- Design and Analysis of Algorithms
- Basics of Algorithms
- DAA - Introduction to Algorithms
- DAA - Analysis of Algorithms
- DAA - Methodology of Analysis
- DAA - Asymptotic Notations & Apriori Analysis
- DAA - Time Complexity
- DAA - Master's Theorem
- DAA - Space Complexities
- Divide & Conquer
- DAA - Divide & Conquer Algorithm
- DAA - Max-Min Problem
- DAA - Merge Sort Algorithm
- DAA - Strassen's Matrix Multiplication
- DAA - Karatsuba Algorithm
- DAA - Towers of Hanoi
- Greedy Algorithms
- DAA - Greedy Algorithms
- DAA - Travelling Salesman Problem
- DAA - Prim's Minimal Spanning Tree
- DAA - Kruskal's Minimal Spanning Tree
- DAA - Dijkstra's Shortest Path Algorithm
- DAA - Map Colouring Algorithm
- DAA - Fractional Knapsack
- DAA - Job Sequencing with Deadline
- DAA - Optimal Merge Pattern
- Dynamic Programming
- DAA - Dynamic Programming
- DAA - Matrix Chain Multiplication
- DAA - Floyd Warshall Algorithm
- DAA - 0-1 Knapsack Problem
- DAA - Longest Common Subsequence Algorithm
- DAA - Travelling Salesman Problem using Dynamic Programming
- Randomized Algorithms
- DAA - Randomized Algorithms
- DAA - Randomized Quick Sort Algorithm
- DAA - Karger's Minimum Cut Algorithm
- DAA - Fisher-Yates Shuffle Algorithm
- Approximation Algorithms
- DAA - Approximation Algorithms
- DAA - Vertex Cover Problem
- DAA - Set Cover Problem
- DAA - Travelling Salesperson Approximation Algorithm
- Sorting Techniques
- DAA - Bubble Sort Algorithm
- DAA - Insertion Sort Algorithm
- DAA - Selection Sort Algorithm
- DAA - Shell Sort Algorithm
- DAA - Heap Sort Algorithm
- DAA - Bucket Sort Algorithm
- DAA - Counting Sort Algorithm
- DAA - Radix Sort Algorithm
- DAA - Quick Sort Algorithm
- Searching Techniques
- DAA - Searching Techniques Introduction
- DAA - Linear Search
- DAA - Binary Search
- DAA - Interpolation Search
- DAA - Jump Search
- DAA - Exponential Search
- DAA - Fibonacci Search
- DAA - Sublist Search
- DAA - Hash Table
- Graph Theory
- DAA - Shortest Paths
- DAA - Multistage Graph
- DAA - Optimal Cost Binary Search Trees
- Heap Algorithms
- DAA - Binary Heap
- DAA - Insert Method
- DAA - Heapify Method
- DAA - Extract Method
- Complexity Theory
- DAA - Deterministic vs. Nondeterministic Computations
- DAA - Max Cliques
- DAA - Vertex Cover
- DAA - P and NP Class
- DAA - Cook's Theorem
- DAA - NP Hard & NP-Complete Classes
- DAA - Hill Climbing Algorithm
- DAA Useful Resources
- DAA - Quick Guide
- DAA - Useful Resources
- DAA - Discussion
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.
Counting Coins Problem
The Counting Coins problem is to count to a desired value by choosing the least possible coins and the greedy approach forces the algorithm to pick the largest possible coin. If we are provided coins of 1, 2, 5 and 10 and we are asked to count 18 then the greedy procedure will be −
1 − Select one 10 coin, the remaining count is 8
2 − Then select one 5 coin, the remaining count is 3
3 − Then select one 2 coin, the remaining count is 1
4 − And finally, the selection of one 1 coins solves the problem
Though, it seems to be working fine, for this count we need to pick only 4 coins. But if we slightly change the problem then the same approach may not be able to produce the same optimum result.
For the currency system, where we have coins of 1, 7, 10 value, counting coins for value 18 will be absolutely optimum but for count like 15, it may use more coins than necessary. For example, the greedy approach will use 10 + 1 + 1 + 1 + 1 + 1, total 6 coins. Whereas the same problem could be solved by using only 3 coins (7 + 7 + 1)
Hence, we may conclude that the greedy approach picks an immediate optimized solution and may fail where global optimization is a major concern.
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.
Most networking algorithms use the greedy approach. Here is a list of few of them −
Job Scheduling Problem
We will discuss these examples elaborately in the further chapters of this tutorial.
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