4. (a) Use Dijkstra's algorithm to find the shortest path from node A to node F in thefollowing network and give its length.Aс25B241363FD14Weight [kg]40506040250200701901E(b) A museum wants to ship 8 Roman statues for a special exhibition. They are tobe transported in crates each holding a maximum weight of 300 kilograms. Thenumbers in the table represent the weight in kilograms of the statues:StatueMercuryVenusTellusMarsJupiterSaturnCaelusNeptune(i) Find the lower bound for the number of crates required to fit all statues.(ii) Use the first fit decreasing algorithm to estimate the minimum number of cratesrequired to ship all statues. Does the first fit decreasing algorithm give anoptimal solution?(iii) Find by trial and error a solution needing only & crates.

(a)Dijkstra's used to find the shortest distance path between any two vertices of the graph. This…

Answered: 4. (a) Use Dijkstra's algorithm to find…

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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DISCRETE STRUCTURE
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.
3. Run both Kruskal and Prim's algorithms on the following weighted graph: 12 7 11 10 3 2 4 1 8 For Prim's algorithm, start at the top-left vertex marked in black. What's the weight of your minimum spanning tree? 1
B 15 D 12 A Use the Brute-Force Algorithm to find the lowest-cost Hamilton circuit. For the first part, give one best answer as a list of vertices visited starting at A (example: ABCDA), and for the second part give the total cost for this best solution. 1. Give a lowest-cost Hamilton circuit: 2. Give the lowest cost:
40 is incorrect
A B C D E F A D -- B 51 51 36 45 -- с 36 45 D E F 8 14 58 35 16 23 47 52 20 55 53 12 8 35 47 14 16 52 55 58 23 20 53 12 - The weights of edges in a graph are shown in the table above. Apply the nearest neighbor algorithm to the graph starting at vertex A. Give your answer as a list of vertices, starting and ending at vertex A. Example: ABCDEFA
6
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.
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
Consider the following network, where each number along a link represents the actual distance between the pair of nodes connected by that link. The objective is to find the shortest path from the origin to the destination. (a) For the forward recursion formulation of this problem, how many stages are there, and what arethe states for each stage? Stage 1: n = 1 Stage 2: n = 2 origin) ( Stage 3: n = 3 S A B C (b) Use forward recursion to solve this problem. However, instead of using the usual tables, show your work graphically. In particular, start with the given network, where the answers already are given for f (Sn) for four of the nodes; then solve for and fill in f2 (B) and fi* (0). Draw an arrowhead that shows the optimal link to traverse out of each of the latter two nodes. Finally, identify the optimal path by following the arrows from node O onward to node T. (c) Use forward recursion to solve this problem by manually constructing the usual tables for n = 3, n = 2, and n = 1.…

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4. (a) Use Dijkstra's algorithm to find the shortest path from node A to node F in the following network and give its length. A C 2 7 5 B 24 13 6 3 F 14 1 E