Minimum Edit Distance Reconstruction

Question

I know there are similar answer to this on stack, as well as online, but I feel I\'m missing something. Given the code below, we need to reconstruct the sequence of events t

Answer 1

I don't know python, but the following C# code works if that's any help.

public class EditDistanceCalculator
{
    public double SubstitutionCost { get; private set; }
    public double DeletionCost { get; private set; }
    public double InsertionCost { get; private set; }

    public EditDistanceCalculator() : this(1,1, 1)
    {
    }

    public EditDistanceCalculator(double substitutionCost, double insertionCost, double deletionCost)
    {
        InsertionCost = insertionCost;
        DeletionCost = deletionCost;
        SubstitutionCost = substitutionCost;
    }

    public Move[] CalcEditDistance(string s, string t)
    {
        if (s == null) throw new ArgumentNullException("s");
        if (t == null) throw new ArgumentNullException("t");

        var distances = new Cell[s.Length + 1, t.Length + 1];
        for (int i = 0; i <= s.Length; i++)
            distances[i, 0] = new Cell(i, Move.Delete);
        for (int j = 0; j <= t.Length; j++)
            distances[0, j] = new Cell(j, Move.Insert);

        for (int i = 1; i <= s.Length; i++)
            for (int j = 1; j <= t.Length; j++)
                distances[i, j] = CalcEditDistance(distances, s, t, i, j);

        return GetEdit(distances, s.Length, t.Length);
    }

    private Cell CalcEditDistance(Cell[,] distances, string s, string t, int i, int j)
    {
        var cell = s[i - 1] == t[j - 1]
                            ? new Cell(distances[i - 1, j - 1].Cost, Move.Match)
                            : new Cell(SubstitutionCost + distances[i - 1, j - 1].Cost, Move.Substitute);
        double deletionCost = DeletionCost + distances[i - 1, j].Cost;
        if (deletionCost < cell.Cost)
            cell = new Cell(deletionCost, Move.Delete);

        double insertionCost = InsertionCost + distances[i, j - 1].Cost;
        if (insertionCost < cell.Cost)
            cell = new Cell(insertionCost, Move.Insert);

        return cell;
    }

    private static Move[] GetEdit(Cell[,] distances, int i, int j)
    {
        var moves = new Stack();
        while (i > 0 && j > 0)
        {
            var move = distances[i, j].Move;
            moves.Push(move);
            switch (move)
            {
                case Move.Match:
                case Move.Substitute:
                    i--;
                    j--;
                    break;
                case Move.Insert:
                    j--;
                    break;
                case Move.Delete:
                    i--;
                    break;
                default:
                    throw new ArgumentOutOfRangeException();
            }
        }
        for (int k = 0; k < i; k++)
            moves.Push(Move.Delete);
        for (int k = 0; k < j; k++)
            moves.Push(Move.Insert);

        return moves.ToArray();
    }

    class Cell
    {
        public double Cost { get; private set; }
        public Move Move { get; private set; }

        public Cell(double cost, Move move)
        {
            Cost = cost;
            Move = move;
        }
    }
}

public enum Move
{
    Match,
    Substitute,
    Insert,
    Delete
}

Some tests:

    [TestMethod]
    public void TestEditDistance()
    {
        var expected = new[]
            {
                Move.Delete, 
                Move.Substitute, 
                Move.Match, 
                Move.Match, 
                Move.Match, 
                Move.Match, 
                Move.Match, 
                Move.Insert,
                Move.Substitute, 
                Move.Match, 
                Move.Substitute, 
                Move.Match, 
                Move.Match, 
                Move.Match, 
                Move.Match
            };
        Assert.IsTrue(expected.SequenceEqual(new EditDistanceCalculator().CalcEditDistance("thou-shalt-not", "you-should-not")));

        var calc = new EditDistanceCalculator(3, 1, 1);
        var edit = calc.CalcEditDistance("democrat", "republican");
        Console.WriteLine(string.Join(",", edit));
        Assert.AreEqual(3, edit.Count(m => m == Move.Match)); //eca
    }