讲解：CS 560、R、R、algorithmProcessing|Prolog

CS 560, HOMEWORK 5 (DUE: SUNDAY NOV 24, 11:59 PM)INSTRUCTOR: HOA VUEach question is worth 27.5 points.When you are asked to design an algorithm, do the following: a) describe the algorithm,b) explain (or more rigorously prove) why it is correct, and c) provide the running time.Unless specified otherwise, the problems are from the textbook by Jeff Erickson.(1) Question 1: Recall the algorithm Dijkstra(G, s) we went over in class:• For all u ∈ V \ {s}, set dist(u) ← ∞.• dist(s) ← 0.• R = {}.• While R 6= V :– Pick u /∈ R with smallest dist(u), then R ← R ∪ {u}.– For all vertices uv ∈ E, if dist(v) > dist(u) + `(uv), then updatedist(v) ← dist(u) + `(uv).Consider Dijkstra’s algorithm for finding single-source shortest paths startingfrom vertex s to all other nodes.What are the different (distinct) values of dist(a) and dist(d) during the executionof Dijkstra’s algorithm (list their values over time) in the above graph.(2) Question 2: Problem 19a page 253. Your algorithm should run in O(|V | log |V | +|E| log |E|) time. Use the following hints.A) First sort each adjacency list A[i]CS 560代做、代写R编程语言、代做R、algorithm (for i = 1, 2, . . . , n) that contains all (outgoing)neighbors of i based on the neighbors’ weights. Explain why this takes12 INSTRUCTOR: HOA VUO(E log E) time. Use the fact thatXni=1(# of edges i → j) = |E| .In particular, you simply sort each adjacency list. But you need to argue why therunning time for this step is O(E log E).B) Sort the nodes by their weights.C) Use Depth-First-Search to find the longest increasing-weight sequence (hint:the order in which you explore unvisited nodes matters).(3) Question 3: Problem 3 page 245 (Hint: try applying an existing algorithm). Therunning time should be O(|V | log |V | + |E|).(4) Question 4: You need to build source code files. If source code file A.cpp refers tofile B.cpp (i.e., “#include B.cpp”) then we need to build file B.cpp first. Supposewe want to build a target file T.cpp without building unncessary files (for example,if there are 3 files A, B, T and T includes A, then we only need to build A then Tand not build B). Design an algorithm (as efficient as possible) to list out the filesand the ordering to build them.转自：http://www.daixie0.com/contents/18/4343.html