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Question 1
Transcribed Image Text:1. Given a strings and a dictionary (set of strings) D we want to split s into the substrings $1,
S2, ..., Sk such that s; E D for all 1 ≤ i ≤ k.
For example for s = catsanddog and D = {cat, cats, and, sand, dog} the two possible splits
are (cats, and, dog) and (cat, sand, dog).
(a) Design a backtracking algorithm that finds all the possible solutions to the problem that
is, all the possible ways to split s into substrings from D. Establish the correctness and
analyze the running times of your algorithm. Also comment on the optimality of your
algorithm.
(b) Modify the algorithm you developed in Question la so that it finds one split of s into
substrings from D as efficiently as possible. Establish the correctness and analyze the
running times of your algorithm.
(c) Design an algorithm that finds efficiently a minimal split that is, a split s₁, S2, .
.../
Sk of
s such that s; Є D for all 1 ≤ i ≤ k and k is minimal. Establish the correctness and
analyze the running times of your algorithm.
(d) Design a nondeterministic algorithm that returns TRUE iff s can be split into substrings
from D. Establish the correctness and analyze the running times of your algorithm.
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