GATE CS 2014 Set 3 — Question 23
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Programming & Data Structures → Graphs (Data Structure) → DFS Traversal
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Question
Suppose depth first search is executed on the graph below starting at some unknown vertex. Assume that a recursive call to visit a vertex is made only after first checking that the vertex has not been visited earlier. Then the maximum possible recursion depth (including the initial call) is _________.
Correct answer
19 to 19
Solution
The maximum recursion depth in a Depth First Search (DFS) is equal to the number of vertices in the graph if the graph is connected and contains a Hamiltonian path.
1.Counting the vertices:
- The left grid is a grid, which has vertices.
- There is a bridge consisting of vertex connecting the two main components.
- The right component consists of a grid with the center vertex missing ( vertices) and one additional vertex connected to the right side.
- Total vertices vertices.
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