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model.go
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model.go
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package rush
import (
"fmt"
"image"
"math"
"math/rand"
"sort"
"strings"
)
// Orientation indicates which direction a Piece can move. Horizontal pieces
// can move left and right. Vertical pieces can move up and down.
type Orientation int
const (
Horizontal Orientation = iota
Vertical
)
// Piece represents a piece (a car or a truck) on the grid. Its position is
// a zero-indexed int, 0 <= Position < W*H. Its size specifies how many cells
// it occupies. Its orientation specifies whether it is vertical or horizontal.
type Piece struct {
Position int
Size int
Orientation Orientation
}
func (piece *Piece) Stride(w int) int {
if piece.Orientation == Horizontal {
return 1
}
return w
}
func (piece *Piece) Row(w int) int {
return piece.Position / w
}
func (piece *Piece) Col(w int) int {
return piece.Position % w
}
// Move represents a move to make on the board. Piece indicates which piece
// (by index) to move and Steps is a non-zero positive or negative int that
// specifies how many cells to move the piece.
type Move struct {
Piece int
Steps int
}
func (move Move) AbsSteps() int {
if move.Steps < 0 {
return -move.Steps
}
return move.Steps
}
func (move Move) Label() string {
return string('A' + move.Piece)
}
func (move Move) String() string {
return fmt.Sprintf("%s%+d", move.Label(), move.Steps)
}
// Board represents the complete puzzle state. The size of the grid, the
// placement, size, orientation of the pieces. The placement of walls
// (immovable obstacles). Which cells are occupied, either by a piece or a
// wall.
type Board struct {
Width int
Height int
Pieces []Piece
Walls []int
occupied []bool
memoKey MemoKey
}
func NewEmptyBoard(w, h int) *Board {
occupied := make([]bool, w*h)
memoKey := MakeMemoKey(nil)
return &Board{w, h, nil, nil, occupied, memoKey}
}
func NewRandomBoard(w, h, primaryRow, primarySize, numPieces, numWalls int) *Board {
board := NewEmptyBoard(w, h)
board.AddPiece(Piece{primaryRow * w, primarySize, Horizontal})
for i := 1; i < numPieces; i++ {
board.mutateAddPiece(100)
}
for i := 0; i < numWalls; i++ {
board.mutateAddWall(100)
}
return board
}
func NewBoardFromString(desc string) (*Board, error) {
s := int(math.Sqrt(float64(len(desc))))
if s*s != len(desc) {
return nil, fmt.Errorf("NewBoardFromString only supports square boards")
}
rows := make([]string, s)
for i := range rows {
rows[i] = desc[i*s : i*s+s]
}
return NewBoard(rows)
}
func NewBoard(desc []string) (*Board, error) {
// determine board size
h := len(desc)
if h < MinBoardSize {
return nil, fmt.Errorf("board height must be >= %d", MinBoardSize)
}
w := len(desc[0])
if w < MinBoardSize {
return nil, fmt.Errorf("board width must be >= %d", MinBoardSize)
}
// identify occupied cells and their labels
occupied := make([]bool, w*h)
positions := make(map[string][]int)
var walls []int
for y, row := range desc {
for x, value := range row {
label := string(value)
if label == "." || label == "o" {
continue
}
i := y*w + x
occupied[i] = true
if label == "x" {
walls = append(walls, i)
} else {
positions[label] = append(positions[label], i)
}
}
}
// find and sort distinct piece labels
labels := make([]string, 0, len(positions))
for label := range positions {
labels = append(labels, label)
}
sort.Strings(labels)
// validate and create pieces
pieces := make([]Piece, 0, len(labels))
for _, label := range labels {
ps := positions[label]
if len(ps) < MinPieceSize {
return nil, fmt.Errorf("piece %s length must be >= %d", label, MinPieceSize)
}
stride := ps[1] - ps[0]
if stride != 1 && stride != w {
return nil, fmt.Errorf("piece %s has invalid shape", label)
}
for i := 2; i < len(ps); i++ {
if ps[i]-ps[i-1] != stride {
return nil, fmt.Errorf("piece %s has invalid shape", label)
}
}
dir := Horizontal
if stride != 1 {
dir = Vertical
}
pieces = append(pieces, Piece{ps[0], len(ps), dir})
}
// create board
board := &Board{w, h, pieces, walls, occupied, MakeMemoKey(pieces)}
return board, board.Validate()
}
func (board *Board) String() string {
w := board.Width
h := board.Height
grid := make([]string, w*h)
for i := range grid {
grid[i] = "."
