// solveByGuessing selects the position with minimum possibilities out of the remaining empty positions.
// For each of the possible values, the grid is solved. For each conflict, the state is backtracked.
// If no conflict is there, then recursively solveByGuessing on the remaining empty positions.
// Prints the solution, if found. Also increments the number of solutions.
func solveByGuessing(grid *datatypes.Grid, positions map[datatypes.Position]bool, iteration int) {
// if all positions have been filled, then return
if len(positions) == 0 {
numSolutions++
grid.Print()
return
}
// copy remaining positions to next iteration, and start guessing for the position with minimum possibilities.
pos := copyValuesForNextIteration(grid, positions, iteration)
existingValue := grid[pos.X][pos.Y].IterationValues[iteration]
for val := range existingValue.Possible {
// update the cell with val for next iteration
nextValue := grid[pos.X][pos.Y].IterationValues[iteration+1]
*grid[pos.X][pos.Y].Val = val
*nextValue.Val = val
for key := range nextValue.Possible {
if key != val {
delete(nextValue.Possible, key)
}
}
// start solving using the set value.
if !eliminateUsingGivenValues(grid, iteration+1, pos.X, pos.Y, val) {
// if no conflict, then call solveByGuessing for remaining positions.
updatedPositions := remainingPositions(grid, positions)
solveByGuessing(grid, updatedPositions, iteration+1)
}
// backtrack to previous state
copyValuesForNextIteration(grid, positions, iteration)
}
return
}
// setInput creates the initial grid for testing.
func setInput(grid *datatypes.Grid) int {
setValue(grid, 0, 4, 4)
setValue(grid, 0, 5, 5)
setValue(grid, 1, 0, 8)
setValue(grid, 1, 6, 2)
setValue(grid, 1, 8, 7)
setValue(grid, 2, 2, 2)
setValue(grid, 2, 8, 4)
setValue(grid, 3, 2, 6)
setValue(grid, 3, 6, 3)
setValue(grid, 3, 8, 2)
setValue(grid, 4, 3, 1)
setValue(grid, 5, 0, 2)
setValue(grid, 5, 2, 7)
setValue(grid, 5, 3, 4)
setValue(grid, 5, 6, 6)
setValue(grid, 6, 0, 6)
setValue(grid, 6, 1, 4)
setValue(grid, 6, 4, 9)
setValue(grid, 6, 5, 8)
setValue(grid, 7, 0, 7)
setValue(grid, 7, 1, 9)
setValue(grid, 7, 5, 4)
setValue(grid, 8, 7, 3)
grid.Print()
return 23
}