GATE | GATE-CS-2007 | Question 79

For the correct answer strings to above question, how many derivation trees are there?
(A) 1
(B) 2
(C) 3
(D) 4


Answer: (B)

Explanation: When it asks about the no of derivations tree, we should consider either left most derivation(LMD) or right most derivations(RMD), but not both.

Here two left most derivations are possible for the correct string of the previous question “aabbab” from the given grammar.

LMD-1

S -> aB [Using S –> aB]
-> aaBB [Using B –> aBB]
-> aabB [Using B –> b]
-> aabbS [Using B –> bS]
-> aabbaB [Using S –> aB]
-> aabbab [Using B –> b]

LMD-2



S -> aB [Using S –> aB]
-> aaBB [Using B –> aBB]
-> aabSB [Using B –> bS]
-> aabbAB [Using S –> bA]
-> aabbaB [Using A –> a]
-> aabbab [Using B –> b]

The Derivation tress are shown below :

derivationTree

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