tictactoe.lua

local function prequire(name) local success, result = pcall(require, name); return success and result end
local bench = script and require(script.Parent.bench_support) or prequire("bench_support") or require("../bench_support")

function test()

    -- https://github.com/stefandd/Tic4
    local negaMax = {maxdepth = 4, minsearchpos = 0, numsearchpos = 0}
    negaMax.__index = negaMax

    function negaMax:evaluate(board, depth)
        --[[
        What can be confusing is how the heuristic value of the current node is calculated. In this implementation, this value is always calculated from the point of view of player A, whose color value is one. In other words, higher heuristic values always represent situations more favorable for player A. This is the same behavior as the normal minimax algorithm. The heuristic value is not necessarily the same as a node's return value due to value negation by negamax and the color parameter. The negamax node's return value is a heuristic score from the point of view of the node's current player.

        Negamax scores match minimax scores for nodes where player A is about to play, and where player A is the maximizing player in the minimax equivalent. Negamax always searches for the maximum value for all its nodes. Hence for player B nodes, the minimax score is a negation of its negamax score. Player B is the minimizing player in the minimax equivalent.
        
        Variations in negamax implementations may omit the color parameter. In this case, the heuristic evaluation function must return values from the point of view of the node's current player.
        --]]
        print ("This function needs to be implemented!")
    end

    function negaMax:move_candidates(board, side_to_move)
        print ("This function needs to be implemented!")
    end

    function negaMax:make_move(board, side_to_move, move)
        print ("This function needs to be implemented!")
    end

    function negaMax:negaMax(board, side_to_move, depth, alpha, beta) -- side_to_move: e.g. 1 is blue, -1 is read
        --
        -- init vars for root call
        --
        if not depth then -- root call 
            depth = 0
            alpha = -math.huge
            beta = math.huge
            self.numsearchpos = 0 -- reset call counter
        end
        --
        -- test if the node is terminal (i.e. full board or win)
        --
        local best_move = -1
        local score, is_term_node = self:evaluate(board, depth)    
        -- we abort the recursion if this is a terminal node, or if one of the search abort conditions are met
        -- 
        if is_term_node or depth == self.maxdepth then
            return side_to_move*score, best_move, is_term_node
        end
        --
        -- if not terminal node, eval child nodes
        --
        local moves = self:move_candidates(board, side_to_move)
        score = -math.huge    

        for _, analyzed_move in pairs(moves) do -- iterate over all boards
            self.numsearchpos = self.numsearchpos + 1
            local b = self:make_move(board, side_to_move, analyzed_move)
            local move_score, _, _ = -self:negaMax(b, -side_to_move, depth+1, -beta, -alpha)
            if move_score > score then
                score = move_score
                best_move = analyzed_move
            end
            -- disable alpha-beta pruning
            --
            alpha = math.max(alpha, score)
            if alpha >= beta then
                break
            end
            --
        end
        if depth == 0 then
            --
            -- exit for root call (depth == 0)
            --    
            -- debug stuff
            --print(string.format("---- Negamax: node info, depth: %d, side: %d, score: %d, best move: %d", depth, side_to_move, score, best_move))
            --print_board(board)
            --print(string.format("----"))
            print("Analyzed positions: " .. self.numsearchpos)
        end
        return score, best_move, game_over
    end

    local empty_board = {0,0,0,0,
                        0,0,0,0,
                        0,0,0,0,
                        0,0,0,0} -- 16 empty positions

    ----------- helper methods
                        
    function copy_board(board)
        local copy = {}
        for i = 1, #board do
            copy[i] = board[i]
        end
        return copy
    end

    function print_board(board)
        gboard = {}
        for i = 1, #board do
            if board[i] == 0 then gboard[i] = '.'
            elseif board[i] == 1 then gboard[i] = 'x'
            else gboard[i] = 'o'
            end
        end
        print(string.format("\n%s %s %s %s\n%s %s %s %s\n%s %s %s %s\n%s %s %s %s\n", unpack(gboard)))
    end

    function is_board_full(board)
        for i = 1, #board do
            if board[i] == 0 then
                return false
            end
        end
        return true
    end

