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board.go
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board.go
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package solver
import (
"errors"
"fmt"
"github.com/RoaringBitmap/roaring"
"strconv"
"strings"
"time"
)
const (
BoardSize = 9
BlockSize = 3
EmptyCellValue = Value(0)
MinimumGivens = 17
Offset = 1
EOL = 0x0A
)
type Difficulty int
const (
Easy Difficulty = iota
Medium
Hard
Expert
Evil
)
var Levels = map[Difficulty]string{
Easy: "Easy",
Medium: "Medium",
Hard: "Hard",
Expert: "Expert",
Evil: "Evil",
}
type Strategy string
const (
NakedQuadsStrategy Strategy = "Naked Quads"
NakedTriplesStrategy Strategy = "Naked Triples"
NakedPairsStrategy Strategy = "Naked Pairs"
XYWingsStrategy Strategy = "XY Wings"
XYZWingsStrategy Strategy = "XYZ Wings"
XWingsStrategy Strategy = "X Wings"
SwordFishStrategy Strategy = "Sword Fish"
HiddenSingleStrategy Strategy = "Hidden Single"
HiddenQuadsStrategy Strategy = "Hidden Quads"
HiddenTripletsStrategy Strategy = "Hidden Triplets"
HiddenPairsStrategy Strategy = "Hidden Pairs"
)
func (s Strategy) ToString() string {
return string(s)
}
var Digits = roaring.BitmapOf(1, 2, 3, 4, 5, 6, 7, 8, 9)
var ValidInputs = roaring.BitmapOf(uint32(EmptyCellValue), 1, 2, 3, 4, 5, 6, 7, 8, 9)
var HexMap = map[byte]Value{
0x2e: 0x00,
0x30: 0x00,
0x31: 0x01,
0x32: 0x02,
0x33: 0x03,
0x34: 0x04,
0x35: 0x05,
0x36: 0x06,
0x37: 0x07,
0x38: 0x08,
0x39: 0x09,
}
// Board is the struct of the Sudoku board
type Board struct {
data [BoardSize][BoardSize]*Cell
initialState string
difficulty Difficulty
givens int
backTrackUsed bool
strategiesUsed []string
}
// NewBoard returns new Sudoku board with the given input matrix, if there are any issues it also returns error
func NewBoard(input [BoardSize][BoardSize]Value) (*Board, error) {
var data [BoardSize][BoardSize]*Cell
givens := 0
id := 0
for i := 0; i < BoardSize; i++ {
for j := 0; j < BoardSize; j++ {
value := input[i][j]
if !ValidInputs.Contains(uint32(value)) {
return nil, fmt.Errorf("%d is not valid input at [%d][%d]\n", value, i, j)
}
cell := &Cell{
ID: id,
Row: i,
Col: j,
Value: input[i][j],
Marks: roaring.NewBitmap(),
}
data[i][j] = cell
id++
if value != EmptyCellValue {
givens++
}
}
}
if givens < MinimumGivens {
return nil, fmt.Errorf("At least %d cells should be given to find out unique solution."+
"Current givens: %d\n", MinimumGivens, givens)
}
var difficulty Difficulty
if givens > 32 {
difficulty = Easy
}
if givens >= 30 && givens <= 32 {
difficulty = Medium
}
if givens >= 28 && givens < 30 {
difficulty = Hard
}
if givens >= 23 && givens < 28 {
difficulty = Expert
}
if givens < 23 {
difficulty = Evil
}
board := &Board{
data: data,
initialState: "",
difficulty: difficulty,
givens: givens,
backTrackUsed: false,
strategiesUsed: make([]string, 0),
}
// Storing the initial state before Solve method is called
board.initialState = board.getState()
return board, nil
}
// GetGivensAndBackTrack returns the givens and backTrackUsed flag
func (b *Board) GetGivensAndBackTrack() (int, bool) {
return b.givens, b.backTrackUsed
}
// addStrategy
func (b *Board) addStrategy(strategy Strategy) {
for _, s := range b.strategiesUsed {
if s == strategy.ToString() {
// This strategy is already added, returning
return
}
}
// New strategy adding it
b.strategiesUsed = append(b.strategiesUsed, strategy.ToString())
}
// Solve is a utility function to start the solving process of given sudoku board
func (b *Board) Solve() *SolveResponse {
begin := time.Now()
threshold := 1
emptyCycles := 0
info := make(map[int]int)
