Greedy algorithm
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This presentation focus on the optimization problem-solving method i.e. greedy method. It also included a basic definition, components of the algorithm, effective steps, general algorithm, and applications.
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Greedy algorithm
- 1. Prepared By: Dr. Chandan Kumar Assistant Professor, Computer Science & Engineering Department Invertis University, Bareilly
- 2. Introduction To understand greedy algorithm, firstly we must know about Optimization problem Feasible solution Optimal solution
- 3. Optimization Problem An optimization problem is one in which you want to find, not just a solution, but the best solution An optimization problem which demands or requires either minimum result or maximum result
- 4. Optimization Problem Example P : X ------700 KM-------------->Y Where P is a problem, X and Y are the locations. Here, I want to travel from location X to location Y. Now, for this problem may be more than one solutions. Such as, S1- travel by auto S4- Travel by bus S2- Travel by bike S5- Travel by train S3- Travel by car S6- Travel by airplane and so on
- 5. Optimization Problem But here is a condition that complete this journey within 10 hours. We cannot complete this journey by solutions S1, S2, S3 but cover by solution S4,S5 and S6. Hence, solutions S4, S5 and S6 are called feasible solutions ( A solution which satisfies a condition for the given problem). Now I want to cover this journey at minimum cost i.e. we want to minimize the problem. Suppose the train fare is minimum then solution S5 is called optimal solution.
- 6. Optimization Problem For any problem, there is only one optimal solution. Similarly, some problems required maximum results. Hence, if a problem requires either minimum or maximum results than we call that type of problem as an optimization problem. The greedy method is used for solving optimization problems.
- 7. Optimization Problem For solving optimization problem there are three strategies Greedy Method Dynamic Programming Branch and Bound
- 8. Greedy Method Simplest and straightforward approach, among all the algorithmic approaches. Easy to implement and quite efficient. 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. In this approach, the decision is taken on the basis of currently available information without worrying about the effect of the current decision in future.
- 9. Greedy Method Suppose that a problem can be solved by a sequence of decisions. The greedy method has that each decision is locally optimal. These locally optimal solutions will finally add up to a globally optimal solution.
- 10. Greedy Algorithm The algorithm makes the optimal choice at each step as it attempts to find the overall optimal way to solve the entire problem. • A greedy algorithm works in phases. At each phase: – You take the best you can get right now, without regard for future consequences – You hope that by choosing a local optimum at each step, you will end up at a global optimum
- 11. Greedy Algorithm Components- 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.
- 12. Greedy Algorithm Steps for achieving a Greedy Algorithm are Feasible: Here we search to see whether it meets all possible constraints or not, to get at least one solution to our problems. Local Optimal Choice: In this, the optimal option that is selected from the currently available should be Unalterable: After taking a decision , the choice is not altered at any subsequent stage.
- 13. Algorithm Algorithm Greedy (x,n) // n is an input size and x is an input { for i= 1 to n do { y=select(x); if feasible(y) then { solution=solution + y; } } }
- 14. Application Greedy method is used to solve a variety of problems including 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 Networking algorithm also uses greedy approach like Travelling Salesman Problem, Graph - Map Coloring ,Graph - Vertex Cover, Knapsack Problem, Job Scheduling Problem etc.