Design & Analysis of Algorithms - Vol 1 | 21. Depth First Search (DFS) by Abraham | Learn Smarter
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21. Depth First Search (DFS)

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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Sections

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  1. 21.1
    Design And Analysis Of Algorithms

    This section explores the Depth First Search (DFS) algorithm for exploring...

  2. 21.1.1
    Depth First Search (Dfs)

    Depth First Search (DFS) is an algorithm used for traversing or searching...

  3. 21.1.2
    Executing The Algorithm By Hand

    This section explains the depth-first search algorithm and its execution on...

  4. 21.1.3
    Recursive Implementation Of Dfs

    The section presents the recursive implementation of Depth First Search...

  5. 21.1.4
    Complexity Of Depth First Search

    This section explores the Depth First Search (DFS) algorithm, detailing its...

  6. 21.1.5
    Dfs Numbering Technique

    This section covers the Depth First Search (DFS) numbering technique,...

  7. 21.1.6
    Example Of Dfs Pre And Post Numbers

    The section covers Depth First Search (DFS), explaining its algorithm,...

  8. 21.1.7
    Applications Of Dfs Numbers

    This section discusses Depth First Search (DFS), emphasizing how it operates...

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.

Additional Learning Materials

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