Operation of algorithm, Data Structure & Algorithms

Assignment Help:

Operation of Algorithm

The following sequence of diagrams shows the operation of Dijkstra's Algorithm. The bold vertices show the vertex to which shortest path has been find out.

Step 1:

Initialize the graph, all of the vertices have infinite costs except the source vertex that has zero cost

1831_Operation of Algorithm.png

 Step 2

From all the adjacent vertices, select the closest vertex to the source s.

As we initialized d[s] through 0, it's s. (illustrated in bold circle)

Add it to S

Relax all vertices adjacent to s, that means u & x

Update vertices u & x by 10 & 5 as the distance from s.

1932_Operation of Algorithm1.png

            Step 3:

Select the nearest vertex, x. Relax all of vertices adjacent to x

Update predecessors for u, v & y. Predecessor of x = s

Predecessor of v = x ,s

Predecessor of y = x ,s

add x to S

248_Operation of Algorithm2.png

Step 4:

Now y is the closest vertex. Add it to S.

Relax v and adjust its predecessor.

 

651_Operation of Algorithm3.png

 Step 5:           

u is now closest, add it to S and adjust its adjacent vertex, v.

724_Operation of Algorithm3.png

Step 6:

Finally, add v to S.

The predecessor list now defines the shortest path from each node to s.


Related Discussions:- Operation of algorithm

Adjacency matrix of an undirected graph, 1) What will call a graph that hav...

1) What will call a graph that have no cycle? 2) Adjacency matrix of an undirected graph is------------- on main diagonal. 3) Represent the following graphs by adjacency matr

Hw7, Handout 15 COMP 264: Introduction to Computer Systems (Section 001) Sp...

Handout 15 COMP 264: Introduction to Computer Systems (Section 001) Spring 2013 R. I. Greenberg Computer Science Department Loyola University Water TowerCampus, Lewis Towers 524 82

How do you find the complexity of an algorithm, How do you find the complex...

How do you find the complexity of an algorithm?  Complexity of an algorithm is the measure of analysis of algorithm. Analyzing an algorithm means predicting the resources that

Linear search, Linear search is not the most efficient way to search an ite...

Linear search is not the most efficient way to search an item within a collection of items. Though, it is extremely simple to implement. Furthermore, if the array elements are arra

Inorder and preorder traversal to reconstruct a binary tree, Q. Using the f...

Q. Using the following given inorder and preorder traversal reconstruct a binary tree Inorder sequence is D, G, B, H, E, A, F, I, C

Define data model, Define data model?  A data model is a collection of ...

Define data model?  A data model is a collection of conceptual tools for explaning data, data relationships, data semantics and consistency constraints.

Sparse matrix, How sparse matrix stored in the memory of a computer?

How sparse matrix stored in the memory of a computer?

Explain the arrays in ruby, Explain the Arrays in Ruby Ruby arrays are ...

Explain the Arrays in Ruby Ruby arrays are dynamic arrays which expand automatically whenever a value is stored in a location beyond current end of the array. To the programmer

Data Structure, Ask consider the file name cars.text each line in the file ...

Ask consider the file name cars.text each line in the file contains information about a car ( year,company,manufacture,model name,type) 1-read the file 2-add each car which is repr

Depth-First Traversal, With the help of a program and a numerical example e...

With the help of a program and a numerical example explain the Depth First Traversal of a tree.

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd