C# State.ApplyMove方法代码示例

        // Classic Expectimax search
        public Move ExpectimaxAlgorithm(State state, int depth, WeightVector weights)
        {
            Move bestMove;

            if (depth == 0 || state.IsGameOver())
            {
                if (state.Player == GameEngine.PLAYER)
                {
                    bestMove = new PlayerMove(); // dummy action, as there will be no valid move
                    bestMove.Score = AI.EvaluateWithWeights(state, weights);
                    return bestMove;
                }
                else if (state.Player == GameEngine.COMPUTER)
                {
                    bestMove = new ComputerMove(); // dummy action, as there will be no valid move
                    bestMove.Score = AI.EvaluateWithWeights(state, weights);
                    return bestMove;
                }
                else throw new Exception();
            }
            if (state.Player == GameEngine.PLAYER) // AI's turn
            {
                bestMove = new PlayerMove();
                double highestScore = Double.MinValue, currentScore = Double.MinValue;

                List<Move> moves = state.GetMoves();
                foreach (Move move in moves)
                {
                    State resultingState = state.ApplyMove(move);
                    currentScore = ExpectimaxAlgorithm(resultingState, depth - 1, weights).Score;
                    if (currentScore > highestScore)
                    {
                        highestScore = currentScore;
                        bestMove = move;
                    }
                }
                bestMove.Score = highestScore;
                return bestMove;
            }
            else if (state.Player == GameEngine.COMPUTER) // computer's turn  (the random event node)
            {
                bestMove = new ComputerMove();

                // return the weighted average of all the child nodes's scores
                double average = 0;
                List<Cell> availableCells = state.GetAvailableCells();
                List<Move> moves = state.GetAllComputerMoves(availableCells);
                foreach (Move move in moves)
                {
                    State resultingState = state.ApplyMove(move);

                    average += StateProbability(((ComputerMove)move).Tile) * ExpectimaxAlgorithm(resultingState, depth - 1, weights).Score;
                }
                bestMove.Score = average / moves.Count;
                return bestMove;
            }
            else throw new Exception();
        }

        // Runs a parallel version of iterative deepening
        // A search is started in a separate thread for each child of root node
        private Move ParallelIterativeDeepening(State state, double timeLimit)
        {
            Move bestMove = new PlayerMove();

            List<Move> moves = state.GetMoves();
            ConcurrentBag<Tuple<double, Move>> scores = new ConcurrentBag<Tuple<double, Move>>();

            if (moves.Count == 0)
            {
                // game over
                return bestMove;
            }

            // create the resulting states before starting the threads
            List<State> resultingStates = new List<State>();
            foreach (Move move in moves)
            {
                State resultingState = state.ApplyMove(move);
                resultingStates.Add(resultingState);
            }

            Parallel.ForEach(resultingStates, resultingState =>
            {
                double score = IterativeDeepening(resultingState, timeLimit).Score;
                scores.Add(new Tuple<double, Move>(score, resultingState.GeneratingMove));
            });
            // find the best score
            double highestScore = Double.MinValue;
            foreach (Tuple<double, Move> score in scores)
            {
                PlayerMove move = (PlayerMove)score.Item2;
                if (score.Item1 > highestScore)
                {
                    highestScore = score.Item1;
                    bestMove = score.Item2;
                }
            }
            return bestMove;
        }

        // Standard Minimax search with no pruning
        Move MinimaxAlgorithm(State state, int depth)
        {
            Move bestMove;

            if (depth == 0 || state.IsGameOver())
            {
                if (state.Player == GameEngine.PLAYER)
                {
                    bestMove = new PlayerMove();
                    bestMove.Score = AI.Evaluate(state);
                    return bestMove;
                }
                else if (state.Player == GameEngine.COMPUTER)
                {
                    bestMove = new ComputerMove();
                    bestMove.Score = AI.Evaluate(state);
                    return bestMove;
                }
                else throw new Exception();
            }

            if (state.Player == GameEngine.PLAYER)
            {
                bestMove = new PlayerMove();

                double highestScore = Double.MinValue, currentScore = Double.MinValue;
                List<Move> moves = state.GetMoves();

                foreach (Move move in moves)
                {
                    State resultingState = state.ApplyMove(move);
                    currentScore = MinimaxAlgorithm(resultingState, depth - 1).Score;

                    if (currentScore > highestScore)
                    {
                        highestScore = currentScore;
                        bestMove = move;
                    }
                }
                bestMove.Score = highestScore;
                return bestMove;
            }
            else if (state.Player == GameEngine.COMPUTER)
            {
                bestMove = new ComputerMove();

