A Lua-based solution to the n-queens problem.

nqueens.lua

-- Call this function as `grid = can_find_solution(N)`.
function can_find_solution(N, x0, y0, grid)
  x0, y0 = x0 or 0, y0 or 1  -- Set default vals (0, 1).
  if grid == nil then
    grid = {}
    for i = 0, N do grid[i] = {} end
  end
  for x = 1, x0 - 1 do
    if grid[x][y0] or grid[x][y0 - x0 + x] or grid[x][y0 + x0 - x] then
      return false
    end
  end
  grid[x0][y0] = true
  if x0 == N then return true end
  for y0 = 1, N do
    if can_find_solution(N, x0 + 1, y0, grid) then return grid end
  end
  grid[x0][y0] = nil
  return false
end

-- Example usage:
local N = 8
local grid = can_find_solution(N)
for y = 1, N do
  for x = 1, N do
    -- Print "|Q" if grid[x][y] is true; "|_" otherwise.
    io.write(grid[x][y] and "|Q" or "|_")
  end
  print("|")
end

I wrote this script for fun. My goal was to illustrate that Lua can achieve a nice balance between readability and brevity.

The function that does all the work is 19 lines, and is relatively straightforward.

For reference, see the Rosetta Code page for the n-queens problem, which has code snippets from various languages solving this problem. As an example, the C++ solution has 102 lines. The JavaScript approach is better - only 32 lines - but I still think the Lua approach feels simpler and more readable. To give it credit, the first C solution on that page is solid.