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- 9. Use the Dijkstra's algorithm to find the shortest path between the nodes A and Z in the diagram shown below: B 10 F 1 2 G 1 10 10 1 A 4 D 5 H Z 8 3 3 6 3 E 2 8Please do not give solution in image formate thanku. Write a Python code for the following scenario : 1: Use Breadth First Search and Recursive Best First Search and implement the algorithms in Python. The program should be able to dynamically take in start and goal nodes from the user at run time. Compare to interpret the results in terms of the algorithm working, performance & shortest path if obtained relevant to the given problem 2: Print the minimum connections that keep the whole network up and running. For each incremental depth limit, the corresponding node generating sequence should be legibly printed in the result Consider Heuristic Value as : The edge cost is an approximation towards the transmission cost between any pair of nodes. For heuristic design, consider all the possible paths between any arbitrary node n to the goal node. The average of the total transmission cost across all these paths is the heuristic value h(n) Consider the following undirected graph…When purifying drinking water you can use a so-called membrane filtration. In an experiment one wishes to examine the relationship between the drop across a membrane and the flux (flow per area) through the membrane. We observe the following 10 related values of pressure (x) and flux (y): pressure 2 3 4 5 6 7 8 9. 10 Pressure (x) 1.02 2.08 2.89 4.01 5.32 5.83 7.26 7.96 9.11 9.99 Flux (y) 1.15 0.85 1.56 1.72 4.32 5.07 5.00 5.31 6.17 7.04 Copy this into R to avoid typing in the data: D <- data.frame( pressure=c(1.02,2.08,2.89,4.01,5.32,5.83,7.26,7.96,9.11,9.99), flux=c(1.15,0.85,1.56,1.72,4.32,5.07,5.00,5.31,6.17,7.04)
- F(x,y.z)= X(Y+Z)+ X.Y.Z[ IConsider the following network: a.) Find the shortest path from node 1 to node 8 using Dijkstra’s algorithm. Write the length of the shortest path as well as the edges that compose it. b.) Write an integer programming formulation to find the second-shortest path from 1 to 8 in this network. (Hint: if the shortest path is not available, the second-shortest path becomes the shortest path.)Page There is a famous railway station in PopPush City. Country there is incredibly hilly. The station was built in last century. Unfortunately, funds wwere extremely limited that time. It was possible to establish only a surface track. Moreover, it turned out that the station could be only a dead-end one (see picture) and due to lack of available space it could have only one track. 5, 4, 3, 2, 1 1, 2, 3, 4, 5 Station The local tradition is that every train arriving from the direction A continues in the direction B with coaches reorganized in some way. • Assume that the train arriving from the direction A has NS 1000 coaches numbered in increasing order 1, 2, . N. • The chieffor train reorganizations must know whether it is possible to marshal coaches continuing in the direction B so that their order will be a, a2. . aN. Help him and write a program that decides whether it is possible to get the required order of coaches. • You can assume that single coaches can be disconnected from…
- 3. Sarah and Jennifer have just graduated from college at the University of Washington in Seattle and want to go on a road trip. They have always wanted to see the mile-high city of Denver. Their road atlas shows the driving time (in hours) between various city pairs, as shown below. Use the Dijkstra's algorithm described in Sec. 10.3 to solve this shortest-path problem to find the quickest route from Seattle to Denver? Show your work of finding the path by using a table. 3 Portland Seattle 9 10 Boise Butte 7 Salt Lake City 4 12 Grand Junction 4 7 1 Billings Cheyenne Denver1. Determine the shortest path from A to B using Dijkstra’s algorithm. A 3 15 8. 5 3 4 4 12 6. 3. 4 10 15 3 3 8. 4 6. B1. A Rook-y Move! In chess, a rook can move horizontally or vertically to any square in the same row or in the same column of a chessboard. Find the number of shortest paths by which a rook can move from the bottom-left corner of a chessboard to the top-right corner. (The length of a path is measured by the number of squares it passes through, including the first and the last squares.) Solve the problem by a dynamic programming method. That is, come up with a relevant recurrence i.e., a recursive definition of the relevant values for a solution, as we've seen in the examples from class and using dynamic programming techniques, calculate the solution. Please show your work by giving an 8 x 8 table (each element in the table represents the corresponding square on the chessboard), where each entry in the table should be the number of paths from the bottom-left corner to that square on the chessboard; therefore, the answer to this exercise will be the number in the top-right element of…
- The below graph shows A, B, C...., I which are the electricity transmission tower locations to be built in a new development town. The numbers next to the lines are the transmission distance in km of the cable which connects is the transmission towers. A 3 2 2 D 3 9 E I 7 8 (a) Apply the Dijkstra's shortest path algorithm to the above graph to find the shortest path and the shortest distance from A to G. [Show your working step by step clearly when applying the algorithm.] GAs steam is heated up, the pressure it generates is increased over the temperature range [220, 300] (degrees Fahrenheit); the pressure, in pounds per square inch, is as given in the table Table. Temperature-pressure values for steam T 220 230 240 250 260 270 280 290 300 P 17.188 20.78 24.97 29.82 35.42 41.85 49.18 57.53 66.98 Construct the Lagrange interpolating polynomial to this data at the interval ranges a) [220,260] b) [260,300] c) [220,300] Plot the data in the table using Excel Spreadsheet. Then get the error by subtracting the Excel values from the pressure values from the table. What can you say about the error?8. X. Let f: RR defined by f(x) = x³ -