COP 3530, Discrete Data Structures and Algorithms, Summer 1999, Homework 7 :: UFL Florida Computer Programming Homework

Class Notes Data Structures and AlgorithmsSummer-C Semester 1999 - M WRF 2nd Period CSE/E119, Section 7344Homework 7 -- Due Wed 21 July 1999 09.30am (Revised Date)In class, we discussed minimum spanning trees (MSTs) and the algorithms that derive MSTs from a represent specification. Using your class notes as a guide, answer the side by side(p) questions.Note The graph specifications from Homework 5 pick out been used with slight modifications, to make the data structures more familiar for you.Comments in response to student questions are in red typeface. * Question 1. Write pseudocode (not umber code) for Prims algorithm that we discussed in class. Beside each(prenominal) step, write the number of external I/O, memory I/O, incrementation, comparison, and other types of operations employed. Note in the above rendering that Prims algorithm (for MST) is to be used, not Dijkstras (for Shortest Path). The use of Dijkstras was a typo...my apologies... Then, construct a work figure for each type of operation, together with a Big-Oh estimate of complexity for each of the following graph representations (a) adjacency matrix, (b) edge list, and (c) adjacency list. * Question 2. Repeat Question 1 for Kruskals algorithm that we discussed in class. * Question 3. Given the following graph specification (assume directed edges only) for G = (V,E), write out the order of edges with which Prims algorithm constructs the MST, scrawling at vertex a. (The third value (integer) in each edge triple is its weight.) (1 point each) (a) V = a,b,c,d,e,f, E = (a,b,1), (b,c,3), (a,c,2), (c,d,4), (c,e,5), (e,f,2),(b,f,3). (b) V = a,b,c,d,e,f, E = (d,a,2), (b,c,4), (a,b,2), (e,b,3), (c,e,1), (b,d,1). (c) Analyze the complexity of each case ((a) and (b), above) by constructing a work budget similar to Question 1, but for the adjacency list representation only, followed by a Big-Oh estimate. (2 points total) * Question 4. Repeat Questio n 3 with b as the start vertex. * Question 5. Repeat Question 3 for Kruskals instead of Prims, without regard to the start vertex. * Question 6. Repeat Question 3 for Kruskals instead of Prims, using the following graph specifications, without regard to the start vertex