private static bool CheckDirection(GridModel grid, Direction direction)
{
var vector = Vector.FromDirection(direction);
foreach (int x in grid.TraversalsX(direction))
{
foreach (int y in grid.TraversalsY(direction))
{
var cell1 = grid[x, y];
var cell2 = grid[x + vector.x, y + vector.y];
if (cell1 != null && cell2 != null)
{
if (cell1.IsOccupied && cell2.IsAvailable)
{
return true;
}
if (cell1.IsOccupied && cell2.IsOccupied)
{
if (cell1.Tile.Value == cell2.Tile.Value)
return true;
}
}
}
}
return false;
}
private double Maximizer(GridModel grid, int depth, double alpha, double beta)
{
double bestScore = alpha;
foreach (var direction in Vector.Directions)
{
var newGrid = new GridModel(grid);
int deltaScore;
if (PlayerTurn.Move(newGrid, direction, out deltaScore))
{
if (depth == 0)
{
// leaf node, static evaluation
return StaticEvaluation(newGrid);
}
else
{
alpha = Math.Max(alpha, AlphaBetaSearch(newGrid, depth-1, false, alpha, beta));
}
if (alpha > beta) // pruning
{
return beta;
}
}
}
return alpha;
}
public override Direction ComputeNextMove(GridModel grid)
{
var input = GridToInput(grid);
var output = _network.Compute(input);
// if output is impossible teach->0
// if output has many merges teach good
// learning mode from human
Direction result = OutputToDirection(output);
var validMoves = ValidDirections(grid);
if (validMoves.Contains(result))
return result;
foreach (Direction direction in validMoves)
{
TrainNextMove(grid, direction);
}
/*
int validMoveCount = validMoves.Count();
if (validMoveCount > 0)
TrainNextMove(grid, validMoves.Last());
*/
return Direction.None;
}
protected Direction[] ValidDirections(GridModel grid)
{
Dictionary<Direction, bool> d = new Dictionary<Direction, bool>();
foreach (Direction direction in Vector.Directions)
{
d[direction] = CheckDirection(grid, direction);
}
return d.Where(x => x.Value).Select(x => x.Key).ToArray();
}
/// <summary>
/// Adds a tile in a random position
/// </summary>
public void Move(GridModel grid)
{
var cells = grid.AvailableCells();
if (cells.Any())
{
int value = _rand.NextDouble() < _percentageOfValue1 ? 1 : 2;
var tile = new TileModel(value);
var position = cells[_rand.Next(cells.Length)];
tile.Position = position;
}
}
public GameModel()
{
_playerTurn = new PlayerTurn();
_computerTurn = new ComputerTurn();
Score = 0;
HighScore = 0;
StartTiles = 2;
KeepPlaying = true;
Grid = new GridModel(4);
}
public bool Move(GridModel grid, Direction direction, out int score)
{
score = 0;
if (direction == Direction.None)
return false;
var vector = Vector.FromDirection(direction);
var moved = false;
var alreadyMerged = new List<TileModel>();
// Traverse the grid in the right direction and move tiles
foreach (int x in grid.TraversalsX(direction))
{
foreach (int y in grid.TraversalsY(direction))
{
CellModel cell = grid[x, y];
if (cell.IsOccupied)
{
TileModel tile = cell.Tile;
CellModel nextCell;
CellModel farthestCell = grid.FindFarthestPosition(cell, vector, out nextCell);
TileModel nextTile = (nextCell == null) ? null : nextCell.Tile;
// Only one merger per row traversal?
if (nextTile != null && nextTile.Value == tile.Value && !alreadyMerged.Contains(nextTile))
{
var merged = new TileModel(tile, nextTile);
alreadyMerged.Add(merged);
tile.Position = null;
nextTile.Position = null;
merged.Position = nextCell;
moved = true;
// Update the score
score += (int)Math.Pow(2, merged.Value);
}
else
{
var oldPosition = tile.Position;
tile.Position = farthestCell;
if ((oldPosition.PosX != tile.Position.PosX)
|| (oldPosition.PosY != tile.Position.PosY))
moved = true;
}
}
}
}
return moved;
}
private static double[] GridToInput(GridModel grid)
{
var input = new double[16];
for (int i = 0; i < 16; i++)
input[i] = grid[i].Value;
double max = input.Max();
if (max > 0)
{
// scale all inputs
for (int i = 0; i < 16; i++)
input[i] = input[i] / max;
}
return input;
}
// use a neural network to compute a score out of different simulated moves
private double StaticEvaluation(GridModel grid, Direction direction)
{
var newGrid = new GridModel(grid);
int score;
if (PlayerTurn.Move(newGrid, direction, out score))
{
var input = new double[16];
for (int i = 0; i < 16; i++)
input[i] = newGrid[i].Value;
var output = _network.Compute(input);
return output[0];
}
return double.NegativeInfinity;
}
public override Direction ComputeNextMove(GridModel grid)
{
Direction bestMove = Direction.None;
double bestScore = double.NegativeInfinity;
foreach (var direction in Vector.Directions)
{
var score = StaticEvaluation(grid, direction);
if (score > bestScore)
{
bestScore = score;
bestMove = direction;
}
}
return bestMove;
}
public override Direction ComputeNextMove(GridModel grid)
{
int maxMerges = 0;
var dirs = ValidDirections(grid);
Direction move = dirs[_rand.Next(dirs.Length)];
foreach (Direction direction in Vector.Directions)
{
int merges = CountMerges(direction, grid);
if (merges > maxMerges)
{
maxMerges = merges;
move = direction;
}
}
return move;
}
/// <summary>
/// Create a deep copy of a grid, history of moves and merges removed.