}
for _, i := range board.Walls {
grid[i] = "x"
}
for i, piece := range board.Pieces {
label := string('A' + i)
idx := piece.Position
stride := piece.Stride(w)
for j := 0; j < piece.Size; j++ {
grid[idx] = label
idx += stride
}
}
rows := make([]string, h)
for y := 0; y < h; y++ {
i := y * w
rows[y] = strings.Join(grid[i:i+w], "")
}
return strings.Join(rows, "\n")
}
func (board *Board) Hash() string {
w := board.Width
h := board.Height
grid := make([]rune, w*h)
for i := range grid {
grid[i] = '.'
}
for _, i := range board.Walls {
grid[i] = 'x'
}
for i, piece := range board.Pieces {
label := rune('A' + i)
idx := piece.Position
stride := 1
if piece.Orientation == Vertical {
stride = w
}
for j := 0; j < piece.Size; j++ {
grid[idx] = label
idx += stride
}
}
return string(grid)
}
func (board *Board) Copy() *Board {
w := board.Width
h := board.Height
pieces := make([]Piece, len(board.Pieces))
walls := make([]int, len(board.Walls))
occupied := make([]bool, len(board.occupied))
memoKey := board.memoKey
copy(pieces, board.Pieces)
copy(walls, board.Walls)
copy(occupied, board.occupied)
return &Board{w, h, pieces, walls, occupied, memoKey}
}
func (board *Board) SortPieces() {
a := board.Pieces[1:]
sort.Slice(a, func(i, j int) bool {
return a[i].Position < a[j].Position
})
board.memoKey = MakeMemoKey(board.Pieces)
}
func (board *Board) HasFullRowOrCol() bool {
w := board.Width
h := board.Height
for y := 0; y < h; y++ {
var size int
for _, piece := range board.Pieces {
if piece.Orientation == Horizontal && piece.Row(w) == y {
size += piece.Size
}
}
if size == w {
return true
}
}
for x := 0; x < w; x++ {
var size int
for _, piece := range board.Pieces {
if piece.Orientation == Vertical && piece.Col(w) == x {
size += piece.Size
}
}
if size == h {
return true
}
}
return false
}
func (board *Board) Validate() error {
w := board.Width
h := board.Height
pieces := board.Pieces
// board size must be >= MinBoardSize
if w < MinBoardSize {
return fmt.Errorf("board width must be >= %d", MinBoardSize)
}
if h < MinBoardSize {
return fmt.Errorf("board height must be >= %d", MinBoardSize)
}
// board must have at least one piece
if len(pieces) < 1 {
return fmt.Errorf("board must have at least one piece")
}
// board must have <= MaxPieces
if len(pieces) > MaxPieces {
return fmt.Errorf("board must have <= %d pieces", MaxPieces)
}
// primary piece must be horizontal
if pieces[0].Orientation != Horizontal {
return fmt.Errorf("primary piece must be horizontal")
}
// validate walls
occupied := make([]bool, w*h)
for _, i := range board.Walls {
// wall must be inside the grid
if i < 0 || i >= w*h {
return fmt.Errorf("a wall is outside of the grid")
}
// walls must not intersect
if occupied[i] {
return fmt.Errorf("a wall intersects another wall")
}
occupied[i] = true
}
// validate pieces
primaryRow := pieces[0].Row(w)
for i, piece := range pieces {
label := string('A' + i)
row := piece.Row(w)
col := piece.Col(w)
// piece size must be >= MinPieceSize
if piece.Size < MinPieceSize {
return fmt.Errorf("piece %s must have size >= %d", label, MinPieceSize)
}
// no horizontal pieces can be on the same row as the primary piece
if i > 0 && piece.Orientation == Horizontal && row == primaryRow {
return fmt.Errorf("no horizontal pieces can be on the primary row")
}
// pieces must be contained within the grid
if piece.Orientation == Horizontal {
if row < 0 || row >= h || col < 0 || col+piece.Size > w {
return fmt.Errorf("piece %s is outside of the grid", label)
}
} else {
if col < 0 || col >= w || row < 0 || row+piece.Size > h {
return fmt.Errorf("piece %s is outside of the grid", label)
}
}
// pieces must not intersect
idx := piece.Position
stride := piece.Stride(w)
for j := 0; j < piece.Size; j++ {
if occupied[idx] {
return fmt.Errorf("piece %s intersects with another piece", label)
}
occupied[idx] = true
