What is a time complexity for finding the longest substring that is common in string S1 and S2 (n1 and n2 are the string lengths of strings s1, s2 respectively)?

Category: QuestionsWhat is a time complexity for finding the longest substring that is common in string S1 and S2 (n1 and n2 are the string lengths of strings s1, s2 respectively)?
Editor">Editor Staff asked 4 weeks ago

What is a time complexity for finding the longest substring that is common in string S1 and S2 (n1 and n2 are the string lengths of strings s1, s2 respectively)?
 
(a) O (log n!)
 
(b) Ɵ (n!)
 
(c) O (n^2+ n1)
 
(d) Ɵ (n1 + n2)
 
Question is taken from Suffix tree in chapter Trie of Data Structures & Algorithms I
 
I had been asked this question at a job interview.

1 Answers
Editor">Editor Staff answered 4 weeks ago

The correct answer is (d) Ɵ (n1 + n2)
 
Easy explanation – Suffix Tree allows fast string operation. To check if a substring is present in a string of a length of n, the time complexity for such operation is found to be O (n). The time complexity for finding the longest substring that is common in string S1 and S2 is Ɵ (n1 + n2).