- Design and Analysis of Algorithms
- Home
- Basics of Algorithms
- DAA - Introduction
- DAA - Analysis of Algorithms
- DAA - Methodology of Analysis
- Asymptotic Notations & Apriori Analysis
- Time Complexity
- Master’s Theorem
- DAA - Space Complexities
- Divide & Conquer
- DAA - Divide & Conquer
- DAA - Max-Min Problem
- DAA - Merge Sort
- DAA - Binary Search
- Strassen’s Matrix Multiplication
- Karatsuba Algorithm
- Towers of Hanoi
- Greedy Algorithms
- DAA - Greedy Method
- Travelling Salesman Problem
- Prim's Minimal Spanning Tree
- Kruskal’s Minimal Spanning Tree
- Dijkstra’s Shortest Path Algorithm
- Map Colouring Algorithm
- DAA - Fractional Knapsack
- DAA - Job Sequencing with Deadline
- DAA - Optimal Merge Pattern
- Dynamic Programming
- DAA - Dynamic Programming
- Matrix Chain Multiplication
- Floyd Warshall Algorithm
- DAA - 0-1 Knapsack
- Longest Common Subsequence
- Travelling Salesman Problem | Dynamic Programming
- Randomized Algorithms
- Randomized Algorithms
- Randomized Quick Sort
- Karger’s Minimum Cut
- Fisher-Yates Shuffle
- Approximation Algorithms
- Approximation Algorithms
- Vertex Cover Problem
- Set Cover Problem
- Travelling Salesperson Approximation Algorithm
- Graph Theory
- DAA - Spanning Tree
- DAA - Shortest Paths
- DAA - Multistage Graph
- Optimal Cost Binary Search Trees
- Heap Algorithms
- DAA - Binary Heap
- DAA - Insert Method
- DAA - Heapify Method
- DAA - Extract Method
- Sorting Techniques
- DAA - Bubble Sort
- DAA - Insertion Sort
- DAA - Selection Sort
- DAA - Shell Sort
- DAA - Heap Sort
- DAA - Bucket Sort
- DAA - Counting Sort
- DAA - Radix Sort
- Searching Techniques
- Searching Techniques Introduction
- DAA - Linear Search
- DAA - Binary Search
- DAA - Interpolation Search
- DAA - Jump Search
- DAA - Exponential Search
- DAA - Fibonacci Search
- DAA - Sublist Search
- Complexity Theory
- Deterministic vs. Nondeterministic Computations
- DAA - Max Cliques
- DAA - Vertex Cover
- DAA - P and NP Class
- DAA - Cook’s Theorem
- NP Hard & NP-Complete Classes
- DAA - Hill Climbing Algorithm
- DAA Useful Resources
- DAA - Quick Guide
- DAA - Useful Resources
- DAA - Discussion
Design and Analysis - Greedy Method
Among all the algorithmic approaches, the simplest and straightforward approach is the Greedy method. In this approach, the decision is taken on the basis of current available information without worrying about the effect of the current decision in future.
Greedy algorithms build a solution part by part, choosing the next part in such a way, that it gives an immediate benefit. This approach never reconsiders the choices taken previously. This approach is mainly used to solve optimization problems. Greedy method is easy to implement and quite efficient in most of the cases. Hence, we can say that Greedy algorithm is an algorithmic paradigm based on heuristic that follows local optimal choice at each step with the hope of finding global optimal solution.
In many problems, it does not produce an optimal solution though it gives an approximate (near optimal) solution in a reasonable time.
Components of Greedy Algorithm
Greedy algorithms have the following five components −
A candidate set − A solution is created from this set.
A selection function − Used to choose the best candidate to be added to the solution.
A feasibility function − Used to determine whether a candidate can be used to contribute to the solution.
An objective function − Used to assign a value to a solution or a partial solution.
A solution function − Used to indicate whether a complete solution has been reached.
Areas of Application
Greedy approach is used to solve many problems, such as
Finding the shortest path between two vertices using Dijkstra’s algorithm.
Finding the minimal spanning tree in a graph using Prim’s /Kruskal’s algorithm, etc.
Where Greedy Approach Fails
In many problems, Greedy algorithm fails to find an optimal solution, moreover it may produce a worst solution. Problems like Travelling Salesman and Knapsack cannot be solved using this approach.
Examples
Most networking algorithms use the greedy approach. Here is a list of few of them −
Travelling Salesman Problem
Prim's Minimal Spanning Tree Algorithm
Kruskal's Minimal Spanning Tree Algorithm
Dijkstra's Minimal Spanning Tree Algorithm
Graph - Map Coloring
Knapsack Problem
Job Scheduling Problem
We will discuss these examples elaborately in the further chapters of this tutorial.