                double lowestScore = Double.MaxValue, currentScore = Double.MaxValue;
                List<Move> moves = state.GetMoves();

                foreach (Move move in moves)
                {
                    State resultingState = state.ApplyMove(move);
                    currentScore = MinimaxAlgorithm(resultingState, depth - 1).Score;

                    if (currentScore < lowestScore)
                    {
                        lowestScore = currentScore;
                        bestMove = move;
                    }
                }
                bestMove.Score = lowestScore;
                return bestMove;
            }
            else throw new Exception();
        }

        // MIN part of Minimax (with alpha-beta pruning)
        Move Min(State state, int depth, double alpha, double beta)
        {
            Move bestMove = new ComputerMove();
            double lowestScore = Double.MaxValue, currentScore = Double.MaxValue;

            List<Move> moves = state.GetMoves();

            if (debug)
                logger.writeParent(state, chosenDepth - depth);

            foreach (Move move in moves)
            {

                State resultingState = state.ApplyMove(move);
                currentScore = AlphaBeta(resultingState, depth - 1, alpha, beta).Score;

                if (debug)
                    logger.writeChild(resultingState, chosenDepth - depth, currentScore);

                if (currentScore < lowestScore)
                {
                    lowestScore = currentScore;
                    bestMove = move;
                }
                beta = Math.Min(beta, lowestScore);
                if (beta <= alpha)
                    break;
            }
            bestMove.Score = lowestScore;
            return bestMove;
        }

        // MAX part of Minimax (with alpha-beta pruning)
        Move Max(State state, int depth, double alpha, double beta)
        {
            Move bestMove = new PlayerMove();

            double highestScore = Double.MinValue, currentScore = Double.MinValue;

            List<Move> moves = state.GetMoves();

            if (depth == chosenDepth)
            {
                int numMax = moves.Count;
            }

            if (debug)
                logger.writeParent(state, chosenDepth - depth);

            foreach (Move move in moves)
            {
                State resultingState = state.ApplyMove(move);
                currentScore = AlphaBeta(resultingState, depth - 1, alpha, beta).Score;

                if (debug)
                    logger.writeChild(resultingState, chosenDepth - depth, currentScore);

                if (currentScore > highestScore)
                {
                    highestScore = currentScore;
                    bestMove = move;
                }
                alpha = Math.Max(alpha, highestScore);
                if (beta <= alpha)
                { // beta cut-off
                    break;
                }
            }

            bestMove.Score = highestScore;
            return bestMove;
        }

        // recursive part of the minimax algorithm when used in iterative deepening search
        // checks at each recursion if timeLimit has been reached
        // if is has, it cuts of the search and returns the best move found so far, along with a boolean indicating that the search was not fully completed
        private Tuple<Move, Boolean> IterativeDeepeningAlphaBeta(State state, int depth, double alpha, double beta, double timeLimit, Stopwatch timer)
        {
            Move bestMove;

            if (depth == 0 || state.IsGameOver())
            {
                if (state.Player == GameEngine.PLAYER)
                {
                    bestMove = new PlayerMove(); // dummy action, as there will be no valid move
                    bestMove.Score = AI.Evaluate(state);
                    return new Tuple<Move, Boolean>(bestMove, true);
                }
                else if (state.Player == GameEngine.COMPUTER)
                {
                    bestMove = new ComputerMove(); // dummy action, as there will be no valid move
                    bestMove.Score = AI.Evaluate(state);
                    return new Tuple<Move, Boolean>(bestMove, true);
                }
                else throw new Exception();
            }
            if (state.Player == GameEngine.PLAYER) // AI's turn
            {
                bestMove = new PlayerMove();

                double highestScore = Double.MinValue, currentScore = Double.MinValue;

                List<Move> moves = state.GetMoves();

                foreach (Move move in moves)
                {
                    State resultingState = state.ApplyMove(move);
                    currentScore = IterativeDeepeningAlphaBeta(resultingState, depth - 1, alpha, beta, timeLimit, timer).Item1.Score;

                    if (currentScore > highestScore)
                    {
                        highestScore = currentScore;
                        bestMove = move;
                    }
                    alpha = Math.Max(alpha, highestScore);
                    if (beta <= alpha)
                    { // beta cut-off
                        break;
                    }

                    if (timer.ElapsedMilliseconds > timeLimit)
                    {
                        bestMove.Score = highestScore;
                        return new Tuple<Move, Boolean>(bestMove, false); // recursion not completed, return false
                    }
                }
                bestMove.Score = highestScore;
                return new Tuple<Move, Boolean>(bestMove, true);

