Write the Dijkstra’s shortest path algorithm. Also, find the time complexity of this shortest path algorithm. Find the shortest paths from the vertex ‘A’ using Dijkstra’s shortest path algorithm for the graph given in Figure 1. Show all the steps of computation.
### **Algorithm Steps** 1. Assign tentative distance for all vertices: 0 for source, ∞ for others. 2. Set source as current. For all neighbors not yet visited, update their distance if path through current is smaller. 3. Mark current as visited. Set next unvisited vertex with smallest tentative distance ___ ___ ______ ________ _________ ________ ____.
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Write an algorithm to multiply two square matrices of order n*n. Also explain the time complexity of this algorithm.
Explain the Merge procedure of the Merge Sort algorithm. Demonstrate the use of recursive Merge sort algorithm for sorting the following data of size 8: [19, 18, 16, 12, 11, 10, 9, 8]. Compute the complexity of Merge Sort algorithm.
Explain the Topological sorting with the help of an example. Also, explain the algorithm of finding strongly connected components in a directed Graph.
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SAT Problem
What are P and NP class of Problems? Explain each class with the help of at least two examples.
Write and explain the Bubble sort algorithm. Discuss its best and worst-case time complexity.