Understanding Greedy Algorithms: Locally Optimal Solutions
Greedy algorithm: makes locally optimal choices, hoping for global optimality. Key characteristics: efficient time complexity, may not always produce globally optimal solution unless problem guarantees correctness.
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...