ISRO | ISRO CS 2014 | Question 5

What is the number of steps required to derive the string ((() ()) ())

S → SS
S → (S)
S → ε

(A) 10
(B) 15
(C) 12
(D) 16

Answer: (A)
Explanation: To generate ((() ()) ()) , following steps are needed:

1) S → (S)
2) S → (SS)
3) S → ((S)S)
4) S → ((SS)S)
5) S → (((S)S))S)
6) S → (((S)(S))S)
7) S → (((S)(S))(S))  [S → ε]  
8) S → ((()(S))S)     [S → ε]
9) S → ((()())S)      [S → ε]  
10) S → ((()()))

Option (A) is correct.
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