Greedy Approach
Greedy Approach
The greedy algorithm design approach is a problem-solving strategy that involves making locally optimal choices at each step with the aim of finding a globally optimal solution. In other words, a greedy algorithm makes the best possible decision in the current moment without considering the overall consequences or future steps.
The greedy approach typically follows a set of steps:
1. Initialization: Initialize the solution to an empty or default state.
2. Greedy Choice: Make a locally optimal choice that appears to be the best at the current step. This decision is typically based on a specific criterion or heuristic that optimizes the solution locally.
3. Feasibility Check: Verify if the chosen solution is feasible and satisfies any constraints imposed by the problem.
4. Objective Function: Evaluate the chosen solution using an objective function that quantifies the quality or optimality of the solution. This function is typically specific to the problem being solved.
5. Update Solution: Update the current solution with the chosen option and modify the problem instance, reducing it to a smaller subproblem.
6. Repeat: Repeat the above steps iteratively until a desired condition or termination criterion is met.
Globally Optimal Solution Not Guaranteed: The greedy approach can be efficient because it often leads to simple and intuitive algorithms. However, it does not guarantee to find the globally optimal solution for every problem. In some cases, a greedy algorithm may find a locally optimal solution that does not yield the best possible outcome in the long run.
When to Apply: It is important to note that the applicability of the greedy approach depends on the problem's characteristics. Greedy algorithms work well when the problem exhibits the "greedy choice property" and the "optimal substructure property." The greedy choice property states that at each step, the locally optimal choice leads to a globally optimal solution. The optimal substructure property implies that an optimal solution to the problem can be obtained by combining optimal solutions to its subproblems.
Common examples of greedy algorithms include the coin change problem, where the goal is to find the minimum number of coins required to make a certain amount of change, and the activity selection problem, where the objective is to select the maximum number of mutually compatible activities. In both cases, the greedy approach leads to efficient solutions. However, it's important to analyze the problem and assess whether the greedy approach is appropriate or if a different algorithmic strategy should be employed.
The links below open Jupyter Notebook pages on Google Colab (https://colab.research.google.com/) and present how to solve the corresponding computer science problem using the Greedy algorithmic design approach.
List of computer science problems that can be solved using the Greedy Approach: