What is the worst-case time complexity of DFS for a graph represented as an adja

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Question: What is the worst-case time complexity of DFS for a graph represented as an adjacency matrix?

Options:

Correct Answer: O(V^2)

Solution:

In the worst case, DFS will check all entries in the adjacency matrix, leading to a time complexity of O(V^2).

What is the worst-case time complexity of DFS for a graph represented as an adjacency matrix?

What is the worst-case time complexity of DFS for a graph represented as an adjacency matrix?

Step 1: Understand what DFS (Depth-First Search) is. It is an algorithm used to explore nodes and edges of a graph.
Step 2: Know that a graph can be represented in different ways, one of which is an adjacency matrix.
Step 3: An adjacency matrix is a 2D array where the rows and columns represent the vertices of the graph.
Step 4: Each entry in the matrix indicates whether there is an edge between two vertices. If there is an edge, the entry is 1; if not, it is 0.
Step 5: In the worst-case scenario, DFS will need to check every entry in the adjacency matrix to explore all vertices.
Step 6: Since there are V vertices in the graph, the adjacency matrix will have V rows and V columns, resulting in V * V = V^2 entries.
Step 7: Therefore, the worst-case time complexity of DFS for a graph represented as an adjacency matrix is O(V^2).

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