A greedy algorithm is a problem-solving technique used in optimization problems where the goal is to find the best solution by making a series of choices. At each step, the algorithm makes the locally optimal choice, which is the best decision based on the current information available, without considering the broader consequences or future implications of that choice. This approach is characterized by its simplicity and efficiency, often providing quick solutions to complex problems.
Key Properties of Greedy Algorithms
Greedy Choice Property: This property states that a global optimal solution can be achieved by making a series of locally optimal choices. In other words, the best choice at each step leads to the best overall solution.
Optimal Substructure: A problem exhibits optimal substructure if an optimal solution to the problem contains optimal solutions to its subproblems. This means that solving each subproblem optimally will lead to an optimal solution for the entire problem.
Characteristics
Simplicity and Efficiency: Greedy algorithms are straightforward to implement and often run faster than other algorithms, making them suitable for problems where time is a constraint.
Non-recoverable Decisions: Once a choice is made, it is not reconsidered, which differentiates greedy algorithms from dynamic programming, where past decisions can be revisited and altered.
Local Optimization: Decisions are made based on the current state without looking ahead, which can sometimes lead to suboptimal solutions.
Examples of Greedy Algorithms
Huffman Coding: Used for data compression, it builds a binary tree by repeatedly combining the two least frequent characters.
Dijkstra's Algorithm: Finds the shortest path between nodes in a graph by always selecting the node with the smallest tentative distanc...
