![Hashing and Graphs
• Presented by: [Your Name]
• Date: [Presentation Date]](https://image.slidesharecdn.com/hashingandgraphspresentationwithbackground-250723153754-549a47ed/85/Hashing_and_Graphs_Presentation_with_Background-pptx-1-320.jpg)
![Graph Representation
• 1. Adjacency Matrix:
• - matrix[i][j] = 1 if edge exists from i to j
• - Space: O(V^2)
• 2. Adjacency List:
• - List of connected nodes
• - Space: O(V + E)](https://image.slidesharecdn.com/hashingandgraphspresentationwithbackground-250723153754-549a47ed/85/Hashing_and_Graphs_Presentation_with_Background-pptx-9-320.jpg)
Hashing_and_Graphs_Presentation_with_Background.pptx
- 1. Hashing and Graphs • Presented by: [Your Name] • Date: [Presentation Date]
- 2. Contents • 1. Hashing • - Introduction • - Hashing Key • - Types of Hashing Key • - Applications • 2. Graph • - Introduction • - Terminology • - Representation
- 3. Hashing - Introduction • • Hashing maps data of arbitrary size to fixed- size values. • • Used for efficient storage and retrieval. • • Hash function converts input into a hash value (index). • • Common in databases, caches, and data structures.
- 4. Hashing Key • • Key is the input to the hash function. • • Hash function maps the key to an index in a table. • • Good keys minimize collisions.
- 5. Types of Hashing Key • 1. Simple Modular Hashing: index = key % table_size • 2. Multiplicative Hashing: index = floor(table_size * (key * A % 1)) • 3. Folding Method: Break key and combine parts • 4. Mid-Square Method: Square key and take middle digits • 5. Universal Hashing: Random hash functions to avoid worst cases
- 6. Applications of Hashing • • Hash Tables • • Symbol Tables in compilers • • Caching (e.g., DNS Cache) • • Cryptography (SHA, MD5) • • Database Indexing
- 7. Graph - Introduction • • Graph = Set of nodes (vertices) + edges • • Directed or Undirected • • Weighted or Unweighted
- 8. Graph Terminology • • Vertex (Node): Graph unit • • Edge: Connects two nodes • • Degree: Number of edges per node • • Path: Sequence of edges • • Cycle: Path that starts and ends at same node
- 9. Graph Representation • 1. Adjacency Matrix: • - matrix[i][j] = 1 if edge exists from i to j • - Space: O(V^2) • 2. Adjacency List: • - List of connected nodes • - Space: O(V + E)
- 10. Graph Traversals • 1. Breadth-First Search (BFS): • - Uses Queue • - Explores neighbors first • 2. Depth-First Search (DFS): • - Uses Stack/Recursion • - Explores deeply before backtracking
- 11. Applications of Graph • • Social Networks • • GPS/Google Maps • • Network Routing • • Dependency Analysis • • Scheduling
- 12. Thank You • Questions & Answers