Consider the following algorithm someAlgo that takes an undirected graph G as input.
someAlgo (G)
1. Let $v$ be any vertex in G. Run BFS on G starting at $v$. Let $u$ be a vertex in G at maximum distance from $v$ as given by the BFS.
2. Run BFS on G again with $u$ as the starting vertex. Let $z$ be the vertex at maximum distance from $u$ as given by the BFS.
3. Output the distance between $u$ and $z$ in G.
The output of someAlgo (T) for the tree shown in the given figure is ____________ (Answer in integer)
=To solve the problem using the someAlgo algorithm on the provided tree, follow these steps:
- Select any vertex as the starting point for BFS. Let's choose the left-most vertex.
- Run BFS from this vertex and find the vertex
uthat is the farthest away. After inspecting, we findu, which is the right-most vertex. - Next, run BFS starting from
u, and determinez, the farthest vertex fromu. The farthest vertex fromuis the left-most vertex. - The algorithm outputs the distance between
uandz.
By examining the tree:
- The distance between the left-most and right-most vertices is
6edges.
This result aligns perfectly with the given range [6, 6], confirming our computation is correct.
Therefore, the output of someAlgo(T) is 6.
Important Questions from Graph Search
Which traversal algorithm is typically implemented using a stack data structure?
- The depth first search will use ________ as a structure to held nodes for further processing.
Which of the following statements about DFS are correct?
A. It can detect cycles in a graph
B. It can be used to find connected components.
C. It works for both directed and undirected graph.
D. Guarantees shortest path in unweighted graphs.
Choose the correct answer from the options given below:
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: Depth first search can be used to perform a topological sort of a directed acyclic graph.
Reason R: A topological sort a directed acyclic graph G =(V, E) is a linear ordering of its vertices such that if G contain an edge (u, v) then u appears before v in the ordering.
In the light of the above statements, choose the most appropriate answer from the options given below