idx += stride
}
}
return nil
}
func (board *Board) isOccupied(piece Piece) bool {
idx := piece.Position
stride := piece.Stride(board.Width)
for i := 0; i < piece.Size; i++ {
if board.occupied[idx] {
return true
}
idx += stride
}
return false
}
func (board *Board) setOccupied(piece Piece, value bool) {
idx := piece.Position
stride := piece.Stride(board.Width)
for i := 0; i < piece.Size; i++ {
board.occupied[idx] = value
idx += stride
}
}
func (board *Board) addPiece(piece Piece) {
i := len(board.Pieces)
board.Pieces = append(board.Pieces, piece)
board.setOccupied(piece, true)
board.memoKey[i] = piece.Position
}
func (board *Board) AddPiece(piece Piece) bool {
if board.isOccupied(piece) {
return false
}
board.addPiece(piece)
return true
}
func (board *Board) AddWall(i int) bool {
if board.occupied[i] {
return false
}
board.Walls = append(board.Walls, i)
board.occupied[i] = true
return true
}
func (board *Board) RemovePiece(i int) {
board.setOccupied(board.Pieces[i], false)
j := len(board.Pieces) - 1
board.Pieces[i] = board.Pieces[j]
board.memoKey[i] = board.Pieces[i].Position
board.Pieces = board.Pieces[:j]
board.memoKey[j] = 0
}
func (board *Board) RemoveLastPiece() {
board.RemovePiece(len(board.Pieces) - 1)
}
func (board *Board) RemoveWall(i int) {
board.occupied[board.Walls[i]] = false
a := board.Walls
a[i] = a[len(a)-1]
a = a[:len(a)-1]
board.Walls = a
}
func (board *Board) Target() int {
w := board.Width
piece := board.Pieces[0]
row := piece.Row(w)
return (row+1)*w - piece.Size
}
func (board *Board) Moves(buf []Move) []Move {
moves := buf[:0]
w := board.Width
h := board.Height
for i, piece := range board.Pieces {
var stride, reverseSteps, forwardSteps int
if piece.Orientation == Vertical {
y := piece.Position / w
reverseSteps = -y
forwardSteps = h - piece.Size - y
stride = w
} else {
x := piece.Position % w
reverseSteps = -x
forwardSteps = w - piece.Size - x
stride = 1
}
// reverse (negative steps)
idx := piece.Position - stride
for steps := -1; steps >= reverseSteps; steps-- {
if board.occupied[idx] {
break
}
moves = append(moves, Move{i, steps})
idx -= stride
}
// forward (positive steps)
idx = piece.Position + piece.Size*stride
for steps := 1; steps <= forwardSteps; steps++ {
if board.occupied[idx] {
break
}
moves = append(moves, Move{i, steps})
idx += stride
}
}
return moves
}
func (board *Board) DoMove(move Move) {
piece := &board.Pieces[move.Piece]
stride := piece.Stride(board.Width)
idx := piece.Position
for i := 0; i < piece.Size; i++ {
board.occupied[idx] = false
idx += stride
}
piece.Position += stride * move.Steps
board.memoKey[move.Piece] = piece.Position
idx = piece.Position
for i := 0; i < piece.Size; i++ {
board.occupied[idx] = true
idx += stride
}
}
func (board *Board) UndoMove(move Move) {
board.DoMove(Move{move.Piece, -move.Steps})
}
func (board *Board) StateIterator() <-chan *Board {
ch := make(chan *Board, 16)
board = board.Copy()
memo := NewMemo()
var f func(int, int)
f = func(depth, previousPiece int) {
if !memo.Add(board.MemoKey(), 0) {
return
}
ch <- board.Copy()
for _, move := range board.Moves(nil) {
if move.Piece == previousPiece {
continue
}
board.DoMove(move)
f(depth+1, move.Piece)
board.UndoMove(move)
}
if depth == 0 {
close(ch)
}
}
go f(0, -1)
return ch
}
func (board *Board) ReachableStates() int {
var count int
memo := NewMemo()
var f func(int)
f = func(previousPiece int) {
if !memo.Add(board.MemoKey(), 0) {
return
}
count++
for _, move := range board.Moves(nil) {
if move.Piece == previousPiece {
continue
}
board.DoMove(move)
f(move.Piece)
board.UndoMove(move)
}
}
f(-1)
return count
}
func (board *Board) MemoKey() *MemoKey {
return &board.memoKey
}
func (board *Board) Solve() Solution {
return NewSolver(board).Solve()
}
func (board *Board) Unsolve() (*Board, Solution) {
return NewUnsolver(board).Unsolve()
}
