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Greedy Algorithm With Examples
Published at
1/10/2025
Categories
algorithms
programming
coding
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Author
shrijanprakash
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shrijanprakash
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A greedy algorithm is a problem-solving approach that makes a sequence of decisions, each of which is the best or most optimal choice at that moment (locally optimal), with the hope that this will lead to a globally optimal solution.
In essence, a greedy algorithm:
- Chooses the best option available at each step without considering the broader consequences.
- Does not revisit previous decisions or backtrack.
- Relies on a specific property, called the greedy choice property, which ensures that local optimization leads to global optimization.
- Assumes the problem has an optimal substructure, meaning the optimal solution can be constructed from the optimal solutions of its subproblems.
Key Characteristics of Greedy Algorithms:
- They are generally more efficient in terms of time complexity compared to exhaustive search methods.
- They may not always produce the globally optimal solution unless the problem guarantees correctness (e.g., greedy choice property and optimal substructure hold).
Common Examples of Greedy Algorithms:
- Activity Selection Problem - Selecting the maximum number of activities that don't overlap.
- Huffman Coding - Building optimal prefix codes for data compression.
- Kruskal's Algorithm - Finding the minimum spanning tree in a graph.
- Prim's Algorithm - Another approach to finding the minimum spanning tree.
- Fractional Knapsack Problem - Maximizing the total value by selecting fractions of items based on value-to-weight ratio.
Greedy algorithms are typically easier to implement but require thorough validation to ensure they are appropriate for the problem at hand.
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