            }
            else if (state.Player == GameEngine.COMPUTER) // computer's turn  (the random event node)
            {
                bestMove = new ComputerMove();
                double lowestScore = Double.MaxValue, currentScore = Double.MaxValue;

                List<Move> moves = state.GetMoves();

                foreach (Move move in moves)
                {
                    State resultingState = state.ApplyMove(move);
                    currentScore = IterativeDeepeningAlphaBeta(resultingState, depth - 1, alpha, beta, timeLimit, timer).Item1.Score;

                    if (currentScore < lowestScore)
                    {
                        lowestScore = currentScore;
                        bestMove = move;
                    }
                    beta = Math.Min(beta, lowestScore);
                    if (beta <= alpha)
                        break;

                    if (timer.ElapsedMilliseconds > timeLimit)
                    {
                        bestMove.Score = lowestScore;
                        return new Tuple<Move, Boolean>(bestMove, false); // recursion not completed, return false
                    }
                }
                bestMove.Score = lowestScore;
                return new Tuple<Move, Boolean>(bestMove, true);
            }
            else throw new Exception();
        }

 // Simulates a game to the end (game over) based on the default policy
 // Returns the game over state
 private State SimulateGame(State state, int POLICY)
 {
     if (POLICY == RANDOM_POLICY)
     {
         while (state.GetMoves().Count != 0)
         {
             state = state.ApplyMove(state.GetRandomMove());
         }
         return state;
     }
     else if (POLICY == BEST_EVAL_POLICY)
     {
         List<Move> moves = state.GetMoves();
         while (moves.Count != 0)
         {
             // random move for computer
             if (state.Player == GameEngine.COMPUTER)
             {
                 state = state.ApplyMove(state.GetRandomMove());
             }
             else
             {
                 // find the move that results in the best child state, based on the evaluation function
                 State bestState = null;
                 double bestScore = Double.MinValue;
                 foreach (Move move in moves)
                 {
                     State result = state.ApplyMove(move);
                     double score = AI.Evaluate(result);
                     if (score > bestScore)
                     {
                         bestScore = score;
                         bestState = result;
                     }
                 }
                 state = bestState;
             }
             moves = state.GetMoves();
         }
         return state;
     }
     else if (POLICY == EXPECTIMAX_POLICY)
     {
         Expectimax expectimax = new Expectimax(gameEngine, 2);
         while (state.GetMoves().Count != 0) {
             if (state.Player == GameEngine.COMPUTER)
             {
                 state = state.ApplyMove(state.GetRandomMove());
             }
             else
             {
                 Move move = expectimax.ExpectimaxAlgorithm(state, 2, weights);
                 state = state.ApplyMove(move);
             }
         }
         return state;
     }
     else throw new Exception();
 }

        // Recursive part of iterative deepening Expectimax with star 1 pruning
        private Tuple<Move, Boolean> RecursiveIterativeDeepeningExpectimaxWithStar1(State state, double alpha, double beta, int depth,
            int timeLimit, Stopwatch timer, WeightVector weights)
        {
            Move bestMove;

            if (depth == 0 || state.IsGameOver())
            {
                if (state.Player == GameEngine.PLAYER)
                {
                    bestMove = new PlayerMove(); // dummy action, as there will be no valid move
                    bestMove.Score = AI.EvaluateWithWeights(state, weights);
                    return new Tuple<Move, Boolean>(bestMove, true);
                }
                else if (state.Player == GameEngine.COMPUTER)
                {
                    bestMove = new ComputerMove(); // dummy action, as there will be no valid move
                    bestMove.Score = AI.EvaluateWithWeights(state, weights);
                    return new Tuple<Move, Boolean>(bestMove, true); ;
                }
                else throw new Exception();
            }
            if (state.Player == GameEngine.PLAYER)
            {
                bestMove = new PlayerMove();
                double highestScore = Double.MinValue, currentScore = Double.MinValue;