func (board *Board) UnsafeSolve() Solution {
return NewSolver(board).UnsafeSolve()
}
func (board *Board) UnsafeUnsolve() (*Board, Solution) {
return NewUnsolver(board).UnsafeUnsolve()
}
func (board *Board) Render() image.Image {
return renderBoard(board)
}
func (board *Board) Impossible() bool {
return theStaticAnalyzer.Impossible(board)
}
func (board *Board) BlockedSquares() []int {
return theStaticAnalyzer.BlockedSquares(board)
}
func (board *Board) Canonicalize() *Board {
bestKey := board.memoKey
bestBoard := board.Copy()
for b := range board.StateIterator() {
if b.memoKey.Less(&bestKey, true) {
bestKey = b.memoKey
bestBoard = b.Copy()
}
}
bestBoard.SortPieces()
return bestBoard
}
// random board mutation below
func (board *Board) Energy() float64 {
solution := board.Solve()
if !solution.Solvable {
return 1
}
e := float64(solution.NumMoves)
e += float64(solution.NumSteps) / 100
return -e
}
type UndoFunc func()
func (board *Board) Mutate() UndoFunc {
const maxAttempts = 100
for {
var undo UndoFunc
switch rand.Intn(7 + 3) {
case 0:
undo = board.mutateAddPiece(maxAttempts)
case 1:
undo = board.mutateAddWall(maxAttempts)
case 2:
undo = board.mutateRemovePiece()
case 3:
undo = board.mutateRemoveWall()
case 4:
undo = board.mutateRemoveAndAddPiece(maxAttempts)
case 5:
undo = board.mutateRemoveAndAddWall(maxAttempts)
default:
undo = board.mutateMakeMove()
}
if undo != nil {
return undo
}
}
}
func (board *Board) mutateMakeMove() UndoFunc {
moves := board.Moves(nil)
if len(moves) == 0 {
return nil
}
move := moves[rand.Intn(len(moves))]
board.DoMove(move)
return func() {
board.UndoMove(move)
}
}
func (board *Board) mutateAddPiece(maxAttempts int) UndoFunc {
if len(board.Pieces) >= 8 {
return nil
}
piece, ok := board.randomPiece(maxAttempts)
if !ok {
return nil
}
i := len(board.Pieces)
board.AddPiece(piece)
return func() {
board.RemovePiece(i)
}
}
func (board *Board) mutateAddWall(maxAttempts int) UndoFunc {
if len(board.Walls) >= 0 {
return nil
}
wall, ok := board.randomWall(maxAttempts)
if !ok {
return nil
}
i := len(board.Walls)
board.AddWall(wall)
return func() {
board.RemoveWall(i)
}
}
func (board *Board) mutateRemovePiece() UndoFunc {
// never remove the primary piece
if len(board.Pieces) < 2 {
return nil
}
i := rand.Intn(len(board.Pieces)-1) + 1
piece := board.Pieces[i]
board.RemovePiece(i)
return func() {
board.AddPiece(piece)
}
}
func (board *Board) mutateRemoveWall() UndoFunc {
if len(board.Walls) == 0 {
return nil
}
i := rand.Intn(len(board.Walls))
wall := board.Walls[i]
board.RemoveWall(i)
return func() {
board.AddWall(wall)
}
}
func (board *Board) mutateRemoveAndAddPiece(maxAttempts int) UndoFunc {
undoRemove := board.mutateRemovePiece()
if undoRemove == nil {
return nil
}
undoAdd := board.mutateAddPiece(maxAttempts)
if undoAdd == nil {
return undoRemove
}
return func() {
undoAdd()
undoRemove()
}
}
func (board *Board) mutateRemoveAndAddWall(maxAttempts int) UndoFunc {
undoRemove := board.mutateRemoveWall()
if undoRemove == nil {
return nil
}
undoAdd := board.mutateAddWall(maxAttempts)
if undoAdd == nil {
return undoRemove
}
return func() {
undoAdd()
undoRemove()
}
}
func (board *Board) randomPiece(maxAttempts int) (Piece, bool) {
w := board.Width
h := board.Height
for i := 0; i < maxAttempts; i++ {
size := 2 + rand.Intn(2) // TODO: weighted?
orientation := Orientation(rand.Intn(2))
var x, y int
if orientation == Vertical {
x = rand.Intn(w)
y = rand.Intn(h - size + 1)
} else {
x = rand.Intn(w - size + 1)
y = rand.Intn(h)
}
position := y*w + x
piece := Piece{position, size, orientation}
if !board.isOccupied(piece) {
return piece, true
}
}
return Piece{}, false
}
func (board *Board) randomWall(maxAttempts int) (int, bool) {
n := board.Width * board.Height
for i := 0; i < maxAttempts; i++ {
p := rand.Intn(n)
if !board.occupied[p] {
return p, true
}
}
return 0, false
}