if computeErr := b.computeAllMarks(); computeErr != nil {
return &SolveResponse{
Difficulty: Levels[b.difficulty],
Givens: b.givens,
InitialState: b.initialState,
Solution: b.getState(),
Duration: time.Since(begin).Seconds(),
IsSolved: false,
BackTrackingUsed: b.backTrackUsed,
StrategiesUsed: b.strategiesUsed,
Error: computeErr,
}
}
iteration := 0
info[iteration] = b.emptyCells()
for {
solve:
if b.hasUniqueSolutions() {
for i := 0; i < BoardSize; i++ {
for j := 0; j < BoardSize; j++ {
cell := b.data[i][j]
if !cell.IsSolved() {
if cell.MarksLength() == 1 {
solution := cell.Marks.ToArray()[0]
if cell.IsValid(b, Value(solution)) {
cell.Value = Value(solution)
cell.Marks.Clear()
if computeErr := b.computeAllMarks(); computeErr != nil {
return &SolveResponse{
Difficulty: Levels[b.difficulty],
Givens: b.givens,
InitialState: b.initialState,
Solution: b.getState(),
Duration: time.Since(begin).Seconds(),
IsSolved: false,
BackTrackingUsed: b.backTrackUsed,
StrategiesUsed: b.strategiesUsed,
Error: computeErr,
}
}
}
}
}
}
}
}
if b.hasUniqueSolutions() {
// There might be new solutions during the loop below, In that case, we should goto solve and continue
goto solve
}
// Naked Quads strategy
if err := b.eliminateNQ(); err != nil {
return &SolveResponse{
Difficulty: Levels[b.difficulty],
Givens: b.givens,
InitialState: b.initialState,
Solution: b.getState(),
Duration: time.Since(begin).Seconds(),
IsSolved: false,
BackTrackingUsed: b.backTrackUsed,
StrategiesUsed: b.strategiesUsed,
Error: err,
}
}
if b.hasUniqueSolutions() {
b.addStrategy(NakedQuadsStrategy)
continue
}
// Naked Triples strategy
if err := b.eliminateNT(); err != nil {
return &SolveResponse{
Difficulty: Levels[b.difficulty],
Givens: b.givens,
InitialState: b.initialState,
Solution: b.getState(),
Duration: time.Since(begin).Seconds(),
IsSolved: false,
BackTrackingUsed: b.backTrackUsed,
StrategiesUsed: b.strategiesUsed,
Error: err,
}
}
if b.hasUniqueSolutions() {
b.addStrategy(NakedTriplesStrategy)
continue
}
// Naked Pairs strategy
if err := b.eliminateNP(); err != nil {
return &SolveResponse{
Difficulty: Levels[b.difficulty],
Givens: b.givens,
InitialState: b.initialState,
Solution: b.getState(),
Duration: time.Since(begin).Seconds(),
IsSolved: false,
BackTrackingUsed: b.backTrackUsed,
StrategiesUsed: b.strategiesUsed,
Error: err,
}
}
if b.hasUniqueSolutions() {
b.addStrategy(NakedPairsStrategy)
continue
}
// XY Wings strategy
s := b.totalMarks()
if err := b.eliminateXYWings(); err != nil {
return &SolveResponse{
Difficulty: Levels[b.difficulty],
Givens: b.givens,
InitialState: b.initialState,
Solution: b.getState(),
Duration: time.Since(begin).Seconds(),
IsSolved: false,
BackTrackingUsed: b.backTrackUsed,
StrategiesUsed: b.strategiesUsed,
Error: err,
}
}
diff := s - b.totalMarks()
if b.hasUniqueSolutions() || diff > 0 {
b.addStrategy(XYWingsStrategy)
continue
}
// XYZ Wings strategy
s = b.totalMarks()
if err := b.eliminateXYZWings(); err != nil {
return &SolveResponse{
Difficulty: Levels[b.difficulty],
Givens: b.givens,
InitialState: b.initialState,
Solution: b.getState(),
Duration: time.Since(begin).Seconds(),
IsSolved: false,
BackTrackingUsed: b.backTrackUsed,
StrategiesUsed: b.strategiesUsed,
Error: err,
}
}
diff = s - b.totalMarks()
if b.hasUniqueSolutions() || diff > 0 {
b.addStrategy(XYZWingsStrategy)
continue
}
// XWings strategy
s = b.totalMarks()
if err := b.eliminateXWings(); err != nil {
return &SolveResponse{
Difficulty: Levels[b.difficulty],
Givens: b.givens,
InitialState: b.initialState,
Solution: b.getState(),
Duration: time.Since(begin).Seconds(),
IsSolved: false,
