Introduction to Greedy Algorithms
Welcome to Gate Smashers. In this video, we discuss the introduction to greedy algorithms, an important topic in algorithms.
What are Greedy Algorithms?
- Definition: Algorithms that follow local optimal choices at each stage to find a global optimum.
- Local Optimal Choice: The best choice at each stage, aiming for the overall best result.
- Example:
- Start from a source point with multiple paths to a destination.
- Costs from source to paths:
- Path 1: Cost = 10
- Path 2: Cost = 20
- Path 3: Cost = 5
- Greedy choice: Select the path with the minimum cost (Path 3).
Solution Space
- Definition: All possible options available for a problem.
- Feasible Solutions: Based on selection criteria, identifying viable paths from the solution space.
- Example:
- If one has studied arts, engineering is not a feasible option.
- Possible feasible solutions:
- Banking sector (IBPS exam, SSE)
- Government jobs (teacher, assistant professor)
- Entrepreneurship (coaching centers)
Optimal Solutions
- Definition: The best choice among feasible solutions based on specific criteria.
- Focus: Minimum cost or maximum profit.
- Example:
- Among paths with costs 10, 20, and 5, the optimal choice is the one with the lowest cost (5).
- For career paths, aim for the lowest costs in education or the highest pay scale.
Greedy Characteristics
- Greed for Profit: Always look for solutions offering maximum profit.
- In Real Life:
- During sales, one seeks the best offers regardless of product quality.
- In investments, choose options with minimum risks.
Application of Greedy Algorithms
- Problems solved using greedy algorithms include:
- Knapsack Problem
- Job Sequencing
- Minimum Cost Spanning Tree
- Optimal Merge Pattern
- Huffman Coding
- Dijkstra’s Algorithm (single-source shortest path)
Conclusion
- Greedy algorithms focus on finding the best local solution at each stage.
- The global solution may not always be guaranteed to be optimal.
- Future videos will delve into specific greedy problems.