5.06-1. Bellman Ford Algorithm (3, part 1). Consider the grid network shown below. All links have a cost of 1. Let's focus on the distance vector (DV) in node L. (AB) E (K) H M N R (W) X When the DV algorithm first begins, what are the initial values of the DV entries in node L for destinations G and H? Enter these components of L's initial DV,below by matching a DV entry to its value in the pull-down menu.
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- 4.Consider F = {BC -> D, B -> E, CE -> D, E -> CA, BF -> G} and R(A,B,C,D,E,F,G) a)Find all many keys for RFrom the textbook NETWORK FLOWS: THEORY, ALGORITHMS, AND APPLICATIONS - Exercise 4.2: Formulate and solve with Python code using a topo-shortest-path algorithm and data below: Beverly owns a vacation home in Cape Cod that she wishes to rent for the period May 1 to August 31. She has solicited a number of bids, each having the following form: the day the rental starts (a rental day starts at 3 P.M.), the day the rental ends (checkout time is noon), and the total amount of the bid (in dollars). Beverly wants to identify a selection of bids that would maximize her total revenue. Find the best bids to accept using python. Data Below: Bid Start End Nights Price 1 1 3 2 581 2 2 6 4 1149 3 2 5 3 844 4 3 8 5 1406 5 4 8 4 1129 6 6 12 6 1701 7 8 12 4 1136 8 8 16 8 2245 9 8 18 10 2829 10 12 16 4 1140 11 12 17 5 1429 12 13 16 3 865 13 15 20 5 1419 14 17 21 4 1120 15 18 20 2 574 16 19 24 5 1401 17 23 30 7 1973 18 25 28 3 866 19 25 29 4 1129 20 27 31 4 1122One can manually count path lengths in a graph using adjacency matrices. Using the simple example below, produces the following adjacency matrix: A B A 1 1 B 1 0 This matrix means that given two vertices A and B in the graph above, there is a connection from A back to itself, and a two-way connection from A to B. To count the number of paths of length one, or direct connections in the graph, all one must do is count the number of 1s in the graph, three in this case, represented in letter notation as AA, AB, and BA. AA means that the connection starts and ends at A, AB means it starts at A and ends at B, and so on. However, counting the number of two-hop paths is a little more involved. The possibilities are AAA, ABA, and BAB, AAB, and BAA, making a total of five 2-hop paths. The 3-hop paths starting from A would be AAAA, AAAB, AABA, ABAA, and ABAB. Starting from B, the 3-hop paths are BAAA, BAAB, and BABA. Altogether, that would be eight 3-hop paths within this graph. Write a program…
- 5.01-4 Dijkstra's Algorithm (1, part 4). Consider the network shown below, and Dijkstra's link-state algorithm. Using the algorithm statement used in the textbook and its visual representation, complete the fourth row in the table below showing the link state algorithm's execution by matching the table entries (a), (b), (C), and (d) with their values. Write down your final [correct] answer, as you'll need it for the next question. The *s shown correspond to your answers to the earlier parts of this question; note that a couple of table entries are given for you (!). [Note: You can find more examples of problems similar to this here.] 4 1 2 3 3 w Step N' D(v),p(v) D(w),p(w) D(x),p(x) D(y),p(y) D(z),p(z) u 1 2 3 (a) 2,u (b) 3,u (c) (d) (a) A. 7, w (b) B. uvxw (C) C. 6,V (d) D. 8,W E. uvxy F. infinity G. 5,x H. 6,W I. 7.y 2, 3/ >>>>b3Consider eight points on the Cartesian two-dimensional x-y plane. a g C For each pair of vertices u and v, the weight of edge uv is the Euclidean (Pythagorean) distance between those two points. For example, dist(a, h) : V4? + 1? = /17 and dist(a, b) = v2? + 0² = 2. Because many pairs of points have identical distances (e.g. dist(h, c) V5), the above diagram has more than one minimum-weight spanning tree. dist(h, b) = dist(h, f) Determine the total number of minimum-weight spanning trees that exist in the above diagram. Clearly justify your answer.
- Shouldn't the number of paths from D to E be C(6,2) and from E to C be C(4,2)?5.04-4. Bellman Ford Algorithm - a change in DV (1, part 4). Consider the network below, and suppose that at t=0, the link between nodes b and c goes down. And so at t=0, node b recomputes its distance vector (DV) and sends out its new DV (as needed). At t=1 this new DV is received at b's neighbors, who then perform their calculation and send out their new DVs (as needed); these new DVs arrive at their neighbors at t=2, and so on. What is the last time in this network at which a DV calculation will take place as a result of the link change at t=0? O a 1 1 ♡ g at t=0 the link (with a cost of 1) between nodes b and c goes down 8 1 6 compute 1 1 -h- 1 1 1 an essentially infinite amount of time; this is the count-to-infinity problemA salesman has a number of cities to visit. They want to calculate the total number of possible paths they could take, visiting each city once before returning home. Return the total number of possible paths a salesman can travel, given n cities. If we have cities A, B and C, possible paths would be: A - B -> C A -> C -> B B -> A -> C B -> C -> A C -> B -> A C -> A > B which gives us 6 as the possible number of paths. Examples paths (4) → 24
- Write the PYTHON programming to solve with breadth-first search and build node-arcs with python code for the attached problem:| Consider the elliptic curve group based on the equation y? = x' + ax + b mod p where a = 4, b = 1, and p = 7. This curve contains the point P = (0, 1). The order of this elliptic curve group is the prime number 5, and therefore we can be sure that P is a primitive element. Another element in this group is Q = (0,6). The index of Q with respect to P is the least positive integer d such that Q = dP. What is d, the index of Q?2.