1
GATE CSE 2016 Set 2
MCQ (Single Correct Answer)
+2
-0.6
In an adjacency list representation of an undirected simple graph $$G = (V,E),$$ each edge $$(u, v)$$ has two adjacency list entries: $$[v]$$ in the adjacency list of $$u,$$ and $$[u]$$ in the adjacency list of $$v.$$ These are called twins of each other. A twin pointer is a pointer from an adjacency list entry to its twin. If $$|E| = m$$ and $$|V| = n,$$ and the memory size is not a constraint, what is the time complexity of the most efficient algorithm to set the twin pointer in each entry in each adjacency list?
A
$$\Theta \left( {{n^2}} \right)$$
B
$$\Theta \left( {n + m} \right)$$
C
$$\Theta \left( {{m^2}} \right)$$
D
$$\Theta \left( {{n^4}} \right)$$
2
GATE CSE 2016 Set 2
Numerical
+1
-0
Breadth First Search $$(BFS)$$ is started on a binary tree beginning from the root vertex. There is a vertex $$t$$ at a distance four from the root. If t is the $$n$$-th vertex in this $$BFS$$ traversal, then the maximum possible value of $$n$$ is ___________.
Your input ____
3
GATE CSE 2016 Set 2
MCQ (Single Correct Answer)
+1
-0.3
$$N$$ items are stored in a sorted doubly linked list. For a $$delete$$ operation, a pointer is provided to the record to be deleted. For a $$decrease$$-$$key$$ operation, a pointer is provided to the record on which the operation is to be performed.

An algorithm performs the following operations on the list in this order:
$$\Theta \left( N \right),\,\,delete,\,\,O\left( {\log N} \right)\,insert,\,$$ $$\,O\left( {\log N} \right)\,fund, and $$ $$\Theta \left( N \right)\,$$ $$decrease$$-$$key.$$ What is the time complexity of all these operations put together?

A
$$O\left( {{{\log }^2}N} \right)$$
B
$$O\left( N \right)$$
C
$$O\left( {{N^2}} \right)$$
D
$$\Theta \left( {{N^2}\log N} \right)$$
4
GATE CSE 2016 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Suppose a database schedule $$S$$ involves transactions $${T_1},\,...,\,{T_n}.$$ Construct the precedence graph of $$S$$ with vertices representing the transactions and edges representing the conflicts. If $$S$$ is serializable, which one of the following orderings of the vertices of the precedence graph is guaranteed to yield a serial schedule?
A
Topological order
B
Depth-first order
C
Breadth-first order
D
Ascending order of transaction indices
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