You are given a string of n characters s[1... n], which you believe to be a corrupted text...

You are given a string of n characters s[1... n], which you believe to be a corrupted text document in which all punctuation has vanished (so that it looks something like “itwasthebestoftimes...”). You wish to reconstruct the document using a dictionary, which is available in the form of a Boolean function dict(.): for any string w,

(a) Give a dynamic programming algorithm that determines whether the string s[.] can be reconstituted as a sequence of valid words. The running time should be at most O(n2), assuming calls to dict take unit time.

(b) In the event that the string is valid, make your algorithm output the corresponding sequence of words.