Exploring Graphs and Their Traversals

What are the common techniques for graph representation?

• Adjacency list, adjacency matrix, edge list, incidence matrix

• Sorting methods

• Graph traversal techniques

• Data structure algorithms

Explain the adjacency list representation of a graph.

• An adjacency list is a single list of all vertices in the graph.

• An adjacency list is a matrix representation of a graph.

• An adjacency list is a collection of lists or arrays where each list corresponds to a vertex and contains its adjacent vertices.

• An adjacency list contains only the edges of the graph.

What is the time complexity of using an adjacency matrix for graph representation?

• O(V^2) for space complexity; O(1) for edge checks, O(V) for listing neighbors.

• O(V) for space complexity; O(V) for edge checks, O(1) for listing neighbors.

• O(E) for space complexity; O(V) for edge checks, O(E) for listing neighbors.

• O(V^3) for space complexity; O(1) for edge checks, O(1) for listing neighbors.

Describe the Depth-First Search (DFS) algorithm.

• Depth-First Search (DFS) is an algorithm for traversing or searching tree or graph data structures by exploring as far as possible along each branch before backtracking.

• DFS guarantees the shortest path in a graph traversal.

• DFS uses a queue to keep track of nodes to visit next.

• DFS explores all nodes at the present depth before moving on to the next level.

How does the stack data structure play a role in DFS?

• The stack stores nodes to be explored and facilitates backtracking in DFS.

• The stack is primarily used for memory management in DFS.

• The stack is used to store the final results of DFS.

• The stack helps in sorting the nodes in ascending order.

What is the time complexity of the DFS algorithm?

• O(V)

• O(E)

• O(V * E)

• O(V + E)

Explain the Breadth-First Search (BFS) algorithm.

• Breadth-First Search (BFS) algorithm explores nodes level by level using a queue.

• BFS explores nodes randomly without a specific order.

• BFS uses a stack to explore nodes.

• BFS is primarily used for sorting data.

What data structure is used in BFS for traversal?

• Stack

• Linked List

• Array

• Queue

What is the time complexity of the BFS algorithm?

• O(E)

• O(V + E)

• O(V)

• O(V * E)

How can you detect a cycle in a directed graph?

• Count the number of edges and vertices to find cycles

• Check for isolated nodes in the graph

• Use Depth-First Search (DFS) with a recursion stack or Kahn's algorithm.

• Use Breadth-First Search (BFS) to traverse all nodes