21.1.4. Complexity of Depth First Search

Try these first

1. 1.

   What does DFS stand for?

   Hint

   Think about how the algorithm explores.

2. 2.

   Which data structure can be used to implement DFS?

   Hint

   Consider the order of operations in DFS.

3. 3.

   What is the time complexity of DFS when represented with an adjacency list?

   • O(n²)
   • O(m + n)
   • O(n)

   Hint

   Think about the relationships between edges and vertices.

4. 4.

   True or False: Depth First Search guarantees the shortest path in a graph.

   • True
   • False

   Hint

   Consider how DFS operates compared to BFS.

5. 5.

   Given a graph represented using an adjacency list, analyze its structure using DFS to determine if it contains cycles. Provide the step-wise execution.

   Hint

   Cycling might reveal itself by re-entering a previously visited node.

6. 6.

   Develop a DFS function that computes the connected components of a graph. Explain how you will classify connected nodes during your traversal.

   Hint

   Think about how you can maintain a list while traversing.