) -- board size
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 -- 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
local line = ""
for j = 1, N do
line = line .. (a[i] == j and "X " or "- ")
end
print(line)
end
print("")
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)