21. Depth First Search (DFS)
This chapter discusses the depth-first search (DFS) algorithm, a strategy for traversing or searching through graph data structures. It begins by explaining how DFS differs from breadth-first search (BFS) and demonstrates the algorithm through a step-by-step example. Additionally, it covers the complexity of DFS, the importance of pre-order and post-order numbering in analyzing graphs, and the structural properties that can be derived from DFS traversal.
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What we have learnt
- DFS explores vertices by going deep into the graph before backtracking, using a stack-like mechanism.
- The complexity of DFS can vary based on the representation of the graph, with linear time performance achievable using an adjacency list.
- Pre-order and post-order numbering during DFS can help identify key properties of a graph, including cycles and cut vertices.
Key Concepts
- -- Depth First Search (DFS)
- A graph traversal algorithm that explores as far down a branch as possible before backtracking.
- -- Preorder and Postorder Numbering
- Tracking the order in which nodes are visited during DFS, which helps in analyzing graph structures.
- -- Graph Complexity
- The time complexity of an algorithm in relation to the number of vertices and edges in a graph, which for DFS can be O(V + E) when using adjacency lists.
- -- Recursive Implementation
- A simpler way to implement DFS that relies on function call stacks rather than explicit stack data structures.
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