local fmt = require "fmt"
require "perm"

local colors  = {"Red", "Green", "White", "Yellow", "Blue"}
local nations = {"English", "Swede", "Danish", "Norwegian", "German"}
local animals = {"Dog", "Birds", "Cats", "Horse", "Zebra"}
local drinks  = {"Tea", "Coffee", "Milk", "Beer", "Water"}
local smokes  = {"Pall Mall", "Dunhill", "Blend", "Blue Master", "Prince"}

local p = perm.list({1, 2, 3, 4, 5})

local function check(a1, a2, v1, v2)
    for i = 1, 5 do
        if p[a1][i] == v1 then return p[a2][i] == v2 end
    end
    return false
end

local function check_left(a1, a2, v1, v2)
    for i = 1, 4 do
        if p[a1][i] == v1 then return p[a2][i + 1] == v2 end
    end
    return false
end

local function check_right(a1, a2, v1, v2)
    for i = 2, 5 do
        if p[a1][i] == v1 then return p[a2][i - 1] == v2 end
    end
    return false
end

local function check_adjacent(a1, a2, v1, v2)
    return check_left(a1, a2, v1, v2) or check_right(a1, a2, v1, v2)
end

local function print_houses(c, n, a, d, s)
    local owner = ""
    print("House  Color   Nation     Animal  Drink   Smokes")
    print("=====  ======  =========  ======  ======  ===========")
    for i = 1, 5 do
        local f = "%3d    %-6s  %-9s  %-6s  %-6s  %-11s"
        local l = {i, colors[p[c][i]], nations[p[n][i]], animals[p[a][i]], drinks[p[d][i]], smokes[p[s][i]]}
        fmt.print(f, l:unpack())
        if animals[p[a][i]] == "Zebra" then owner = nations[p[n][i]] end
    end
    print($"\nThe {owner} owns the Zebra\n")
end

local function fill_houses()
    local solutions = 0
    for c = 1, 120 do
        if !check_left(c, c, 2, 3) then continue end                      -- C5 : Green left of white
        for n = 1, 120 do
            if p[n][1] != 4 then continue end                             -- C10: Norwegian in First
            if !check(n, c, 1, 1) then continue end                       -- C2 : English in Red
            if !check_adjacent(n, c, 4, 5) then continue end              -- C15: Norwegian next to Blue
            for a = 1, 120 do
                if !check(a, n, 1, 2) then continue end                   -- C3 : Swede has Dog
                for d = 1, 120 do
                    if p[d][3] != 3 then continue end                     -- C9 : Middle drinks Milk
                    if !check(d, n, 1, 3) then continue end               -- C4 : Dane drinks Tea
                    if !check(d, c, 2, 2) then continue end               -- C6 : Green drinks Coffee
                    for s = 1, 120 do
                        if !check(s, a, 1, 2) then continue end           -- C7 : Pall Mall has Birds
                        if !check(s, c, 2, 4) then continue end           -- C8 : Yellow smokes Dunhill
                        if !check(s, d, 4, 4) then continue end           -- C13: Blue Master drinks Beer
                        if !check(s, n, 5, 5) then continue end           -- C14: German smokes Prince
                        if !check_adjacent(s, a, 3, 3) then continue end  -- C11: Blend next to Cats
                        if !check_adjacent(s, a, 2, 4) then continue end  -- C12: Dunhill next to Horse
                        if !check_adjacent(s, d, 3, 5) then continue end  -- C16: Blend next to Water
                        ++solutions
                        print_houses(c, n, a, d, s)
                    end
                end
            end
        end
    end
    return solutions
end

local solutions = fill_houses()
local plural = fmt.plural(solutions, "solution")
print($"{solutions} {plural} found")