1.
This question requires you to demonstrate your understanding of graph modeling and traversal within the context of a social network.
- Model a Social Network as a Graph: Describe how a social network, where users can be 'friends' with each other, would be represented as a graph. Clearly define what constitutes a node (vertex) and an edge, and explain whether the graph should be directed or undirected for this scenario.
- Choose a Graph Representation: Discuss suitable data structures for representing the modeled social network graph (e.g., adjacency list, adjacency matrix). Justify the choice based on typical social network characteristics (e.g., sparsity, operations).
- Apply Depth-First Search (DFS): Detail the step-by-step process of using the Depth-First Search (DFS) algorithm to determine if a path of friendships exists between two specified users (a 'source' user and a 'target' user) in the graph. Include how to handle visited nodes to prevent infinite loops and redundant work.
- Auxiliary Data Structures: Specify any additional data structures (e.g., stack, set) that would be required for the efficient implementation of the DFS algorithm for this problem.
- Time and Space Complexity: Analyze the time and space complexity of the proposed DFS solution in terms of the number of users (V) and friendships (E) in the network.