GATE CS 2014 Set 1 — Question 21
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Programming & Data Structures → Graphs (Data Structure) → Adjacency Matrix & List
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Question
Let be a graph with vertices and edges. What is the tightest upper bound on the running time of Depth First Search on , when is represented as an adjacency matrix?
Correct answer
(C) Θ(n²)
Solution
In a Depth First Search (DFS), every vertex is visited. When a vertex is visited, we must iterate through all possible neighbors to find adjacent vertices. In an adjacency matrix representation, finding the neighbors of a vertex requires scanning the entire row corresponding to that vertex, which takes time. Since there are vertices, the total time complexity is . Note that for an adjacency list, the complexity would be .
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