/// </summary>
/// <param name="grid"></param>
public GridModel(GridModel grid)
{
SizeX = grid.SizeX;
SizeY = grid.SizeY;
_cells = new List<CellModel>(SizeX * SizeY);
for (int i = 0; i < SizeX * SizeY; i++)
{
int x = i % SizeY;
int y = i / SizeX;
var cell = new CellModel(x, y);
_cells.Add(cell);
var sourceCell = grid[x,y];
if (sourceCell.IsOccupied)
{
var tileCopy = new TileModel(sourceCell.Tile);
tileCopy.Position = cell;
}
}
}
private static double StaticEvaluation(GridModel grid)
{
double
smoothWeight = 0.1,
monoWeight = 0.1,
//islandWeight = 0.0,
mono2Weight = 1.0,
emptyWeight = 2.7,
maxWeight = 1.0;
return
// grid.Smoothness() * smoothWeight
//grid.Monotonicity() * monoWeight
//- grid.islands() * islandWeight
+ grid.Monotonicity2() * mono2Weight
//+ Math.Log(grid.EmptyCells()) * emptyWeight
//+ grid.MaxValue() * maxWeight
;
}
public override Direction ComputeNextMove(GridModel grid)
{
Direction bestMove = Direction.None;
double bestScore = double.NegativeInfinity;
var timer = new Stopwatch();
timer.Start();
int depth = 2;
do
{
foreach (var direction in Vector.Directions)
{
var score = AlphaBetaSearch(grid, depth, true, Double.NegativeInfinity, Double.PositiveInfinity);
if (score > bestScore)
{
bestScore = score;
bestMove = direction;
}
}
depth++;
} while (depth < 3);//timer.ElapsedMilliseconds < _minSearchTime);
return bestMove;
}
private int CountMerges(Direction direction, GridModel grid)
{
var vector = Vector.FromDirection(direction);
int merges = 0;
foreach (int x in grid.TraversalsX(direction))
{
foreach (int y in grid.TraversalsY(direction))
{
var cell1 = grid[x, y];
var cell2 = grid[x + vector.x, y + vector.y];
if (cell1 != null && cell2 != null)
{
if (cell1.IsOccupied && cell2.IsOccupied)
{
if (cell1.Tile.Value == cell2.Tile.Value)
merges++;
}
}
}
}
return merges;
}
public void SetGridSize(int value)
{
Grid = new GridModel(value);
Restart();
}
private double Minimizer(GridModel grid, int depth, double alpha, double beta)
{
// computer's turn, we'll do heavy pruning to keep the branching factor low
var availableCells = grid.AvailableCells().ToList();
// try out all combinations possible
foreach (var value in new int[] { 1, 2 })
{
foreach (CellModel cell in availableCells)
{
var tile = new TileModel(value);
tile.Position = cell;
beta = Math.Min(beta, AlphaBetaSearch(grid, depth, true, alpha, beta));
tile.Position = null;
if (beta < alpha) // pruning
{
return alpha;
}
}
}
/*
// try a 2 and 4 in each cell and measure how annoying it is
// with metrics from eval
//var scores = { 2: [], 4: [] };
foreach (var value in new int[] { 1, 2 })
{
foreach (CellModel cell in availableCells)
{
scores[value].push(null);
var tile = new TileModel(value);
tile.Position = cell;
scores[value][i] = -grid.Smoothness() + grid.Islands();
tile.Position = null;
}
}
// now just pick out the most annoying moves
var candidates = new List<CellModel>();
var maxScore = Math.Max(Math.Max(null, scores[2]), Math.Max(null, scores[4]));
foreach (var value in new int[] { 1, 2 })
{
for (var i = 0; i < scores[value].length; i++)
{
if (scores[value][i] >= maxScore)
{
candidates.Add(cells[i]);
}
}
}
// search on each candidate
foreach (CellModel position in candidates)
{
}
*/
return beta;
}
public abstract Direction ComputeNextMove(GridModel grid);
private double AlphaBetaSearch(GridModel grid, int depth, bool playerTurn, double alpha, double beta)
{
if (playerTurn)
{
return Maximizer(grid, depth, alpha, beta);
}
else
{
return Minimizer(grid, depth, alpha, beta);
}
}
public override Direction ComputeNextMove(GridModel grid)
{
return Direction.Up;
}
/*
* Grid.prototype.monotonicity = function() {
* var self = this;
* var marked = [];
* var queued = [];
* var highestValue = 0;
* var highestCell = {x:0, y:0};
* for (var x=0; x<4; x++) {
* marked.push([]);
* queued.push([]);
* for (var y=0; y<4; y++) {
* marked[x].push(false);
* queued[x].push(false);
* if (this.cells[x][y] &&
