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, dict(w) = true if w is a valid word false otherwise . (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.

provided in the explanation section

Explanation:

Given that:

Assume D(k) =║ true it is [1 : : : k] is valid sequence  words or false otherwise

now the sub problem s[1 : : : k] is a valid sequence of words IFF s[1 : : : 1] is a valid sequence of words and s[ 1 + 1 : : : k] is valid word.

So, from here we have that D(k) is given by the following recorance relation:

D(k) = ║ false maximum (d[l]∧DICT(s[1 + 1 : : : k]) otherwise

Algorithm:

Valid sentence (s,k)

D [1 : : : k]             ∦ array of boolean variable.

for a ← 1 to m

do ;

d(0) ← false

for b ← 0 to a - j

for b ← 0 to a - j

do;

if D[b] ∧ DICT s([b + 1 : : : a])

d (a) ← True

(b). Algorithm Output

      if D[k] = = True

stack = temp stack           ∦stack is used to print the strings in order

c = k

while C > 0

stack push (s [w(c)] : : : C] // w(p) is the position in s[1 : : : k] of the valid world at // position c

P = W (p) - 1

output stack

= 0 =

cheers i hope this helps !!!