BackTrackingUsed: b.backTrackUsed,
StrategiesUsed: b.strategiesUsed,
Error: err,
}
}
diff = s - b.totalMarks()
if b.hasUniqueSolutions() || diff > 0 {
b.addStrategy(XWingsStrategy)
continue
}
// Sword Fish strategy
s = b.totalMarks()
if err := b.eliminateSwordFish(); err != nil {
return &SolveResponse{
Difficulty: Levels[b.difficulty],
Givens: b.givens,
InitialState: b.initialState,
Solution: b.getState(),
Duration: time.Since(begin).Seconds(),
IsSolved: false,
BackTrackingUsed: b.backTrackUsed,
StrategiesUsed: b.strategiesUsed,
Error: err,
}
}
diff = s - b.totalMarks()
if b.hasUniqueSolutions() || diff > 0 {
b.addStrategy(SwordFishStrategy)
continue
}
// Hidden Single strategy
s = b.totalMarks()
if err := b.eliminateHS(); err != nil {
return &SolveResponse{
Difficulty: Levels[b.difficulty],
Givens: b.givens,
InitialState: b.initialState,
Solution: b.getState(),
Duration: time.Since(begin).Seconds(),
IsSolved: false,
BackTrackingUsed: b.backTrackUsed,
StrategiesUsed: b.strategiesUsed,
Error: err,
}
}
diff = s - b.totalMarks()
if b.hasUniqueSolutions() || diff > 0 {
b.addStrategy(HiddenSingleStrategy)
continue
}
// Hidden Quads strategy
s = b.totalMarks()
if err := b.eliminateHQ(); err != nil {
return &SolveResponse{
Difficulty: Levels[b.difficulty],
Givens: b.givens,
InitialState: b.initialState,
Solution: b.getState(),
Duration: time.Since(begin).Seconds(),
IsSolved: false,
BackTrackingUsed: b.backTrackUsed,
StrategiesUsed: b.strategiesUsed,
Error: err,
}
}
diff = s - b.totalMarks()
if b.hasUniqueSolutions() {
b.addStrategy(HiddenQuadsStrategy)
continue
}
// Hidden Triplets strategy
s = b.totalMarks()
if err := b.eliminateHT(); err != nil {
return &SolveResponse{
Difficulty: Levels[b.difficulty],
Givens: b.givens,
InitialState: b.initialState,
Solution: b.getState(),
Duration: time.Since(begin).Seconds(),
IsSolved: false,
BackTrackingUsed: b.backTrackUsed,
StrategiesUsed: b.strategiesUsed,
Error: err,
}
}
diff = s - b.totalMarks()
if b.hasUniqueSolutions() {
b.addStrategy(HiddenTripletsStrategy)
continue
}
// Hidden Pairs strategy
s = b.totalMarks()
if err := b.eliminateHP(); err != nil {
return &SolveResponse{
Difficulty: Levels[b.difficulty],
Givens: b.givens,
InitialState: b.initialState,
Solution: b.getState(),
Duration: time.Since(begin).Seconds(),
IsSolved: false,
BackTrackingUsed: b.backTrackUsed,
StrategiesUsed: b.strategiesUsed,
Error: err,
}
}
diff = s - b.totalMarks()
if b.hasUniqueSolutions() || diff > 0 {
b.addStrategy(HiddenPairsStrategy)
continue
}
iteration++
info[iteration] = b.emptyCells()
if info[iteration-1] == info[iteration] {
// Increasing the empty cycles
emptyCycles++
} else {
// We have some solutions, reset the empty cycles
emptyCycles = 0
}
if emptyCycles == threshold {
// Empty cycles reached to the threshold, giving up using strategies and using backtrack
b.backTrack()
break
}
if b.isSolved() {
break
}
}
if b.isSolved() {
return &SolveResponse{
Difficulty: Levels[b.difficulty],
Givens: b.givens,
InitialState: b.initialState,
Solution: b.getState(),
Duration: time.Since(begin).Seconds(),
IsSolved: true,
BackTrackingUsed: b.backTrackUsed,
StrategiesUsed: b.strategiesUsed,
Error: nil,
}
} else {
if b.hasInvalidMarks() {
return &SolveResponse{
Difficulty: Levels[b.difficulty],
Givens: b.givens,
InitialState: b.initialState,
Solution: b.getState(),
Duration: time.Since(begin).Seconds(),
IsSolved: false,
BackTrackingUsed: b.backTrackUsed,
StrategiesUsed: b.strategiesUsed,
Error: errors.New("invalid board; some cells have invalid marks"),
}
} else {
return &SolveResponse{
Difficulty: Levels[b.difficulty],
Givens: b.givens,
