GATE CS 2016 Set 1 — Question 21
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Algorithms → Graph Algorithms → Topological Sort
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Question
Consider the following directed graph:
The number of different topological orderings of the vertices of the graph is _______.
Correct answer
6 to 6
Solution
The graph is a Directed Acyclic Graph (DAG). The edges are:
, ,
, , In any topological sort:
Due to the edges, must precede , and must precede .
We need to find the number of ways to interleave the sequence and .The number of ways to merge two sequences of lengths and while preserving relative order is given by .
Here, and . So, .The valid orderings are:
, ,
, , In any topological sort:
- Vertex must appear first (in-degree 0).
- Vertex must appear last (out-degree 0, depends on and ).
Due to the edges, must precede , and must precede .
We need to find the number of ways to interleave the sequence and .The number of ways to merge two sequences of lengths and while preserving relative order is given by .
Here, and . So, .The valid orderings are:
1.
2.
3.
4.
5.
6.
Total topological orderings = 6.Continue learning with Success Tracker
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