A graph is a non-linear data structure, which comprises vertices connected by edges. An edge may...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
A graph is a non-linear data structure, which comprises vertices connected by edges. An edge may be directed or undirected. Graph theory has a huge application in a plethora of fields. For example, Wang et al. (2020) uses the improved Dijkstra's algorithm to seek the shortest paths between node pairs in large-scale bridge network. Wen et al. (2020) analyses e-mail account probing attack based on graph mining. Google maps adopted graphs for constructing its transportation system. The navigation system finds the shortest path between two cities using graph algorithms. Suppose the graph shown in Fig.1 depicts a network of urban transportation system, where each vertex denotes a city and edges are roads connecting each neighbourhood cities. The weights on the edges represent the travel distance. S B 2 Figure 1: A sample graph. E 2 F Figure 1: A sample graph. (a) Construct an adjacency list representation for the graph shown in Fig.1. i. Dijkstra's algorithm. ii. Bellman-Ford's algorithm. (b) Another possible directed graph representation is the multilinked list representation. The representation is very similar to (a). However, instead of array, a linked list is adopted. Draw the multilinked list representation for the graph in Fig. 1. Hints: The list that replace the array is made up of double linked list. Each node comprises the (1) data (vertex), (2) a pointer to a list of edges, and (3) a pointer to the next vertex. The list of adjacent vertices is replaced by a list of edges made up of edges that emanate (outgoing) from the node. A node of edge comprises (1) pointer to the node that the edge terminates, and (2) pointer to the next edge. (c) Simulate the following algorithms to obtain the shortest path starting with city S (aka. source) to the other cities. Show your steps. A graph is a non-linear data structure, which comprises vertices connected by edges. An edge may be directed or undirected. Graph theory has a huge application in a plethora of fields. For example, Wang et al. (2020) uses the improved Dijkstra's algorithm to seek the shortest paths between node pairs in large-scale bridge network. Wen et al. (2020) analyses e-mail account probing attack based on graph mining. Google maps adopted graphs for constructing its transportation system. The navigation system finds the shortest path between two cities using graph algorithms. Suppose the graph shown in Fig.1 depicts a network of urban transportation system, where each vertex denotes a city and edges are roads connecting each neighbourhood cities. The weights on the edges represent the travel distance. S B 2 Figure 1: A sample graph. E 2 F Figure 1: A sample graph. (a) Construct an adjacency list representation for the graph shown in Fig.1. i. Dijkstra's algorithm. ii. Bellman-Ford's algorithm. (b) Another possible directed graph representation is the multilinked list representation. The representation is very similar to (a). However, instead of array, a linked list is adopted. Draw the multilinked list representation for the graph in Fig. 1. Hints: The list that replace the array is made up of double linked list. Each node comprises the (1) data (vertex), (2) a pointer to a list of edges, and (3) a pointer to the next vertex. The list of adjacent vertices is replaced by a list of edges made up of edges that emanate (outgoing) from the node. A node of edge comprises (1) pointer to the node that the edge terminates, and (2) pointer to the next edge. (c) Simulate the following algorithms to obtain the shortest path starting with city S (aka. source) to the other cities. Show your steps.
Expert Answer:
Answer rating: 100% (QA)
Answer i include using namespace std include Number of vertices in the graph define V 9 A utility fu... View the full answer
Related Book For
Introduction to Algorithms
ISBN: 978-0262033848
3rd edition
Authors: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest
Posted Date:
Students also viewed these marketing questions
-
The adjacency list representation of a directed graph G is given by the lists in Table 7.6. Construct G from this representation. st 14558000 1 2 3 4 5 6 7 8 1236334536 7-a le d 1 2 3 4 5 6 7 8 9
-
Construct the vertex matrix for each of the directed graphs illustrated in the accompanying figure. (a) (b) (c) Ps
-
Suppose that all edge weights in a graph are integers in the range from 1 to |V|. How fast can you make Prim s algorithm run? What if the edge weights are integers in the range from 1 to W for some...
-
Selected accounts of Holly Company are shown as follows. Instructions After analyzing the accounts, journalize (a) The July transactions (b) The adjusting entries that were made on July 31. Supplies...
-
If you fail to account for the real options available in a given project, what error might you make in your capital budgeting decision?
-
(a) What is the decay constant of fluorine-17 if its half-life is known to be 66.0 s? (b) How long will it take for the activity of a sample of 17F to decrease to of its initial value? (c) Repeat...
-
What is horizontal analysis?
-
(NOL without Valuation Account) Jennings Inc. reported the following pretax income (loss) and related tax rates during the years 2006' ?2012. Pretax financial income (loss) and taxable income (loss)...
-
In September, Larson Inc. sold 40,000 units of its only product for $361,000, and incurred a total cost of $335,000, of which $36,000 was fixed costs. The flexible budget for September showed total...
-
You are given the following payoff table (in units of thousands of dollars) for a decision analysis problem: (a) Which alternative should be chosen under the maximin payoff criterion? (b) Which...
-
Suppose the two doctors play a one shot game that is they interact only once and never again What will be the Nash non cooperative equilibrium pricing strategy in this one shot game
-
9. Power Corporation's accounting records include the following items, listed in no particular order, at December 31, 2024: (Click the icon to view the data.) The income tax rate for Power...
-
The Ohio EPA has projected the dissolved oxygen in the Mahoning River to be less than 4.0 g/m3 during low-flow conditions; therefore, discharges of BOD demanding substances will be restricted along...
-
1.Fill the 1040 for Eric who is married and has two kids.(So 4 people in his family) Eric has the following information for the current tax year: earningfrom wages 80000 interest earned on savings 80...
-
How far back should you pull your slingshot in order for the rock to be traveling at only 2 m/s when it hits the window? You can assume that the rock is pulled back so that its change in height is...
-
A structural element supports loads of P at C in z direction and P at B in x direction on the bar (with a cross-section area of A, the area moment of inertia of I and Young's modulus of E) shown in...
-
The Primary erogenous zones are: - Places in the body that have become paired with sexual sensations and are learned through experience - context dependent - The same as secondary erogenous zones -...
-
The following data are supplied for the common stocks of Nikola Corporation, Tesla, Inc. and General Motors: Nikola Corp (NKLA) Tesla Inc. (TSLA) Close Price ($) Close Price ($) 67.53 30.00 40.81...
-
Suppose we use RANDOMIZED-SELECT to select the minimum element of the array A = 3, 2, 9, 0, 7, 5, 4, 8, 6, 1. Describe a sequence of partitions that results in a worst-case performance of...
-
Professor Borden proposes a new divide-and-conquer algorithm for computing minimum spanning trees, which goes as follows. Given a graph G = (V, E), partition the set V of vertices into two sets V 1...
-
Prove that we can also express the total cost of a tree for a code as the sum, over all internal nodes, of the combined frequencies of the two children of the node.
-
Find the greatest common divisor of 1,400 and 250 by listing all divisors of each number.
-
Find the greatest common divisor of 600 and 784 by using their prime factorizations.
-
Find the greatest common divisor of 1,400 and 250 by using their prime factorizations.
Study smarter with the SolutionInn App