Greedy Algorithms

A paradigm that builds a solution step by step, choosing the locally optimal choice at each step, with the hope that this leads to a globally optimal solution.

Definition

A paradigm that builds a solution step by step, choosing the locally optimal choice at each step, with the hope that this leads to a globally optimal solution.

Steps

  1. Identify the problem's greedy property.
  2. Make the locally optimal choice.
  3. Verify that this approach results in a global optimum.

Examples

  • Dijkstra's Algorithm: Finds the shortest path in a weighted graph.
  • Prim's Algorithm: Constructs a minimum spanning tree.
  • Activity Selection Problem: Selects the maximum number of activities that don't overlap.

Advantages

  • Simpler and faster than other methods.
  • Efficient for problems with the greedy-choice property.

Limitations

  • May not always produce the best solution.
  • Requires careful analysis to verify applicability.