* this.cells[x][y].value > highestValue) {
* highestValue = this.cells[x][y].value;
* highestCell.x = x;
* highestCell.y = y;
* }
* }
* }
*
* increases = 0;
* cellQueue = [highestCell];
* queued[highestCell.x][highestCell.y] = true;
* markList = [highestCell];
* markAfter = 1; // only mark after all queued moves are done, as if searching in parallel
*
* var markAndScore = function(cell) {
* markList.push(cell);
* var value;
* if (self.cellOccupied(cell)) {
* value = Math.log(self.cellContent(cell).value) / Math.log(2);
* } else {
* value = 0;
* }
* for (direction in [0,1,2,3]) {
* var vector = self.getVector(direction);
* var target = { x: cell.x + vector.x, y: cell.y+vector.y }
* if (self.withinBounds(target) && !marked[target.x][target.y]) {
* if ( self.cellOccupied(target) ) {
* targetValue = Math.log(self.cellContent(target).value ) / Math.log(2);
* if ( targetValue > value ) {
* //console.log(cell, value, target, targetValue);
* increases += targetValue - value;
* }
* }
* if (!queued[target.x][target.y]) {
* cellQueue.push(target);
* queued[target.x][target.y] = true;
* }
* }
* }
* if (markAfter == 0) {
* while (markList.length > 0) {
* var cel = markList.pop();
* marked[cel.x][cel.y] = true;
* }
* markAfter = cellQueue.length;
* }
* }
*
* while (cellQueue.length > 0) {
* markAfter--;
* markAndScore(cellQueue.shift())
* }
*
* return -increases;
* }
*/
// measures how monotonic the grid is. This means the values of the tiles are strictly increasing
// or decreasing in both the left/right and up/down directions
public static double Monotonicity2(this GridModel grid)
{
// scores for all four directions
var totals = new Dictionary <Direction, double>();
totals[Direction.Up] = 0;
totals[Direction.Down] = 0;
totals[Direction.Left] = 0;
totals[Direction.Right] = 0;
// up/down direction
for (var x = 0; x < grid.SizeX; x++)
{
var next = 1;
var currentValue = grid[x, 0].Value;
while (next < grid.SizeY)
{
var nextValue = grid[x, next].Value;
if (nextValue > 0)
{
if (currentValue > nextValue)
{
totals[Direction.Up] += nextValue - currentValue;
}
else if (nextValue > currentValue)
{
totals[Direction.Down] += currentValue - nextValue;
}
currentValue = nextValue;
}
next++;
}
}
// left/right direction
for (var y = 0; y < grid.SizeY; y++)
{
var next = 1;
var currentValue = grid[0, y].Value;
while (next < grid.SizeX)
{
var nextValue = grid[next, y].Value;
if (nextValue > 0)
{
if (currentValue > nextValue)
{
totals[Direction.Left] += nextValue - currentValue;
}
else if (nextValue > currentValue)
{
totals[Direction.Right] += currentValue - nextValue;
}
currentValue = nextValue;
}
next++;
}
}
return(Math.Max(totals[Direction.Left], totals[Direction.Right]) +
Math.Max(totals[Direction.Up], totals[Direction.Down]));
}
public static CellModel FindFarthestPosition(this GridModel grid, CellModel cell, Direction direction, out CellModel next)
{
return(FindFarthestPosition(grid, cell, Vector.FromDirection(direction), out next));
}
public virtual void TrainNextMove(GridModel grid, Direction direction)
{
}
public override void TrainNextMove(GridModel grid, Direction direction)
{
var input = GridToInput(grid);
var output = DirectionToOutput(direction);
double error = _teacher.Run(input, output);
// also train rotated boards at the same time!
input = RotateLeft(input);
output = DirectionToOutput(RotateLeft(direction));
error = Math.Max(_teacher.Run(input, output), error);
input = RotateLeft(input);
output = DirectionToOutput(RotateLeft(direction));
error = Math.Max(_teacher.Run(input, output), error);
input = RotateLeft(input);
output = DirectionToOutput(RotateLeft(direction));
error = Math.Max(_teacher.Run(input, output), error);
Console.WriteLine("Error: {0}", error);
}
public void SetGridSize(int value)
{
Grid = new GridModel(value);
Restart();
}
public GridViewModel(GridModel model)
{
Model = model;
}
public static double EmptyCells(this GridModel grid)
{
return(grid.Cells
.Count(x => x.IsAvailable));
}