The decision of the naked three in Sudoku

Question

I would like to pay more attention to math classes in Uni. :)

How to implement this mathematical formula for bare triples?

Naked triples
Take three cells C = {c1, c2, c3} that separate the unit U. Take three numbers N = {n1, n2, n3}. If each cell in C has its own candidates ci ⊆ N, then we can remove all ni ∈ N from other cells in U. **

I have a method that takes a parameter (e.g. a field, row or column) as a parameter. The block contains 9 cells, so I need to compare all combinations of 3 cells at a time, which out of the box, perhaps put them on a stack or collection for further calculations.

The next step is to take these 3-cell combinations one by one and compare their candidates against 3 numbers. Again, these 3 numbers can be any possible combination from 1 to 9. That's all I need.

But how would I do that? How many combinations will I get? I get 3 x 9 = 27 combinations for cells, and then the same for numbers (N)?

How would you solve this in classic C # loops? There is no Lambda expression, please, I'm already quite confused :)

Code: I had to shorten classes to introduce them here.

public class Cell : INotifyPropertyChanged
    {

public ObservableCollection<ObservableCollection<Candidate>> CandidateActual {...}

public int Id { ... }

//Position of the Cell inside a box if applicable
public int CellBoxPositionX { get; private set; }  
public int CellBoxPositionY { get; private set; }

//Position of the Cell inside the game board
public int CellBoardPositionX { get; private set; }
public int CellBoardPositionY { get; private set; }

//Position of the Box inside the game board
public int BoxPositionX { get; private set; }
public int BoxPositionY { get; private set; }

public int CountCandidates { ... }    
public int? Value { ...}

public Candidate this[int number]
        {
            get
            {
                if (number < 1 || number > PossibleValues.Count)
                {
                    throw new ArgumentOutOfRangeException("number", number, "Invalid Number Index");
                }

                switch (number)
                {
                    case 1:
                        return CandidateActual[0][0];
                    case 2:
                        return CandidateActual[0][1];
                    case 3:
                        return CandidateActual[0][2];
                    case 4:
                        return CandidateActual[1][0];
                    case 5:
                        return CandidateActual[1][1];
                    case 6:
                        return CandidateActual[1][2];
                    case 7:
                        return CandidateActual[2][0];
                    case 8:
                        return CandidateActual[2][1];
                    case 9:
                        return CandidateActual[2][2];
                    default:
                        return null;
                }
            }
        }
}

candidate

public class Candidate : INotifyPropertyChanged
    {

        private int? _value;

        public int? Value { ... }

    }

Box:

public class Box : INotifyPropertyChanged
    {

public ObservableCollection<ObservableCollection<Cell>> BoxActual { ... }

public Cell this[int row, int column]
        {
            get
            {
                if(row < 0 || row >= BoxActual.Count)
                {
                    throw new ArgumentOutOfRangeException("row", row, "Invalid Row Index");
                }
                if(column < 0 || column >= BoxActual.Count)
                {
                    throw new ArgumentOutOfRangeException("column", column, "Invalid Column Index");
                }
                return BoxActual[row][column];
            }
        }
}

Tip

public class Board : INotifyPropertyChanged 
    {

 public ObservableCollection<ObservableCollection<Box>> GameBoard {...}

public Cell this[int boardRowPosition, int boardColumnPosition]
        {
            get
            {
                int totalSize = GameBoard.Count*GameBoard.Count();
                if (boardRowPosition < 0 || boardRowPosition >= totalSize) 
                    throw new ArgumentOutOfRangeException("boardRowPosition", boardRowPosition, "Invalid boardRowPosition index");
                if (boardColumnPosition < 0 || boardColumnPosition >= totalSize)
                    throw new ArgumentOutOfRangeException("boardColumnPosition", boardColumnPosition, "Invalid boardColumnPosition index");
                return
                    GameBoard[boardRowPosition/GameBoard.Count][boardColumnPosition/GameBoard.Count][
                        boardRowPosition%GameBoard.Count, boardColumnPosition%GameBoard.Count];
            }
        }



        public Box this[int boardRowPosition, int boardColumnPosition, bool b]
        {
            get
            {
                int totalSize = GameBoard.Count * GameBoard.Count();
                if (boardRowPosition < 0 || boardRowPosition >= totalSize)
                    throw new ArgumentOutOfRangeException("boardRowPosition", boardRowPosition, "Invalid boardRowPosition index");
                if (boardColumnPosition < 0 || boardColumnPosition >= totalSize)
                    throw new ArgumentOutOfRangeException("boardColumnPosition", boardColumnPosition, "Invalid boardColumnPosition index");
                return
                    GameBoard[boardRowPosition / GameBoard.Count][boardColumnPosition / GameBoard.Count];
            }
        }
}

Thanks so much for any help,

Answer 1

Psuedo-Code Algorithm; my C is a little rusty.

. 6 504 , , ( n!/(3! * (N-3)!)).

, , , . , .

combos = (array containing 3-long combination of candidates)
for each combo in combos                 # iterate through every combo
  matches = new array                    # initialize a blank array
  for each cell in unit
    if (cell does not contain candidates other than the ones in your current combo)
      matches.add(cell)                  # this is a match!
    end
  end

  if matches.size >= 3                   # naked triple found! (three matches for given combo)
    for each cell in unit
      if (cell is not in matches)
        (delete every candidate in current combo in this cell)
      end
    end
  end
  delete matches                         # clear up memory
end

, ! C-ify, ; , .

, , , Sudoku , . , .

---

, ; . google: ... C .

, , . n = 3 , . n = 1 n = 2, .