GATE DA 2024 Set 1 — Question 51
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Programming, Data Structures & Algorithms → Graphs → Topological Sort
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Question
Consider the directed acyclic graph (DAG) below:
Which of the following is/are valid vertex orderings that can be obtained from a topological sort of the DAG?
Which of the following is/are valid vertex orderings that can be obtained from a topological sort of the DAG?
Correct answer
(B) P R Q V S U T; (D) P R Q S V T U
Solution
The dependencies in the DAG are:
(A) P Q R S T U V: appears before , but
(B) P R Q V S U T:
(D) P R Q S V T U:
P → QR → QQ → SQ → VS → UV → T
(A) P Q R S T U V: appears before , but
R → Q. Invalid.(B) P R Q V S U T:
- before (Valid)
- before (Valid)
- before (Valid)
- before (Valid)
- All constraints satisfied. Valid.
R → Q. Invalid.(D) P R Q S V T U:
- before (Valid)
- before (Valid)
- before (Valid)
- before (Valid)
- All constraints satisfied. Valid.
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