MountainWalk.cs

    using System;
    using System.Globalization;
    using System.Text;

    public class MountainWalk 
    {
        private string[] _areaMap;

        private int _height;

        public string[] AreaMap
        {
            get
            {
                return this._areaMap;
            }

            set
            {
                this._areaMap = value;
            }
        }

        public int Height
        {
            get
            {
                return this._height;
            }
            set
            {
                this._height = value;
            }
        }

        public class Position
        {
            private int _i;

            private int _j;

            public int I
            {
                get
                {
                    return this._i;
                }
                set
                {
                    this._i = value;
                }
            }

            public int J
            {
                get
                {
                    return this._j;
                }
                set
                {
                    this._j = value;
                }
            }

            public Position(int i, int j)
            {
                I = i;
                J = j;
            }
        }

        public int cellsVisited(string[] areaMap, int heightDifference)
        {
            Position position = new Position(0, 0);
            int result = 0;

            AreaMap = areaMap;
            Height = heightDifference;

            do
            {
                result++;
                char oldValue = AreaMap[position.I][position.J];
                MarkVisited(position);
                position = this.MoveNext(oldValue, position);

                if (position == null)
                {
                    break;
                }
            }
            while (true);

            return result;
        }

        public Position MoveNext(char oldValue, Position position)
        {
            Position newPosition = new Position(position.I + 1, position.J);
            if (CanMove(oldValue, newPosition))
            {
                return newPosition;
            }

            newPosition = new Position(position.I, position.J - 1);
            if (CanMove(oldValue, newPosition))
            {
                return newPosition;
            }

            newPosition = new Position(position.I - 1, position.J);
            if (CanMove(oldValue, newPosition))
            {
                return newPosition;
            }

            newPosition = new Position(position.I, position.J + 1);
            if (CanMove(oldValue, newPosition))
            {
                return newPosition;
            }

            return null;
        }

        public bool CanMove(char oldValue, Position position)
        {
            return position.I >= 0 && position.J >= 0 && AreaMap.Length > position.I
                   && AreaMap[position.I].Length > position.J && AreaMap[position.I][position.J] != 'x'
                   && Math.Abs(
                       int.Parse(oldValue.ToString(CultureInfo.InvariantCulture))
                       - int.Parse(AreaMap[position.I][position.J].ToString(CultureInfo.InvariantCulture))) <= Height;

        }

        public void MarkVisited(Position position)
        {
            StringBuilder sb = new StringBuilder(AreaMap[position.I]);
            sb[position.J] = 'x';
            AreaMap[position.I] = sb.ToString();
        }
    }