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Greedy Algorithms

Last Updated : 28 Mar, 2024
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Greedy algorithms are a class of algorithms that make locally optimal choices at each step with the hope of finding a global optimum solution. In these algorithms, decisions are made based on the information available at the current moment without considering the consequences of these decisions in the future. The key idea is to select the best possible choice at each step, leading to a solution that may not always be the most optimal but is often good enough for many problems.

Greedy Algorithms

What is a Greedy Algorithm?

A greedy algorithm is a type of optimization algorithm that makes locally optimal choices at each step with the goal of finding a globally optimal solution. It operates on the principle of “taking the best option now” without considering the long-term consequences.

Steps for Creating a Greedy Algorithm:

  1. Define the problem: Clearly state the problem to be solved and the objective to be optimized.
  2. Identify the greedy choice: Determine the locally optimal choice at each step based on the current state.
  3. Make the greedy choice: Select the greedy choice and update the current state.
  4. Repeat: Continue making greedy choices until a solution is reached.

Greedy Algorithm Examples:

Below are some example of Greedy Algorithm:

  • Fractional Knapsack: Optimizes the value of items that can be fractionally included in a knapsack with limited capacity.
  • Dijkstra’s algorithm: Finds the shortest path from a source vertex to all other vertices in a weighted graph.
  • Kruskal’s algorithm: Finds the minimum spanning tree of a weighted graph.
  • Huffman coding: Compresses data by assigning shorter codes to more frequent symbols.

Applications of Greedy Algorithm:

Below are some applications of Greedy Algorithm:

  • Assigning tasks to resources to minimize waiting time or maximize efficiency.
  • Selecting the most valuable items to fit into a knapsack with limited capacity.
  • Dividing an image into regions with similar characteristics.
  • Reducing the size of data by removing redundant information.

Disadvantages/Limitations of Using a Greedy Algorithm:

Below are some disadvantages of Greedy Algorithm:

  • Greedy algorithms may not always find the best possible solution.
  • The order in which the elements are considered can significantly impact the outcome.
  • Greedy algorithms focus on local optimizations and may miss better solutions that require considering a broader context.
  • Greedy algorithms are not applicable to problems where the greedy choice does not lead to an optimal solution.

Basics of Greedy Algorithm:

Standard Greedy Algorithms:

Greedy Problems on Array:

Greedy Problems on Operating System:

Greedy Problems on Graph:

Approximate Greedy Algorithm for NP Complete:

Greedy for Special cases of DP:

Easy Problems on Greedy Algorithm:

Medium Problems on Greedy Algorithm:

Hard Problems on Greedy Algorithm:

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