**Dijkstra's Algorithm (1, part 1)**In this exercise, you will learn to apply Dijkstra's link-state algorithm to identify the least cost path from source node **U** to all other destinations within a network. The diagram below represents the network and displays the nodes and link costs.### Network Diagram:- The diagram is a circular network consisting of 6 nodes: U, V, W, X, Y, and Z.- Each edge is labeled with a cost, indicating the expense of traveling from one node to another.- Node U is the source node.### Table Explanation:- **Step**: Represents the iteration of the algorithm.- **N'**: Nodes whose least cost path is definitively known.- **D(v), p(v); D(w), p(w); D(x), p(x); D(y), p(y); D(z), p(z)**: Each column provides the current cost and predecessor node for nodes V, W, X, Y, and Z respectively. The current task is to determine the values for these nodes.### Instructions:1. Complete the first row in the table using Dijkstra’s algorithm by matching the table entries (a), (b), (c), and (d) with their respective values.2. Make use of the dropdown options provided for each part to select the correct values.3. Ensure your final answers are correct, as they are essential for the next part of the exercise.### Dropdown Options:For each part labeled (a), (b), (c), and (d), you can select from the following options:- 5,x- 6,v- 3,u- 4,v- 1,u- 8,u- 2,u- infinity- 7,uRemember: The objective is to iteratively determine the least cost path from node U to the other nodes by selecting the smallest costs and updating the paths accordingly. Complete this task to gain a deeper understanding of Dijkstra’s algorithm.

Dijkstra's algorithm is used to find shortest path between two vertices and it is a greedy algorithm. This algorithm is mostly used to solve single source shortest path problems having non negative edge weight in the graph. It finds the path by always going to the nearest vertex.Given network contains 6 vertices that are u, v, w, x, y, zThe starting vertex is uIn the table D() represents distance and p() represents previous vertex.From starting vertex u, link state algorithm first finds the distance for adjacent vertices and mark distance as infinity for non adjacent vertices for vertex u.So, from vertex u, the adjacent vertices are v, w, xThe distance from u to v is 2 so D(v)=2 and previous vertex is u that is p(v)=uThe distance from u to w is 2 so D(w)=8 and previous vertex is u that is p(w)=uThe distance from u to x is 2 so D(x)=3 and previous vertex is u that is p(x)=uNon adjacent vertices from u are y, z. So their distance is infinity.So, the values in the table are:StepN'D(v),p(v)D(w),p(w)D(x),p(x)D(y),p(y)D(z),p(z)0u2,u8,u3,uinfinityConclusion:Hence, the values are:(a) 2, u(b) 8,u(c) 3,u(d) infinity

Engineering

Data Structures and Algorithms

5.01-1. Dijkstra's Algorithm (1, part 1). Consider the network shown below, and Dijkstra's link-stat algorithm to find the least cost path from source node U to all other destinations. Using the algorithm statement and its visual representation used in the textbook, complete the first row in the table below showing the link state algorithm's execution by matching the table entries (a), (b), (c), an (d) with their values. Write down your final [correct] answer, as you'll need it for the next question. Step 0 (a) (b) (c) (d) 3 8 2 -X N' u 4 2 6 W 3 1 Z 1 W X D(v),p(v) D(w),p(w) D(x),p(x) (b) (a) (c) [Choose ] [Choose ] 5,x 6,v 3,u 4,v 1,u 8,u 2,u infinity 7,u [Choose] Z D(y),p(y) D(z).p(z) (d)

5.01-1. Dijkstra's Algorithm (1, part 1). Consider the network shown below, and Dijkstra's link-stat algorithm to find the least cost path from source node U to all other destinations. Using the algorithm statement and its visual representation used in the textbook, complete the first row in the table below showing the link state algorithm's execution by matching the table entries (a), (b), (c), an (d) with their values. Write down your final [correct] answer, as you'll need it for the next question. Step 0 (a) (b) (c) (d) 3 8 2 -X N' u 4 2 6 W 3 1 Z 1 W X D(v),p(v) D(w),p(w) D(x),p(x) (b) (a) (c) [Choose ] [Choose ] 5,x 6,v 3,u 4,v 1,u 8,u 2,u infinity 7,u [Choose] Z D(y),p(y) D(z).p(z) (d)