                List<Move> moves = state.GetMoves();
                foreach (Move move in moves)
                {
                    State resultingState = state.ApplyMove(move);
                    currentScore = RecursiveIterativeDeepeningExpectimaxWithStar1(resultingState, alpha, beta, depth - 1, timeLimit, timer, weights).Item1.Score;
                    if (currentScore > highestScore)
                    {
                        highestScore = currentScore;
                        bestMove = move;
                    }
                    alpha = Math.Max(alpha, highestScore);
                    if (beta <= alpha)
                    { // beta cut-off
                        break;
                    }
                    if (timer.ElapsedMilliseconds > timeLimit)
                    {
                        bestMove.Score = highestScore;
                        return new Tuple<Move, Boolean>(bestMove, false); // recursion not completed, return false
                    }
                }

                bestMove.Score = highestScore;
                return new Tuple<Move, Boolean>(bestMove, true);
            }
            else if (state.Player == GameEngine.COMPUTER) // computer's turn  (the random event node)
            {
                bestMove = new ComputerMove();

                List<Cell> availableCells = state.GetAvailableCells();
                List<Move> moves = state.GetAllComputerMoves(availableCells);

                int numSuccessors = moves.Count;
                double upperBound = AI.GetUpperBound(weights);
                double lowerBound = AI.GetLowerBound(weights);
                double curAlpha = numSuccessors * (alpha - upperBound) + upperBound;
                double curBeta = numSuccessors * (beta - lowerBound) + lowerBound;

                double scoreSum = 0;
                int i = 1;
                foreach (Move move in moves)
                {

                    double sucAlpha = Math.Max(curAlpha, lowerBound);
                    double sucBeta = Math.Min(curBeta, upperBound);

                    State resultingState = state.ApplyMove(move);

                    double score = StateProbability(((ComputerMove)move).Tile) *
                        RecursiveIterativeDeepeningExpectimaxWithStar1(resultingState, sucAlpha, sucBeta, depth - 1, timeLimit, timer, weights).Item1.Score;
                    scoreSum += score;
                    if (score <= curAlpha)
                    {
                        scoreSum += upperBound * (numSuccessors - i);
                        bestMove.Score = scoreSum / numSuccessors;
                        return new Tuple<Move, Boolean>(bestMove, true); // pruning
                    }
                    if (score >= curBeta)
                    {
                        scoreSum += lowerBound * (numSuccessors - i);
                        bestMove.Score = scoreSum / numSuccessors;
                        return new Tuple<Move, Boolean>(bestMove, true); // pruning
                    }
                    if (timer.ElapsedMilliseconds > timeLimit)
                    {
                        bestMove.Score = scoreSum / i;
                        return new Tuple<Move, Boolean>(bestMove, false); // recursion not completed, return false
                    }
                    curAlpha += upperBound - score;
                    curBeta += lowerBound - score;

                    i++;

//.........这里部分代码省略.........

        // Used by Star2 in probing phase
        private State PickSuccessor(State state)
        {
            List<Move> moves = state.GetMoves();

            int numSuccessors = moves.Count;
            if (numSuccessors < 2) return state.ApplyMove(moves[0]);
            else
            {
                State choice = state.ApplyMove(moves[0]);
                double best = AI.Evaluate(choice);
                for (int i = 1; i < numSuccessors; i++)
                {
                    State resultingState = state.ApplyMove(moves[i]);
                    double score = AI.Evaluate(resultingState);
                    if (score > best)
                    {
                        best = score;
                        choice = resultingState;
                    }
                }
                return choice;
            }
        }

        // Runs a parallel expectimax search to speed up search
        // A search is started in a separate thread for each child of the given root node
        // This method should only be called for the the root, where depth will always
        // be > 0 and player will always be GameEngine.PLAYER - the recursion is started
        // for the children of the root using standard Expectimax algorithm
        private Move ParallelExpectimax(State state, int depth, WeightVector weights)
        {
            Move bestMove = new PlayerMove();

            List<Move> moves = state.GetMoves();
            ConcurrentBag<Tuple<double, Move>> scores = new ConcurrentBag<Tuple<double, Move>>();

            if (moves.Count == 0)
            {
                // game over
                return bestMove;
            }

            // create the resulting states before starting the threads
            List<State> resultingStates = new List<State>();
            foreach (Move move in moves)
            {
                State resultingState = state.ApplyMove(move);
                resultingStates.Add(resultingState);
            }

            // start a thread for each child
            Parallel.ForEach(resultingStates, resultingState =>
            {
                double score = ExpectimaxAlgorithm(resultingState, depth - 1, weights).Score;
                scores.Add(new Tuple<double, Move>(score, resultingState.GeneratingMove));
            });
            // find the best score
            double highestScore = Double.MinValue;
            foreach (Tuple<double, Move> score in scores)
            {
                PlayerMove move = (PlayerMove)score.Item2;
                if (score.Item1 > highestScore)
                {
                    highestScore = score.Item1;
                    bestMove = score.Item2;
                }
            }
            return bestMove;
        }

