1
GATE CSE 2016 Set 2
Numerical
+2
-0
The given diagram shows the flowchart for a recursive function $$A(n).$$ Assume that all statements, except for the recursive calls, have $$O(1)$$ time complexity. If the worst case time complexity of this function is $$O\left( {{n^\alpha }} \right),$$ then the least possible value (accurate up to two decimal positions) of $$\alpha $$ is ____________ . GATE CSE 2016 Set 2 Algorithms - Complexity Analysis and Asymptotic Notations Question 8 English
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2
GATE CSE 2016 Set 2
Numerical
+2
-0
Let $${A_1},{A_2},{A_3},$$ and $${A_4}$$ be four matrices of dimensions $$10 \times 5,\,\,5 \times 20,\,\,20 \times 10,$$ and $$10 \times 5,\,$$ respectively. The minimum number of scalar multiplications required to find the product $${A_1}{A_2}{A_3}{A_4}$$ using the basic matrix multiplication method is ______________.
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3
GATE CSE 2016 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Match the following:

GROUP - 1 GROUP - 2
(P) Lexical analysis (i) Leftmost derivation
(Q) Top down parsing (ii) Type checking
(R) Semantic analysis (iii) Regular expressions
(S) Runtime environments (iv) Activation records

A
$$P \leftrightarrow i,\,\,Q \leftrightarrow ii,\,\,R \leftrightarrow iv,\,\,S \leftrightarrow iii$$
B
$$P \leftrightarrow iii,\,\,Q \leftrightarrow i,\,\,R \leftrightarrow ii,\,\,S \leftrightarrow iv$$
C
$$P \leftrightarrow ii,\,\,Q \leftrightarrow iii,\,\,R \leftrightarrow i,\,\,S \leftrightarrow iv$$
D
$$P \leftrightarrow iv,\,\,Q \leftrightarrow i,\,\,R \leftrightarrow ii,\,\,S \leftrightarrow iii$$
4
GATE CSE 2016 Set 2
MCQ (Single Correct Answer)
+2
-0.6
Which one of the following grammars is free from $$left$$ $$recursion$$?
A
$$\eqalign{ & S\,\, \to \,\,AB \cr & A\,\, \to \,\,Aa\,\,|\,\,b \cr & B \to c \cr} $$
B
$$\eqalign{ & S\,\, \to \,\,AB\,\,|\,\,Bb\,\,|\,\,c \cr & A\,\, \to \,\,Bd\,\,|\,\,\varepsilon \cr & B \to e \cr} $$
C
$$\eqalign{ & S\,\, \to \,\,Aa\,\,|\,\,B\,\,|\,\, \cr & A\,\, \to \,\,Bd\,\,|\,\,Sc\,\,|\,\,\varepsilon \cr & B \to d \cr} $$
D
$$\eqalign{ & S\,\, \to \,\,Aa\,\,|\,\,Bb\,\,|\,\,c \cr & A\,\, \to \,\,Bd\,\,|\,\,\varepsilon \cr & B \to Ae\,\,|\,\,\varepsilon \cr} $$
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