Due: Day 8ExercisesCSE 101: Homework 1Due: Day 8When presenting an algorithm, make sure you have:• A clear (pseudo-code) description of the algorithm• A proof that it is correct (loop invariants may help)• An analysis of its runtime (stating the runtime isn’t sufficient, pro-vide a proof or justification).For full credit, you need all three pieces.ExercisesKleinberg refers to the class textbook Algorithm Design by Kleinberg andTardos.1. For the following graph, use Dykstra’s algorithm to determine thedistances from node 1 to each other node. Show the distances in theorder that Dykstra’s algorithm determines them. 10 pts.12345678151089117654612142312. For the previous graph, provide the edges added to the MST in orderusing Prim’s algorithm (starting with node 1) and Kruskal’s algo-rithm. 10 pts.3. Kleinberg Chapter 4, Exercise 2. 10 pts.4. Kleinberg Chapter 4, Exercise 3. 10 pts.5. Kleinberg Chapter 4, Exercise 12. 20 pts.6. Kleinberg Chapter 4, Exercise 19. 20 pts.7. Kleinberg Chapter 4, Exercise 21. 20 pts.8. Kleinberg Chapter 4, Exercise 29. Extra credit, 20
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