Question

Given a non-empty string s and a dictionary containing a list of unique words, design a dynamic programming algorithm to determine if s can be segmented into a space-separated sequence of one or more dictionary words. if s="algorithmdesign" and your dictionary contains "algorithm" and "design". your algorithm should answer yes as s can be segmented as "algorithmdesign

Answer 1

Let s(i),k denote the substring s(i)s(i+1)...s k. Let Opt(k) denote whether the sub-string s1,k can be segmented using the words in the dictionary, namely (k) =1 if the segmentation is possible and 0 otherwise. A segmentation of this sub-string s1,k is possible if only the last word (say si  k) is in the dictionary theremaining substring s1,i can be segmented. 
Therefore, we have equation:Opt(k) =                    max                       Opt(i)          0<i<k and s(i+1),kis a word in the dictionary
We can begin solving the above recurrence with the initial condition that Opt(0) =1 and then go on to comput eOpt(k) for k= 1, 2. The answer correspond-ing to Opt(n) is the solution and can be computed in Θ(n2) time.