Greedy Algorithms
Master greedy algorithmic techniques with interactive simulators designed for university curriculum
Fractional Knapsack
High
Solve the fractional knapsack problem using greedy approach
Complexity:
O(n log n)Job Sequencing with Deadlines
High
Maximize profit by scheduling jobs within deadlines
Complexity:
O(n²)Kruskal's MST Algorithm
Very High
Find minimum spanning tree using edge-based greedy approach
Complexity:
O(E log E)Prim's MST Algorithm
Very High
Find minimum spanning tree using vertex-based greedy approach
Complexity:
O(V²) or O(E log V)Dijkstra's Shortest Path
Very High
Find shortest paths from source to all vertices using greedy approach
Complexity:
O(V²) or O((V + E) log V)Understanding Greedy Algorithms
Overview
Greedy algorithms make locally optimal choices at each step, hoping to find a global optimum. They are efficient for problems where local optimization leads to global optimization.
Key Characteristics
- •Make the best choice at each step
- •Never reconsider previous choices
- •Often used for optimization problems
- •Greedy choice property must hold
- •Optimal substructure required
Applications
- •Network routing algorithms
- •Activity selection problems
- •Huffman coding for data compression
- •Currency change problems
- •Task scheduling systems
Exam Tips
- •Understand when greedy approach gives optimal solution
- •Know the difference between greedy and dynamic programming
- •Practice proving greedy choice property
- •Learn time complexity analysis
- •Study counter-examples where greedy fails
University Exam Preparation
Question Types
- •Prove that greedy choice leads to optimal solution
- •Analyze time and space complexity
- •Compare greedy vs dynamic programming approaches
- •Design greedy algorithms for given problems
- •Find counter-examples where greedy fails
Practice Problems
- •Activity Selection Problem
- •Fractional vs 0/1 Knapsack comparison
- •Minimum number of coins problem
- •Job scheduling with profits and deadlines
- •Graph algorithms (MST, shortest path)
Exam Pattern
Universities typically ask 1-2 questions on greedy algorithms worth 10-15 marks total, focusing on algorithm design and complexity analysis.
Key Tips
- •Focus on understanding the greedy choice property
- •Practice algorithm design and complexity analysis
- •Study graph algorithms (MST) thoroughly
- •Learn to identify when greedy approach works
Quick Algorithm Reference
When Greedy Works
- • Greedy choice property holds
- • Optimal substructure exists
- • Local optimum = Global optimum
- • No need to reconsider choices
Common Patterns
- • Sort by some criteria first
- • Make greedy choice at each step
- • Prove choice leads to optimal solution
- • Analyze time complexity