Greedy Algorithm With Examples

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:

1. Chooses the best option available at each step without considering the broader consequences.
2. Does not revisit previous decisions or backtrack.
3. Relies on a specific property, called the greedy choice property, which ensures that local optimization leads to global optimization.
4. 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:

1. They are generally more efficient in terms of time complexity compared to exhaustive search methods.
2. 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:

1. Activity Selection Problem - Selecting the maximum number of activities that don't overlap.
2. Huffman Coding - Building optimal prefix codes for data compression.
3. Kruskal's Algorithm - Finding the minimum spanning tree in a graph.
4. Prim's Algorithm - Another approach to finding the minimum spanning tree.
5. 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.