🧩

Understanding Generate and Test Algorithm

Apr 15, 2025

Lecture Notes: Generate and Test Algorithm

Introduction

  • Topic: Generate and test algorithm
  • Relevance: Useful for competitive exams, college, and university exams
  • Video Actions: Like, subscribe, and press the bell button for notifications

Generate and Test Method

  • Type: Heuristic technique
  • Category: Informed search technique
  • Relative Simplicity: Simplest among heuristic methods like Best First Search, Hill Climbing, and A* Algorithm

Key Characteristics

  • Uses: Depth First Search (DFS) with backtracking
  • Modules:
    • Generate: Continuously generate possible solutions
    • Test: Evaluate generated solutions against a goal state
  • Process:
    1. Generate possible solutions
    2. Test against goal state
    3. Accept solution if it matches goal state; otherwise, discard and generate again

Properties of a Good Generator

  1. Complete: Covers all possible states to ensure an optimal solution
  2. Non-redundant: Avoids generating redundant solutions to save time and prevent exponential increase in states
  3. Informed: Utilizes knowledge of the local domain for faster solution finding

Example: 3-Digit PIN Code

  • Problem: Find a possible answer for a 3-digit pin where each digit is a 2-digit number
  • Brute Force Method:
    • Number of Solutions: 100^3 = 1,000,000 possible solutions
    • Time Complexity: Exponential
    • Generation Rate: 5 solutions/minute
    • Total Time Required: Approximately 10 weeks (without heuristic)

Informed Search Technique

  • Heuristic Example: Knowing all numbers are prime numbers
  • Solution Space Reduction:
    • Prime Numbers: 25 prime numbers between 0 to 99
    • Reduced Possible Solutions: 25^3 = ~15,000
    • Efficiency: Within less than 2 days using informed search

Conclusion

  • Heuristic Impact: Reduces time complexity from exponential to more manageable levels
  • Worst-Case Complexity: Remains exponential in time and space
  • Heuristic Benefit: Improves generator performance and increases probability of quickly finding a solution

Summary: Generate and test algorithm is a simple yet powerful heuristic technique used to solve problems by continuously generating and testing solutions against a goal state. Using informed search techniques can significantly reduce the time required to find a solution.

Full transcript