C++

Q1)Provide an example that shows that Djkstra's algorithm fails to produce the correct shortest path when a negative cost edge is present. the example should have only one negative cost edge and should include a full explanation, justify your answer. Q2)Let u and v be vertices of a digraph having no weights on the edge. Give a linear time algorithm to find the number of shortest paths from u to v. Include a clear, well written, and easy to understand english description. Justify the corretness of your algorithm and its running time. Q3) You are given a set of nonnegative integers A = {a1, a2,...an}. Design an efficient dynamic programming algorithm that returns yes if there exists a subset S of A whose elements have a sum equal to the sum of the elements from A not included in S. What is the running of your algorithm? What is the space usage of your algorithm? ## Deliverables 1) Complete and fully-functional working program(s) in executable form as well as complete source code of all work done. 2) Deliverables must be in ready-to-run condition, as follows (depending on the nature of the deliverables): a) For web sites or other server-side deliverables intended to only ever exist in one place in the Buyer's environment--Deliverables must be installed by the Seller in ready-to-run condition in the Buyer's environment. b) For all others including desktop software or software the buyer intends to distribute: A software installation package that will install the software in ready-to-run condition on the platform(s) specified in this bid request. 3) All deliverables will be considered "work made for hire" under U.S. Copyright law. Buyer will receive exclusive and complete copyrights to all work purchased. (No GPL, GNU, 3rd party components, etc. unless all copyright ramifications are explained AND AGREED TO by the buyer on the site per the coder's Seller Legal Agreement). ## Platform N/A