InitialState: b.initialState,
Solution: b.getState(),
Duration: time.Since(begin).Seconds(),
IsSolved: false,
BackTrackingUsed: b.backTrackUsed,
StrategiesUsed: b.strategiesUsed,
Error: errors.New("unable to find a solution"),
}
}
}
}
// row returns the row in the given index
func (b *Board) row(index int) []*Cell {
return Row(b.data, index)
}
// col returns the col in the given index
func (b *Board) col(index int) []*Cell {
return Col(b.data, index)
}
// box returns the box cells in the given cell index by row and col ids
func (b *Board) box(rowID int, colID int) []*Cell {
return Box(b.data, rowID, colID)
}
// emptyCells returns the number of the unsolved cells
func (b *Board) emptyCells() int {
empty := 0
for i := 0; i < BoardSize; i++ {
for j := 0; j < BoardSize; j++ {
cell := b.data[i][j]
if !cell.IsSolved() {
empty++
}
}
}
return empty
}
// isSolved simply returns whether the board is solved or not
func (b *Board) isSolved() bool {
return b.emptyCells() == 0
}
// solutions returns the number of marks with the given length
func (b *Board) solutions(length int) int {
solutions := 0
for i := 0; i < BoardSize; i++ {
for j := 0; j < BoardSize; j++ {
cell := b.data[i][j]
if !cell.IsSolved() {
if cell.MarksLength() == length {
solutions++
}
}
}
}
return solutions
}
// uniqueSolutions returns the number of unique solutions (having single candidate)
func (b *Board) uniqueSolutions() int {
return b.solutions(1)
}
// hasUniqueSolutions returns whether there are any unique solutions or not
func (b *Board) hasUniqueSolutions() bool {
return b.uniqueSolutions() > 0
}
// hasInvalidMarks returns whether board have invalid marks or not. This happens if the initial board is wrong
func (b *Board) hasInvalidMarks() bool {
for i := 0; i < BoardSize; i++ {
for j := 0; j < BoardSize; j++ {
cell := b.data[i][j]
// Cell is not solved and having zero marks
if !cell.IsSolved() && cell.MarksLength() == 0 {
return true
}
}
}
return false
}
// getState returns the current state of the board
func (b *Board) getState() string {
var builder strings.Builder
for i := 0; i < BoardSize; i++ {
if i%BlockSize == 0 {
builder.WriteString("*_______*_______*______*\n")
}
row := b.row(i)
for j := 0; j < len(row); j++ {
cell := row[j]
if j%BlockSize == 0 {
builder.WriteString("| ")
}
if !cell.IsSolved() {
builder.WriteString("_ ")
} else {
builder.WriteString(strconv.Itoa(int(cell.Value)) + " ")
}
}
builder.WriteString("\n")
}
return builder.String()
}
// unsolvedCells simply returns all unsolved cells within a slice
func (b *Board) unsolvedCells() []*Cell {
unsolved := make([]*Cell, 0)
for i := 0; i < BoardSize; i++ {
for j := 0; j < BoardSize; j++ {
cell := b.data[i][j]
if !cell.IsSolved() {
unsolved = append(unsolved, cell)
}
}
}
return unsolved
}
// totalMarks returns the total marks/candidates of the unsolved cells
func (b *Board) totalMarks() int {
total := uint64(0)
for _, cell := range b.unsolvedCells() {
total += cell.Marks.GetCardinality()
}
return int(total)
}
// computeAllMarks simply computes all marks/candidates of each unsolved cells
func (b *Board) computeAllMarks() error {
for i := 0; i < BoardSize; i++ {
for j := 0; j < BoardSize; j++ {
cell := b.data[i][j]
if !cell.IsSolved() {
cell.Marks = cell.ComputeCellMarks(b)
if cell.Marks.IsEmpty() {
return fmt.Errorf("Compute All marks: Cell: %+v\n", cell)
}
}
}
}
return nil
}
// eliminateNP simply eliminates marks/candidates using naked pair elimination strategy for each unsolved cells
func (b *Board) eliminateNP() error {
for i := 0; i < BoardSize; i++ {
for j := 0; j < BoardSize; j++ {
cell := b.data[i][j]
