Word break problem with dynamic programming

This is the original question.

I have implemented it in both ways. If I enter the word "icecream", should I output "ice" "cream" and also "icecream", or just "ice" and "cream"?

Is this a good example of dynamic programming?

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApplication2
{


    public class DynamicProgramming
    {
        public DynamicProgramming()
        {            
            List<string> dictionary = new List<string>{"mobile","samsung","sam","sung","man","mango",
                           "icecream","and","go","i","like","ice","cream"};
            var result = ContainsWordRecursive("ilike",dictionary);
            var result2 = ContainsWordDP("icecream", dictionary);
        }

        private List<string> ContainsWordRecursive(string word, List<string> dictionary)
        {
            List<string> res = new List<string>();
            for (int i = 0; i <= word.Length; i++)
            {
                if(dictionary.Contains(word.Substring(0,i)))
                {
                    res.Add(word.Substring(0,i));
                    var list = ContainsWordRecursive(word.Substring(i, word.Length - i ),dictionary);
                    if(list.Count > 0)
                    {
                        res.AddRange(list);
                    }
                }
            }
            return res;
        }

        private List<string> ContainsWordDP(string word, List<string> dictionary)
        {
            List<string> list = new List<string>();
            bool[] wb= new bool[word.Length+1];
            for (int i = 0; i <= word.Length; i++)
            {
                list.Clear();
                if (wb[i] == false && dictionary.Contains(word.Substring(0, i)))
                {
                    wb[i] = true;
                    list.Add(word.Substring(0, i));
                }

                if (wb[i] == true)
                {
                    if (i == word.Length)
                    {
                        return list;
                    }
                    for (int j = i + 1; j <= word.Length; j++)
                    {
                        if (wb[j] == false && dictionary.Contains(word.Substring(i, j - i)))
                        {
                            wb[j] = true;
                            list.Add(word.Substring(i, j - i));
                        }
                        // If we reached the last character
                        if (j == word.Length && wb[j] == true)
                        {
                            return list ;
                        }
                    }
                }
            }
            return list;
        }
    }
}