EBK DATA STRUCTURES AND ALGORITHMS IN C
4th Edition
ISBN: 9781285415017
Author: DROZDEK
Publisher: YUZU
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Consider the network shown below, and Dijkstra’s link-state algorithm. Here, we are interested in computing the least cost path from node E to all other nodes using Dijkstra's algorithm. Using the algorithm statement used in the textbook and its visual representation, complete the "Step 3" row in the table below showing the link state algorithm’s execution by matching the table entries (i), (ii), (iii), (iv) and (v) with their values.
Please answer the following question in detail and explain all the proofs and assumptions for all parts. The question has three parts, (a), (b) and (c).
Iterative lengthening search is an iterative analogue of uniform-cost search. The basic idea is to use increasing limits on path cost. If a node is generated whose path cost exceeds the current limit, it is immediately discarded. For each new iteration, the limit is set to the lowest path cost of any node discarded in the previous iteration. (a) Show that this algorithm is optimal for general path costs. You may assume that all costs are integers (this is not a loss of generality if the search space is finite). You may wish to consider the minimal path cost C; what happens when we set the path cost to be some limit l < C? (b) Consider a uniform tree with branching factor b, solution depth d, and unit step costs (each action costs one unit). How many iterations will iterative lengthening require? (c) (7 points) Now consider the…
ll businesses want to keep their customers happy. To do that, many companies assign a certain amount of time to each customer to optimize the business. The alternative would be to hire more employees, which would lead to higher costs.
This problem requires you to simulate how authorities optimize the number of cashiers at the entrance of a toll bridge to make sure drivers are satisfied. Make the following assumptions:
There is one cashier per line. The line works as a queue with no cars cutting the line or leaving it.
One car arrives at the entrance every 10 seconds.
It takes 90 seconds (1.5 minutes) to process the payment, starting from the moment a cashier is available. Assume there is no pause between cars.
Your Tasks:
Design class CarInLine, with the following specifications:
The class has two instance variables: arrivalTime and DepartureTime, stored as integers.
Define a constructor that accepts an integer as an argument representing the arrival time, in which you set the…
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EBK DATA STRUCTURES AND ALGORITHMS IN C
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- P5. Consider the network shown below, and assume that each node initially knows the costs to each of its neighbors. Consider the distance-vector algorithm and show the distance table entries at node z. The resulting answer should replicate the technique used in Fig 5.6, though it will vary slightly as there are more than three variables in this specific problem.arrow_forwardPart 3: Comparison of Dijkstra and Bellman-Ford algorithms In part 3, please answer the following five questions in your PDF. Question 1: What is the time complexity of Dijkstra's algorithm? Please briefly describe the steps of the algorithm to justify the time complexity. Question 2: What is the time complexity of Bellman-Ford algorithm? Please briefly describe the steps of the algorithm to justify the time complexity. Question 3: How does the distance vector routing algorithm send routing packets? (To all nodes or only to neighbors) Question 4: How does the link state routing algorithm send routing packets? (To all nodes or only to neighbors) Question 5: When a link cost changes, which steps does the distance vector algorithm take?arrow_forwardAll businesses want to keep their customers happy. To do that, many companies assign a certain amount of time to each customer to optimize the business. The alternative would be to hire more employees, which would lead to higher costs. This problem requires you to simulate how authorities optimize the number of cashiers at the entrance of a toll bridge to make sure drivers are satisfied. Make the following assumptions: There is one cashier per line. The line works as a queue with no cars cutting the line or leaving it. One car arrives at the entrance every 10 seconds. It takes 90 seconds (1.5 minutes) to process the payment, starting from the moment a cashier is available. Assume there is no pause between cars. Written in java, Your Tasks: Design class CarInLine, with the following specifications: The class has two instance variables: arrivalTime and DepartureTime, stored as integers. Define a constructor that accepts an integer as an argument representing the arrival time, in…arrow_forward
- 2. Consider two strings X and Y as given below; X= {a, c, b, a, e, d} Y = {a, b, c, a, d, f} Construct a LCS table and find out the length of the longest common subsequence (LCS) and the LCS itself, using Dynamic Programming Algorithm.arrow_forwardWrite the algorithm that finds and returns how many paths in k units of length between any given two nodes (source node, destination node; source and target nodes can also be the same) in a non-directional and unweighted line of N nodes represented as a neighborhood matrix. (Assume that each side in the unweighted diagram is one unit long.) Note: By using the problem reduction method of the Transform and Conquer strategy, you have to make the given problem into another problem. Algorithm howManyPath (M [0..N-1] [0..N-1], source, target, k)// Input: NxN neighborhood matrix, source, target nodes, k value.// Ouput: In the given line, there are how many different paths of k units length between the given source and target node.arrow_forwardWrite a program that will accept a sequence of `insert’ and `delete’ operations in dynamic table and compute the potential and amortized cost after each operation. The output of the program is a graph showing changes in size, num, potential and amortized cost (c i’) for the entire sequence of operations.arrow_forward
- In the diagram attached, a flow network has been depicted. Perform the following tasks using the Push Re-label Algorithm: - Optimize the maximum flow between S1 to t2 S2 to t1 S1 & S2 to t2 S1 & S2 to t1 Evaluate your final results for any shortcomings, and propose changes to solve them. 12 14 34 33 16 18 30 Note: Please assign the values (individual digits - one digit per edge) from your mobile number (0967910053) to the unmarked edges. 10 unmarked edges will be given with 10 digits in your mobile number and any 'O digit should be replaced with value '10'arrow_forwardProblem 3. Recollect that the standard implementation of the Dijkstra's algorithm uses a priority queue that supports the Extract-min() and Decrease-Key() operations. Describe a method to implement Dijkstra's algorithm in O((m + n) log n) time without the use of Decrease-Key operation, i.e., your algorithm can use the Extract-Min() operation but not the Decreased-Key() operation. Solution:arrow_forward3. Floyd's algorithm for the shortest Paths (algorithm 3.3) can be used to construct the matrix D, which contains the lengths of the shortest paths from any point to any other point. Given the following graph, construct the adjacency matrix W and use the recursive relation to construct D¹. Note that the entire process starting with W is W (= Dº) -> D¹ -> D² -> D³ ->.........-> D^ (= D). You only need to show the step from W to D¹. To get extra credit show the remaining steps to obtain D5 (=D). V5 3 3 5 V1 1 V4 2 9 1 4 2 V2 V3 3arrow_forward
- In this question, we consider the operation of the Ford-Fulkerson algorithm on the network shown overleaf: 0/16 0/12 0/8 0/4 0/8 0/5 19 0/11 174 0/13 0/14 0/2 0/11 0/10 Each edge is annotated with the current flow (initially zero) and the edge's capacity. In general, a flow of x along an edge with capacity y is shown as x/y. (a) Show the residual graph that will be created from this network with the given (empty) flow. In drawing a residual graph, to show a forward edge with capacity x and a backward edge with capacity y, annotate the original edge *;ỹ. (b) What is the bottleneck edge of the path (s.₁,vs,t) in the residual graph you have given in answer to part (a)?arrow_forwardUse the worksheets to show, one path augmentation at a time, how to use the Ford-Fulkerson Algorithm to compute a max flow and a min cut for the flow network. As you go along, write the flows for each edge in the little squares. When you reach the end of the algorithm, shade in the nodes that are on the "A side" of the minimum cut. You may want to review the Ford-Fulkerson Algorithm before starting on the problem.arrow_forwardConsider the following graph: 3 7 S 3 8 What is the maximum flow in this graph? Give the actual flow as well as its value. Justify your answerarrow_forward
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