        // Recursive part of iterative deepening Expectimax
        private Tuple<Move, Boolean> IterativeDeepeningExpectimax(State state, int depth, double timeLimit, Stopwatch timer, WeightVector weights)
        {
            Move bestMove;

            if (depth == 0 || state.IsGameOver())
            {
                if (state.Player == GameEngine.PLAYER)
                {
                    bestMove = new PlayerMove(); // dummy action, as there will be no valid move
                    bestMove.Score = AI.EvaluateWithWeights(state, weights);
                    return new Tuple<Move, Boolean>(bestMove, true);
                }
                else if (state.Player == GameEngine.COMPUTER)
                {
                    bestMove = new ComputerMove(); // dummy action, as there will be no valid move
                    bestMove.Score = AI.EvaluateWithWeights(state, weights);
                    return new Tuple<Move, Boolean>(bestMove, true);
                }
                else throw new Exception();
            }
            if (state.Player == GameEngine.PLAYER) // AI's turn
            {
                bestMove = new PlayerMove();
                double highestScore = Double.MinValue, currentScore = Double.MinValue;

                List<Move> moves = state.GetMoves();
                foreach (Move move in moves)
                {
                    State resultingState = state.ApplyMove(move);
                    currentScore = IterativeDeepeningExpectimax(resultingState, depth - 1, timeLimit, timer, weights).Item1.Score;

                    if (currentScore > highestScore)
                    {
                        highestScore = currentScore;
                        bestMove = move;
                    }
                    if (timer.ElapsedMilliseconds > timeLimit)
                    {
                        bestMove.Score = highestScore;
                        return new Tuple<Move, Boolean>(bestMove, false); // recursion not completed, return false
                    }
                }
                bestMove.Score = highestScore;
                return new Tuple<Move, Boolean>(bestMove, true);
            }
            else if (state.Player == GameEngine.COMPUTER) // computer's turn  (the random event node)
            {
                bestMove = new ComputerMove();

                // return the weighted average of all the child nodes's scores
                double average = 0;
                List<Cell> availableCells = state.GetAvailableCells();
                List<Move> moves = state.GetAllComputerMoves(availableCells);
                int moveCheckedSoFar = 0;
                foreach (Move move in moves)
                {
                    State resultingState = state.ApplyMove(move);

                    average += StateProbability(((ComputerMove)move).Tile) * IterativeDeepeningExpectimax(resultingState, depth - 1, timeLimit, timer, weights).Item1.Score;
                    moveCheckedSoFar++;
                    if (timer.ElapsedMilliseconds > timeLimit)
                    {
                        bestMove.Score = average / moveCheckedSoFar;
                        return new Tuple<Move, Boolean>(bestMove, false); // recursion not completed, return false
                    }
                }
                bestMove.Score = average / moves.Count;
                return new Tuple<Move, Boolean>(bestMove, true);
            }
            else throw new Exception();
        }

        // Expectimax with Star2 pruning
        // NB: DO NOT USE - way too slow
        private Move Star2Expectimax(State state, double alpha, double beta, int depth, WeightVector weights)
        {
            Move bestMove;

            if (depth == 0 || state.IsGameOver())
            {
                if (state.Player == GameEngine.PLAYER)
                {
                    bestMove = new PlayerMove(); // dummy action, as there will be no valid move
                    bestMove.Score = AI.Evaluate(state);
                    return bestMove;
                }
                else if (state.Player == GameEngine.COMPUTER)
                {
                    bestMove = new ComputerMove(); // dummy action, as there will be no valid move
                    bestMove.Score = AI.Evaluate(state);
                    return bestMove;
                }
                else throw new Exception();
            }
            if (state.Player == GameEngine.PLAYER)
            {
                bestMove = new PlayerMove();
                double highestScore = Double.MinValue, currentScore = Double.MinValue;

