GATE CS 2014 Set 1 — Question 23
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Algorithms → Graph Algorithms → Topological Sort
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Question
Consider the directed graph given below.
Which one of the following is TRUE?
Correct answer
(C) Both PSRQ and SPRQ are topological orderings.
Solution
A topological ordering lists the vertices so that for every directed edge , appears before .From the figure, the edges are:
P → Q, P → R, R → Q, S → R, S → Q.The graph has no directed cycle ( and have no incoming edges and has no outgoing edges), so it is a DAG and topological orderings exist. In-degrees: , , , . So and must come first (in either order), then (it needs both and ), then (it needs , , ).The topological orderings are exactly PSRQ and SPRQ.- (A) False: the graph is acyclic, so orderings exist.
- (B) False: in PQRS, comes before but
R → Q; SRQP puts after and . - (C) True: both PSRQ and SPRQ satisfy every edge.
- (D) False: SPRQ is also a valid ordering.
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