Q53 Consider the following grammar gate computer science 2017
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Q.53) Consider the following grammar: -gate computer science 2017

stmt  -> if expr then else expr; stmt | ε
expr -> term relop term | term
term -> id | number
id ->  a | b | c
number -> [0-9]

where relop is a relational operate (e.g < >, ….), ε refers to the empty statement, and if ,then, else are terminals. Consider a program P following the above grammar containing ten if terminals. The number of control flows paths in P is ____________. For example, the program
 if e1 then e2 else e3 
has 2 control flow paths, e1 -> e2 and e1 -> e3

A) 20
B) 1024
C) 2048
D) 10


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B) 1024

Number of control flow paths for 10 if terminals
if then else ; stmt
if then else ; if then else ; stmt
10 times. Observe that there is a semi-colon after every if structure. Since, every if structure has 2 control flows. Therefore, 1st terminal has 2 control flows, 2nd terminal has 2 control flows, 3rd terminal has 2 control flows, ........... 9th terminal has 2 control flows, and 10th terminal has 2 control flows. Using multiplication law of counting, we get = 2*2*2*2*2......10 times = 2^10 = 1024 number of control flow paths for 10 if terminals. 1024 is correct answer.

This explanation is contributed by Deepak Raj


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