Weighted Graph:
A graph is termed as weighted graph if each edge of the graph is assigned a weight. The weighted edges stored in the weighted graphs can be stored in adjacency lists.
Weighted edges can be represented using a two-dimensional array. An weighted edge can be represented as “WeightedEdge(u,v,w)”, where “u” and “v” are edges and “w” represents the weight between them.
Example of storing edge in a weighted graph:
Object[][] edges =
{ new Integer(0), new Integer(1), new SomeTypeForWeight(8) };
Dijkstra’s
In computer science, the Dijkstra’s Algorithm is a greedy algorithm that is used compute the minimal distance from a node to all the other nodes in a weighted graph.
Want to see the full answer?
Check out a sample textbook solutionChapter 29 Solutions
Introduction to Java Programming and Data Structures, Comprehensive Version, Student Value Edition (11th Edition)
- Explain how the minimum-sum descent problem can be solved by Dijkstra’s algorithm. This is a problem from my textbook and I am not sure how to approach it.arrow_forwardUse a software program or a graphing utility with matrix capabilities to find the eigenvalues of the matrix. (Enter your answers as a comma-separated list.) 1 0 -1 1 1 1 -3 0 3 -3 0 3 3 λ = 0 030arrow_forwardExplain how Dijkstra's method may be used to solve the minimum-sum descent issue. This is an issue from my textbook that I'm not sure how to go about addressing.arrow_forward
- You have to run Prim's algorithm for the problem defined by adjacency matrix: 1 2 3 4 5 6 7 8 9 1 0 10 9 999 999 17 999 999 999 2 10 10 3 9 11 0 14 4 2 999 999 13 999 14 0 7 999 999 999 999 999 4 999 4 7 0 999 2 8 999 999 567 999 2 999 999 0 6 999 1 999 17 999 999 2 6 0 999 7 999 999 999 999 8 999 999 0 11 4 8 999 13 999 999 1 7 11 0 8 9 999 999 999 999 999 999 4 8 0 1. We started from the vertex vl, so initially we have Y = {v1}: initial nearest 1 2 3 4 5 6 7 8 9 16 1 1 1 1 1 1 1 1 distance -1 10 9 999 999 17 999 999 999 Print out the values stored in the nearest and distance arrays after first iteration of Prim's algorithm. Specify the value of vnear and the next vertex that has to be added to Y Hint: use (copy) the table above to record your answer.arrow_forwardThe algorithm for computing the Hamming distance between two sequences of the same length implemented in R, for instance, by first splitting the sequences into vectors with the strsplit function and then using the sum function to count the number of positions at which the two vectors differ.arrow_forwardWrite is a Java example to solve Dijkstra's Shortest Path Algorithm using Adjacency Matrix.arrow_forward
- Given an n-element sequence of integers, an algorithm executes an O(n)-time computation for each even number in the sequence, and an O(logn)-time computation for each odd number in the sequence. What are the best-case and worst-case running times of this algorithm? Why? Show with proper notations.arrow_forwardThink about the problems with representing weighted graphs using adjacency lists.arrow_forwardComputer Science How would you modify Strassen's algorithm to multiply n n matrices in which n is not an exact power of 2? Explain how your algorithm works for the case where n = 30.arrow_forward
- Write the Python code to find the transitive closure when given zero-one matrix. DO NOT use the Warshall Algorithm in this code. Pseudo code: A := MR B := A for i := 2 to n A:= A ⊙ MR B:= B ∨ A return B (the zero-one matrix for R*)arrow_forwardThis is discrete math: Find f ? g and g ? f , where f (x) = x^2 + 1 and g(x) = x + 2, are functions from R to Rarrow_forwardGiven A={1,2,3,4,5,6}, B={4,5,6,7,8,9}. Compute (c)A−B=arrow_forward
- Database System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill EducationStarting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSONDigital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSON
- C How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSONDatabase Systems: Design, Implementation, & Manag...Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage LearningProgrammable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education