1. Use Dijkstra's algorithm to find the shortest path length betweenthe vertices a and z in each of the following weighted graphs.(a)(b)aa2b 2 c2d3f4+533eN8C2

Given two weighted graphs. To find the shortest distance between the points a and z using the…

Answered: 1. Use Dijkstra's algorithm to find the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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4. Use the tree rooted at A to answer the following questions. A K E L B M O H P D N Q R (a) List the order of the vertices produced by using Breadth-First Search. (b) List the order of the vertices produced by using Pre-Order Depth First Search. (c) List the order of the vertices produced by using Post-Order Depth First Search.
F 12 10 14 11 13 Consider the graph given above. Use the sorted edges algorithm to find a Hamiltonian circuit. a. List the weights of the edges separated by commas in the Hamiltonian circuit in the order they are chosen as specified by the algorithm.
1. Use Dijkstra's algorithm to find the shortest path length between the vertices a and z in each of the following weighted graphs. (a) (b) 1 2 b 2 d 3 b 2 19 4 4 5 3 C 3 e 7 8 6 2 2. Use Huffman coding to encode these symbols with given frequen- cies: (a) a 0.35, b: 0.4, c: 0.2, d: 0.05. (b) a 0.15, b: 0.35, c: 0.23, d: 0.22, e: 0.04, f: 0.01.
Use the high-level version of Dijkstra's algorithm to find the shortest paths from the vertex v4 to all the other vertices of the graph below. Show the actions step by step. Assume that each undirected edge represents two directed edges with the same weight.
A B с D E F A 40 B 40 : с 9 30 DE F -- 9 30 19 5 6 35 31 50 44 8 18 42 23 T 19 35 8 5 31 18 6 50 42 44 23 29 29 The weights of edges in a graph are shown in the table above. Apply the sorted edges algorithm to the graph. Give your answer as a list of vertices, starting and ending at vertex A. Example: ABCDEFA
For the Graph G1 in Figure, starting with the matching M={av,bw} and a maximum matching using the bipartite matching algorithm). Show each step, and provide a certificate of optimality (obtained from the algorithm).
6
(5) The definition of weighted graph is such that every edge has positive weight. If the def- inition was changed to permit negative (or zero) weights, would Kruskal's and Dijkstra's algorithms continue to work? Give a proof or counterexample in each case.
Use Djkstra's algorithm to find the shortest path from a to z. in order to get credit for this question you must SHOW ALL WORK. 3.
(h) Suppose that G is an unconnected graph that consists of 4 connected components. The first component is K4, the second is K2,2, the third is C4 and the fourth is a single vertex. Your job is to show how to add edges to G so that the graph has an Euler tour. Justify that your solution is the minimum number of edges added.
Given the graph A 1 Edge EF Edge BC O Edge CE B O Edge DF 2 D 3 F 2 3 5 E نیا 7 G 3 10 All the following edges have weight equal to 3 EXCEPT 6 H
1. Use Dijkstra's algorithm to find the shortest path length between the vertices a and z in each of the following weighted graphs. (a) (b) a a 2 1 2 1 2 d 3 b d b f 2 4 4 5 3 1 с e 7 g с e 1 6 2

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1. Use Dijkstra's algorithm to find the shortest path length between the vertices a and z in each of the following weighted graphs. (a) (b) a a 2 b2c 2 3 4 3 f58 3 2