if !cell.IsSolved() {
if eliminateErr := EliminateNakedPairs(cell.CellUnits(b)); eliminateErr != nil {
return eliminateErr
}
}
}
}
return nil
}
// eliminateNT simply eliminates marks/candidates using naked triple elimination strategy for each unsolved cells
func (b *Board) eliminateNT() error {
for i := 0; i < BoardSize; i++ {
for j := 0; j < BoardSize; j++ {
cell := b.data[i][j]
if !cell.IsSolved() {
if eliminateErr := EliminateNakedTriplets(cell.CellUnits(b)); eliminateErr != nil {
return eliminateErr
}
}
}
}
return nil
}
// eliminateNQ simply eliminates marks/candidates using naked quad elimination strategy for each unsolved cells
func (b *Board) eliminateNQ() error {
for i := 0; i < BoardSize; i++ {
for j := 0; j < BoardSize; j++ {
cell := b.data[i][j]
if !cell.IsSolved() {
if eliminateErr := EliminateNakedQuads(cell.CellUnits(b)); eliminateErr != nil {
return eliminateErr
}
}
}
}
return nil
}
// eliminateHS simply eliminates marks/candidates using hidden single elimination strategy for each unsolved cells
func (b *Board) eliminateHS() error {
for i := 0; i < BoardSize; i++ {
for j := 0; j < BoardSize; j++ {
cell := b.data[i][j]
if !cell.IsSolved() {
if eliminateErr := EliminateHiddenSingles(cell.CellUnits(b)); eliminateErr != nil {
return eliminateErr
}
}
}
}
return nil
}
// eliminateHP simply eliminates marks/candidates using hidden pair eliminations strategy for each unsolved cells
func (b *Board) eliminateHP() error {
for i := 0; i < BoardSize; i++ {
for j := 0; j < BoardSize; j++ {
cell := b.data[i][j]
if !cell.IsSolved() {
if eliminateErr := EliminateHiddenPairs(cell.CellUnits(b)); eliminateErr != nil {
return eliminateErr
}
}
}
}
return nil
}
// eliminateHT simply eliminates marks/candidates using hidden triplet eliminations strategy for each unsolved cells
func (b *Board) eliminateHT() error {
for i := 0; i < BoardSize; i++ {
for j := 0; j < BoardSize; j++ {
cell := b.data[i][j]
if !cell.IsSolved() {
if eliminateErr := EliminateHiddenTriplets(cell.CellUnits(b)); eliminateErr != nil {
return eliminateErr
}
}
}
}
return nil
}
// eliminateHQ simply eliminates marks/candidates using hidden quads eliminations strategy for each unsolved cells
func (b *Board) eliminateHQ() error {
for i := 0; i < BoardSize; i++ {
for j := 0; j < BoardSize; j++ {
cell := b.data[i][j]
if !cell.IsSolved() {
if eliminateErr := EliminateHiddenQuads(cell.CellUnits(b)); eliminateErr != nil {
return eliminateErr
}
}
}
}
return nil
}
// eliminateXYWings simply eliminates marks/candidates using XY Wings strategy for the board
func (b *Board) eliminateXYWings() error {
return EliminateXYWings(b.unsolvedCells(), b)
}
// eliminateXYZWings simply eliminates marks/candidates using XYZ Wings strategy for the board
func (b *Board) eliminateXYZWings() error {
return EliminateXYZWings(b.unsolvedCells(), b)
}
// eliminateXWings simply eliminates marks/candidates using X Wings strategy for the board
func (b *Board) eliminateXWings() error {
return EliminateXWings(b)
}
// eliminateSwordFish simply eliminates marks/candidates using Sword Fish strategy for the board
func (b *Board) eliminateSwordFish() error {
return EliminateSwordFish(b)
}
// backTrack simply tries to find out a unique solution where strategies no more producing solutions or eliminating candidates
func (b *Board) backTrack() bool {
clone := CloneData(b.data)
solved, solution := BackTrack(clone)
if solved {
b.backTrackUsed = true
for i := 0; i < BoardSize; i++ {
for j := 0; j < BoardSize; j++ {
b.data[i][j].Value = solution[i][j].Value
b.data[i][j].Marks.Clear()
}
}
return true
}
return false
}