                List<Move> moves = state.GetMoves();
                foreach (Move move in moves)
                {
                    State resultingState = state.ApplyMove(move);
                    currentScore = Star2Expectimax(resultingState, alpha, beta, depth - 1, weights).Score;
                    if (currentScore > highestScore)
                    {
                        highestScore = currentScore;
                        bestMove = move;
                    }
                    alpha = Math.Max(alpha, highestScore);
                    if (beta <= alpha)
                    { // beta cut-off
                        break;
                    }
                }

                bestMove.Score = highestScore;
                return bestMove;
            }
            else if (state.Player == GameEngine.COMPUTER) // computer's turn  (the random event node)
            {
                bestMove = new ComputerMove();
                List<Cell> availableCells = state.GetAvailableCells();
                List<Move> moves = state.GetAllComputerMoves(availableCells);

                int numSuccessors = moves.Count;
                double upperBound = AI.GetUpperBound(weights);
                double lowerBound = AI.GetLowerBound(weights);

                double curAlpha = numSuccessors * (alpha - upperBound);
                double curBeta = numSuccessors * (beta - lowerBound);

                double sucAlpha = Math.Max(curAlpha, lowerBound);

                double[] probeValues = new double[numSuccessors];

                // probing phase
                double vsum = 0;
                int i = 1;
                foreach (Move move in moves)
                {
                    curBeta += lowerBound;
                    double sucBeta = Math.Min(curBeta, upperBound);

                    State resultingState = state.ApplyMove(move);
                    probeValues[i - 1] = Probe(resultingState, sucAlpha, sucBeta, depth - 1, weights);
                    vsum += probeValues[i - 1];
                    if (probeValues[i - 1] >= curBeta)
                    {
                        vsum += lowerBound * (numSuccessors - i);
                        bestMove.Score = vsum / numSuccessors;
                        return bestMove; // pruning
                    }
                    curBeta -= probeValues[i - 1];
                    i++;
                }

                // search phase
                vsum = 0;
                i = 1;
                foreach (Move move in moves)
                {
                    curAlpha += upperBound;
                    curBeta += probeValues[i - 1];
                    sucAlpha = Math.Max(curAlpha, lowerBound);
                    double sucBeta = Math.Min(curBeta, upperBound);

                    State resultingState = state.ApplyMove(move);
                    double score = StateProbability(((ComputerMove)move).Tile) * Star2Expectimax(resultingState, sucAlpha, sucBeta, depth - 1, weights).Score;
                    vsum += score;

                    if (score <= curAlpha)
//.........这里部分代码省略.........

        // Expectimax search with Star1 pruning and forward pruning
        private Move Star1WithUnlikelyPruning(State state, double alpha, double beta, int depth, int lastSpawn, WeightVector weights)
        {
            Move bestMove;

            if (depth == 0 || state.IsGameOver())
            {
                if (state.Player == GameEngine.PLAYER)
                {
                    bestMove = new PlayerMove(); // dummy action, as there will be no valid move
                    bestMove.Score = AI.EvaluateWithWeights(state, weights);
                    return bestMove;
                }
                else if (state.Player == GameEngine.COMPUTER)
                {
                    bestMove = new ComputerMove(); // dummy action, as there will be no valid move
                    bestMove.Score = AI.EvaluateWithWeights(state, weights);
                    return bestMove;
                }
                else throw new Exception();
            }
            if (state.Player == GameEngine.PLAYER)
            {
                bestMove = new PlayerMove();
                double highestScore = Double.MinValue, currentScore = Double.MinValue;

                List<Move> moves = state.GetMoves();
                foreach (Move move in moves)
                {
                    State resultingState = state.ApplyMove(move);
                    currentScore = Star1WithUnlikelyPruning(resultingState, alpha, beta, depth - 1, lastSpawn, weights).Score;
                    if (currentScore > highestScore)
                    {
                        highestScore = currentScore;
                        bestMove = move;
                    }
                    alpha = Math.Max(alpha, highestScore);
                    if (beta <= alpha)
                    { // beta cut-off
                        break;
                    }
                }

                bestMove.Score = highestScore;
                return bestMove;
            }
            else if (state.Player == GameEngine.COMPUTER) // computer's turn  (the random event node)
            {
                bestMove = new ComputerMove();

                List<Cell> availableCells = state.GetAvailableCells();
                List<Move> moves = state.GetAllComputerMoves(availableCells);

                int numSuccessors = moves.Count;
                double upperBound = AI.GetUpperBound(weights);
                double lowerBound = AI.GetLowerBound(weights);
                double curAlpha = numSuccessors * (alpha - upperBound) + upperBound;
                double curBeta = numSuccessors * (beta - lowerBound) + lowerBound;

                double scoreSum = 0;
                int i = 1;
                foreach (Move move in moves)
                {
                    int value = ((ComputerMove)move).Tile;
                    if (value == 4 && lastSpawn == 4) continue; // unlikely event pruning (2 4-spawns in sequence only has 1% chance)

                    double sucAlpha = Math.Max(curAlpha, lowerBound);
                    double sucBeta = Math.Min(curBeta, upperBound);

