xdamcnt2.pln

--
--       n Damen Problem loesen;
--       DAMCOUNT;
--       entworfen am 31.03.1985;
--       geschrieben am 02.04.1985;
--       revidiert am 18.04.1985 Do vorm.
--
--       in C++ umgewandelt am 17.04.1994
--       in Lua umgewandelt am 28.04.2020
--       in Pallene umgewandelt am 30.04.2020
--
--     2   4    6     8      10         12           14
--   1 0 0 2 10 4 40 92 352 724 2680 14200 73712 365596




-- Check if k-th queen is attacked by any other prior queen.
-- Return nonzero if configuration is OK, zero otherwise.

function configOkay (k:integer, a:{integer}):boolean
	local z:integer = a[k]
	local l:integer
	local kmj:integer

	for j=1, k-1 do
		l = z - a[j]
		kmj = k - j
		if (l == 0  or  l == kmj  or  -l == kmj) then
			return false
		end
	end
	return true
end



function solve (N:integer, a:{integer}):integer	-- return number of positions
	local cnt:integer = 0
	local k:integer = 1
	local N2:integer = N  --(N + 1) / 2;
	local flag:integer
	a[1] = 1

	while true do
		flag = 0
		--print(string.format("\tN=%d, flag=%d, a[%d]=%d\n",N, flag, k, a[k]))
		if (configOkay(k,a)) then
			if (k < N) then
				k = k + 1;  a[k] = 1; flag = 1
			else
				cnt = cnt + 1; flag = 0
			end
		end
		if (flag == 0) then
			flag = 0
			repeat
				if (a[k] < N) then
					a[k] = a[k] + 1;  flag = 1; break;
				end
				k = k - 1
			until (k <= 1)
			if (flag == 0) then
				a[1] = a[1] + 1
				if (a[1] > N2) then return cnt; end
				k = 2;  a[2] = 1;
			end
		end
	end
end