Exact Pattern Matching Algorithms

Exact Pattern Matching

• Input: Strings T (Text) and P (Pattern)
• Output: All positions in T where P appears as a substring.

Brute Force Algorithm

• Slides the Pattern down Text
• Running time: Θ(|T||P|)

Skipping Positions

• Allows for skipping positions when comparing the pattern to the text.

Definitions

• Border: Prefix of a string that is also a suffix, but not the entire string.
• Example:
  • "a" is a border of "arba"
  • "ab" is a border of "abcdab"
  • "abab" is a border of "ababab"
  • "ab" is not a border of "ab"

Shifting Pattern

• Finds the longest common prefix 'u' between the pattern and the text.
• Finds the longest border 'w' of 'u'.
• Moves the pattern such that the prefix 'w' in the pattern aligns with the suffix 'w' in the text.

Algorithm Efficiency

• Definition: Algorithm performance measured in terms of time and space usage.
• Time Complexity: How runtime changes with input size, often expressed using Big O notation (e.g., O(n), O(log n)).
• Space Complexity: Amount of memory used by the algorithm as input size changes.
• Trade-offs: Balancing time efficiency against memory usage, some algorithms are faster but might need more memory.

Data Structures

• Definition: Organized ways to store and manage data efficiently.
• Types:
  • ** Primitive:** Basic data types like integers, characters, floats
  • Composite: Collections of primitive data types like arrays, structures, classes
  • Abstract Data Types (ADTs): Conceptual representations of data like lists, stacks, queues, trees, and graphs.
• Key Operations: Common actions performed on data structures like insertion, deletion, traversal, searching.
• Choice of Data Structure: Depends on the algorithm's requirements, efficiency of operations, and memory usage.

Complexity Analysis

• Purpose: Evaluating algorithm performance and efficiency.
• Big O Notation: Describes the worst-case scenario of an algorithm's time complexity.
• Big Θ Notation: Describes the average-case performance of an algorithm.
• Big Ω Notation: Describes the best-case scenario of an algorithm's time complexity.
• Asymptotic Analysis: Examining how algorithms behave as input size increases infinitely.

Graph Algorithms

• Definition: Algorithms designed for processing and analyzing graphs.
• Key Algorithms:
  • Dijkstra’s Algorithm: Finding the shortest path in a weighted graph.
  • Depth-First Search (DFS): Exploring a graph by going as deep as possible along a branch before backtracking.
  • Breadth-First Search (BFS): Exploring a graph by examining all neighbors at the current depth before moving on.
  • Prim’s and Kruskal’s Algorithms: Finding the minimum spanning tree in a graph.
• Applications: Network routing, scheduling, social network analysis.

Design Patterns

• Definition: Standardized solutions for common software design problems.
• Categories:
  • Creational Patterns: Focus on object creation (e.g., Singleton, Factory Method).
  • Structural Patterns: Deal with object composition (e.g., Adapter, Composite).
  • Behavioral Patterns: Manage algorithms and responsibilities between objects (e.g., Observer, Strategy).
• Importance: Promote reusability, scalability, and maintainability in software design.

This quiz dives into exact pattern matching techniques, particularly focusing on the brute force algorithm. You will learn about how to identify all positions in a given text where a specified pattern appears, the concept of borders, and how skipping positions can optimize searching. Test your understanding of key definitions and methodologies.