                    State resultingState = state.ApplyMove(move);

                    double score = StateProbability(((ComputerMove)move).Tile) * Star1WithUnlikelyPruning(resultingState, sucAlpha, sucBeta, depth - 1, value, weights).Score;
                    scoreSum += score;
                    if (score <= curAlpha)
                    {
                        scoreSum += upperBound * (numSuccessors - i);
                        bestMove.Score = scoreSum / numSuccessors;
                        return bestMove; // pruning
                    }
                    if (score >= curBeta)
                    {
                        scoreSum += lowerBound * (numSuccessors - i);
                        bestMove.Score = scoreSum / numSuccessors;
                        return bestMove; // pruning
                    }
                    curAlpha += upperBound - score;
                    curBeta += lowerBound - score;

                    i++;

                }
                bestMove.Score = scoreSum / numSuccessors;
                return bestMove;
            }

            else throw new Exception();
        }

        // Recursive part of ^^ iterative deepening Expectimax with Star1, move ordering and transposition table
        private Tuple<Move, Boolean> RecursiveTTStar1(State state, double alpha, double beta, int depth, double timeLimit, Stopwatch timer, WeightVector weights)
        {
            Move bestMove;

            if (depth == 0 || state.IsGameOver())
            {
                if (state.Player == GameEngine.PLAYER)
                {
                    bestMove = new PlayerMove(); // dummy action, as there will be no valid move
                    bestMove.Score = AI.EvaluateWithWeights(state, weights);
                    return new Tuple<Move, Boolean>(bestMove, true);
                }
                else if (state.Player == GameEngine.COMPUTER)
                {
                    bestMove = new ComputerMove(); // dummy action, as there will be no valid move
                    bestMove.Score = AI.EvaluateWithWeights(state, weights);
                    return new Tuple<Move, Boolean>(bestMove, true);
                }
                else throw new Exception();
            }
            if (state.Player == GameEngine.PLAYER) // AI's turn
            {
                DIRECTION bestDirection = (DIRECTION)(-1);
                bestMove = new PlayerMove();
                double highestScore = Double.MinValue, currentScore = Double.MinValue;

                // transposition table look-up
                long zob_hash = GetHash(state);
                if (transposition_table.ContainsKey(zob_hash) && transposition_table[zob_hash].depth > depth)
                {
                    Move move = new PlayerMove(transposition_table[zob_hash].direction);
                    move.Score = transposition_table[zob_hash].value;
                    return new Tuple<Move, Boolean>(move, true);
                }
                    // move ordering - make sure we first check the move we believe to be best based on earlier searches
                else if (transposition_table.ContainsKey(zob_hash))
                {
                    bestDirection = transposition_table[zob_hash].direction;
                    State resultingState = state.ApplyMove(new PlayerMove(bestDirection));
                    currentScore = RecursiveTTStar1(resultingState, alpha, beta, depth - 1, timeLimit, timer, weights).Item1.Score;

                    if (currentScore > highestScore)
                    {
                        highestScore = currentScore;
                        bestMove = new PlayerMove(bestDirection);
                    }
                    if (timer.ElapsedMilliseconds > timeLimit)
                    {
                        bestMove.Score = highestScore;
                        return new Tuple<Move, Boolean>(bestMove, false); // recursion not completed, return false
                    }
                }

                // now check the rest of moves
                List<Move> moves = state.GetMoves();
                foreach (Move move in moves)
                {
                    if (((PlayerMove)move).Direction != bestDirection)
                    {
                        State resultingState = state.ApplyMove(move);
                        currentScore = RecursiveTTStar1(resultingState, alpha, beta, depth - 1, timeLimit, timer, weights).Item1.Score;

                        if (currentScore > highestScore)
                        {
                            highestScore = currentScore;
                            bestMove = move;
                        }
                        alpha = Math.Max(alpha, highestScore);
                        if (beta <= alpha)
                        { // beta cut-off
                            break;
                        }
                        if (timer.ElapsedMilliseconds > timeLimit)
                        {
                            bestMove.Score = highestScore;
                            return new Tuple<Move, Boolean>(bestMove, false); // recursion not completed, return false
                        }
                    }

