Given a string (say alpha) and a dictionary database from where I can find if a word is present in the dictionary by a O(1) time look up. Find if there exists a path from the root word(aplha) to leaf node having a single letter such that a child is formed by removing one letter at a time such that each word intermediately formed is also in the dictionery. Eg. If there is a path aplha->plha->pha->pa->a. And all the nodes are in dictionery. Dynamic programming solution exists