Lua括号生成：回溯枚举合法配对序列

-- 全排列后过滤，n=3 时枚举 64 次只剩 5 个

local out = {}
local function build(path, left, right, n)
    if #path == 2 * n then
        table.insert(out, table.concat(path))
        return
    end
    if left < n then
        table.insert(path, "(")
        build(path, left + 1, right, n)
        table.remove(path)
    end
    if right < left then
        table.insert(path, ")")
        build(path, left, right + 1, n)
        table.remove(path)
    end
end
build({}, 0, 0, 3)
-- out 共 5 项：((())), (()()), (())(), ()(()), ()()()