    ----------- implement negaMax methods

    negaMax.index_quadruplets = {
        {1,2,3,4}, {5,6,7,8}, {9,10,11,12}, -- rows
        {13,14,15,16}, {1,5,9,13}, {2,6,10,14}, -- cols
        {3,7,11,15}, {4,8,12,16}, {1,6,11,16}, {4,7,10,13}, -- diags
        {1,2,5,6}, {2,3,6,7}, {3,4,7,8}, -- squares
        {5,6,9,10}, {6,7,10,11}, {7,8,11,12},
        {9,10,13,14}, {10,11,14,15}, {11,12,15,16}
    }

    function negaMax:evaluate(board, depth) -- return format is score, is_terminal_position
        --[[
        What can be confusing is how the heuristic value of the current node is calculated. In this implementation, this value is always calculated from the point of view of player A, whose color value is one. In other words, higher heuristic values always represent situations more favorable for player A. This is the same behavior as the normal minimax algorithm. The heuristic value is not necessarily the same as a node's return value due to value negation by negamax and the color parameter. The negamax node's return value is a heuristic score from the point of view of the node's current player.

        Negamax scores match minimax scores for nodes where player A is about to play, and where player A is the maximizing player in the minimax equivalent. Negamax always searches for the maximum value for all its nodes. Hence for player B nodes, the minimax score is a negation of its negamax score. Player B is the minimizing player in the minimax equivalent.
        
        Variations in negamax implementations may omit the color parameter. In this case, the heuristic evaluation function must return values from the point of view of the node's current player.
        --]]
        local player_plus_score, player_minus_score = 0, 0
        local game_won = false
        for _, curr_qdr in pairs(negaMax.index_quadruplets) do -- iterate over all index quadruplets
            -- count the empty positions and positions occupied by the side whos move it is
            local player_plus_fields, player_minus_fields, empties = 0, 0, 0
            for _, index in next, curr_qdr do -- iterate over all indices
                if board[index] == 0 then
                    empties = empties + 1
                elseif board[index] == 1 then
                    player_plus_fields = player_plus_fields + 1
                elseif board[index] == -1 then
                    player_minus_fields = player_minus_fields + 1
                end
            end
            -- evaluate the quadruplets score by looking at empty vs occupied positions
            if empties == 3 then 
                if player_plus_fields == 1 then
                    player_plus_score = player_plus_score + 3
                elseif player_minus_fields == 1 then
                    player_minus_score = player_minus_score + 3
                end
            elseif empties == 2 then
                if player_plus_fields == 2 then
                    player_plus_score = player_plus_score + 13
                elseif player_minus_fields == 2 then
                    player_minus_score = player_minus_score + 13
                end
            elseif empties == 1 then
                if player_plus_fields == 3 then
                    player_plus_score = player_plus_score + 31
                elseif player_minus_fields == 3 then
                    player_minus_score = player_minus_score + 31
                end
            elseif empties == 0 then
                -- check for winning situations
                if player_plus_fields == 4 then
                    player_plus_score = 999-depth
                    player_minus_score = 0
                    game_won = true
                    break
                elseif player_minus_fields == 4 then
                    -- this should not happen if there is a proper terminal node detection!
                    player_plus_score = 0
                    player_minus_score = 999-depth
                    game_won = true
                    break
                end
            end
        end
        -- return format is score, is_terminal_position
        if not game_won and is_board_full(board) then
            return 0, true -- DRAW
        else
            return (player_plus_score - player_minus_score), game_won -- >0 is good for player 1 [+], <0 means good for the other player (player 2 [-]))
        end
    end

    function negaMax:move_candidates(board, side_to_move)
        local moves = {}
        for i = 1, #board do
            if board[i] == 0 then -- empty?
                moves[#moves + 1] = i -- save move that was made
            end
        end
        return moves
    end

    function negaMax:make_move(board, side_to_move, move)
        local copy = copy_board(board)
        copy[move] = side_to_move
        return copy
    end

    local human_player = 1
    local AI_player = -human_player
    local game_board = copy_board(empty_board)
    local curr_move = -1
    local curr_player = human_player -- human player goes first
    local score = 0
    local stop_loop = false
    local game_over = false

    negaMax.maxdepth = 5

    local t0 = os.clock()
    score, curr_move = negaMax:negaMax(game_board, curr_player)
    local t1 = os.clock()

    return t1-t0
end

bench.runCode(test, "tictactoe")