                }
                bestMove.Score = highestScore;

                // add result to transposition table
                TableRow row = new TableRow((short)depth, ((PlayerMove)bestMove).Direction, bestMove.Score);
                transposition_table.AddOrUpdate(zob_hash, row, (key, oldValue) => row);
                return new Tuple<Move, Boolean>(bestMove, true);
            }
            else if (state.Player == GameEngine.COMPUTER) // computer's turn  (the random event node)
            {
                bestMove = new ComputerMove();
                int moveCheckedSoFar = 0;

                List<Cell> availableCells = state.GetAvailableCells();
                List<Move> moves = state.GetAllComputerMoves(availableCells);

                int numSuccessors = moves.Count;
                double upperBound = AI.GetUpperBound(weights);
                double lowerBound = AI.GetLowerBound(weights);
                double curAlpha = numSuccessors * (alpha - upperBound) + upperBound;
//.........这里部分代码省略.........

        // Recursive part of iterative deepening Expectimax with transposition table
        private Tuple<Move, Boolean> RecursiveTTExpectimax(State state, int depth, double timeLimit, Stopwatch timer, WeightVector weights)
        {
            Move bestMove;

            if (depth == 0 || state.IsGameOver())
            {

                if (state.Player == GameEngine.PLAYER)
                {
                    bestMove = new PlayerMove(); // dummy action, as there will be no valid move
                    bestMove.Score = AI.EvaluateWithWeights(state, weights);
                    return new Tuple<Move, Boolean>(bestMove, true);
                }
                else if (state.Player == GameEngine.COMPUTER)
                {
                    bestMove = new ComputerMove(); // dummy action, as there will be no valid move
                    bestMove.Score = AI.EvaluateWithWeights(state, weights);
                    return new Tuple<Move, Boolean>(bestMove, true);
                }
                else throw new Exception();
            }
            if (state.Player == GameEngine.PLAYER) // AI's turn
            {
                // transposition table look-up
                long zob_hash = GetHash(state);
                if (transposition_table.ContainsKey(zob_hash) && transposition_table[zob_hash].depth > depth)
                {
                    Move move = new PlayerMove(transposition_table[zob_hash].direction);
                    move.Score = transposition_table[zob_hash].value;
                    return new Tuple<Move, Boolean>(move, true);
                }

                bestMove = new PlayerMove();
                double highestScore = Double.MinValue, currentScore = Double.MinValue;

                List<Move> moves = state.GetMoves();
                foreach (Move move in moves)
                {
                    State resultingState = state.ApplyMove(move);
                    currentScore = RecursiveTTExpectimax(resultingState, depth - 1, timeLimit, timer, weights).Item1.Score;

                    if (currentScore > highestScore)
                    {
                        highestScore = currentScore;
                        bestMove = move;
                    }
                    if (timer.ElapsedMilliseconds > timeLimit)
                    {
                        bestMove.Score = highestScore;
                        return new Tuple<Move, Boolean>(bestMove, false); // recursion not completed, return false
                    }
                }
                bestMove.Score = highestScore;

                // add result to transposition table
                TableRow row = new TableRow((short)depth, ((PlayerMove)bestMove).Direction, bestMove.Score);
                transposition_table.AddOrUpdate(zob_hash, row, (key, oldValue) => row);
                return new Tuple<Move, Boolean>(bestMove, true);
            }
            else if (state.Player == GameEngine.COMPUTER) // computer's turn  (the random event node)
            {
                bestMove = new ComputerMove();

                // return the weighted average of all the child nodes's scores
                double average = 0;
                List<Cell> availableCells = state.GetAvailableCells();
                List<Move> moves = state.GetAllComputerMoves(availableCells);
                int moveCheckedSoFar = 0;
                foreach (Move move in moves)
                {
                    State resultingState = state.ApplyMove(move);

                    average += StateProbability(((ComputerMove)move).Tile) * RecursiveTTExpectimax(resultingState, depth - 1, timeLimit, timer, weights).Item1.Score;
                    moveCheckedSoFar++;
                    if (timer.ElapsedMilliseconds > timeLimit)
                    {
                        bestMove.Score = average / moveCheckedSoFar;
                        return new Tuple<Move, Boolean>(bestMove, false); // recursion not completed, return false
                    }
                }
                bestMove.Score = average / moves.Count;
                return new Tuple<Move, Boolean>(bestMove, true);
            }
            else throw new Exception();
        }