Calculate the edit distance

EditDistance.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Diagnostics;
using SimpleTest;

namespace EditDistance
{
    class Program
    {
        static void Main(string[] args)
        {
            Test.Assert(new EditDistance("A", "B").solve(), 1);
            Test.Assert(new EditDistance("abc", "abb").solve(), 1);
            Test.Assert(new EditDistance("abcd", "bcde").solve(), 2);
            Test.Assert(new EditDistance("a", "a").solve(), 0);
            Test.Assert(new EditDistance("", "").solve(), 0);
        }
    }

    class EditDistance
    {
        public int m, n;
        public string A, B;
        private int[,] table, trace;

        public EditDistance(string A, string B)
        {
            this.A = A;
            this.n = A.Length;
            this.B = B;
            this.m = B.Length;

            this.table = new int[n + 1, m + 1];
            this.trace = new int[n + 1, m + 1];

            for (int i = 0; i < n + 1; i++)
            {
                for (int j = 0; j < m + 1; j++)
                {
                    table[i, j] = -1;
                    trace[i, j] = -1;
                }
            }

            for (int i = 0; i < n+1; i++)
            {
                table[i, 0] = i;
                trace[i, 0] = 1;
            }

            for (int j = 0; j < m+1; j++)
            {
                table[0, j] = j;
                trace[0, j] = 0;
            }

            trace[0, 0] = -1;
        }

        private int D(int i, int j)
        {
            if (i == 0) return j;
            if (j == 0) return i;
            Debug.Assert(i != 0 && j != 0);
            if (table[i, j] != -1) return table[i, j];
            if (A[i - 1] == B[j - 1])
            {
                trace[i, j] = 2;
                table[i, j] = D(i - 1, j - 1);
            }
            else
            {
                var minPair = new int[] { D(i, j - 1), D(i - 1, j), D(i - 1, j - 1) }.Zip(
                    Enumerable.Range(0, 3), (distance, index) => Tuple.Create(index, distance)).Aggregate(
                    (a1, a2) => a1.Item2 < a2.Item2 ? a1 : a2);
                table[i, j] = minPair.Item2 + 1;
                trace[i, j] = minPair.Item1;
            }
            return table[i, j];
        }

        public int solve()
        {
            int minDist = D(n, m);
            // TODO: trace the solution
            return minDist;
        }
    }
}