// Reference implementation of a Sudoku solver
// https://en.wikipedia.org/wiki/Sudoku_solving_algorithms#Backtracking
func (s *Solver) backtrack(b *puzzle.Board) (*puzzle.Board, bool) {
if b.Solved() {
return b, true
}
for row := 0; row < 9; row++ {
for col := 0; col < 9; col++ {
if b.ValueAt(row, col) == 0 {
for i := 1; i < 10; i++ {
if b.Allowed(row, col, i) {
if bb, s := s.backtrack(b.SetAndCopy(row, col, i)); s {
return bb, s
}
}
}
// None of the numbers [1,9] can be inserted in this empty cell
// so the board is unsolvable
return b, false
}
}
}
return b, false
}
// exactCover takes the basic cover and updates it with extra
// contraints for the numbers we have been given through the board
func exactCover(board *puzzle.Board) [][]int {
base := baseCover()
for i := 0; i < size; i++ {
for j := 0; j < size; j++ {
n := board.ValueAt(i, j)
if n != 0 {
for v := 0; v < size; v++ {
if v != n-1 {
arr := base[index(i, j, v)]
for k := range arr {
arr[k] = 0
}
}
}
}
}
}
return base
}