Class Notes: Data Structures and Algorithms
Summer-C Semester 1999 - M WRF 2nd Period CSE/E119, Section 7344
Homework #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 graph specification. Using your class notes as a guide, answer the following questions.
Note: The graph specifications from Homework #5 have 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 Java code) for Prim's algorithm that we discussed in class. Beside each step, write the number of external I/O, memory I/O, incrementation, comparison, and other types of operations employed.
Note in the above description that Prim's algorithm (for MST) is to be used, not Dijkstra's (for Shortest Path). The use of Dijkstra's was a typo...my apologies...
Then, construct a work budget 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 Kruskal's 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 Prim's algorithm constructs the MST, starting 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 Question 3 with b as the start vertex.
* Question 5. Repeat Question 3 for Kruskal's instead of Prim's, without regard to the start vertex.
* Question 6. Repeat Question 3 for Kruskal's instead of Prim's, using the following graph specifications, without regard to the start vertex:
7. Define the Fibonacci binary tree of order n as follows: If n=0 or n=1, the tree consists of a single node. If n>1, the tree consists of a root, with the Fibonacci tree of order n-1 as the left subtree and the Fibonacci tree of order n-2 as the right subtree. Write a method that builds a Fibonacci binary tree of order n and returns a pointer to it.
1) I believe that my theoretical curves don’t really match like figure 4 but then again it somewhat does. My immigration curve and extinction curve do hit each other once, but not like in figure 4 where they hit each other twice. Also my extinction curve is going up like in figure 4 and my immigration curve is going down just like in figure 4. So I guess you could say that my curves represent the curves on figure 4.
3) In the Drop_NoFast scenario, obtain the overlaid graph that compares Sent Segment Sequence Number with Received Segment ACK Number for Server_West. Explain the graph.
I’m convinced that much learning has occurred in this course, both on your part and on mine. So I’m most interested in your telling me what you have learned, rather than asking questions on this exam that require you to demonstrate your learning. So, look back over the course and compose a page each on what you have learned about each of these course objectives.
[40] Ponemon. 2013 State of the Endpoint 2012. [Online] Available from: http://www.ponemon.org/local/upload/file/2013%20State%20of%20Endpoint%20Security%20WP_FINAL4.pdf p6. [Accessed 01 Dec 2013]
Chapter three: complete questions 2, 3, 4 and 6 found on page 97 of your
Finding myself lost in the solution of these questions, I decide to bypass them with no solution at all. (From the Author. The Brothers Karamazov)
4.10. For each of the following UML terms (see Sections 3.8 and 4.6), discuss the
[7] Elmasri & Navathe. Fundamentals of database systems, 4th edition. Addison-Wesley, Redwood City, CA. 2004.
17. Given the state diagram in Figure 4.6, which test case is the minimum series of valid transitions to cover every state?
4. A. Crespo and H. Garcia-Molina. Routing indices for peer-to-peer systems. In Proc. of the 28th International Conference on Distributed Computing Systems, July 2002.
1) Sort all edges of the graph in the decreasing order of the weight edge.
CART is characterized by the fact that it constructs binary trees, namely each internal node has exactly two outgoing edges. The splits are selected using the twoing criteria and the obtained tree is pruned by cost–complexity Pruning.
Sorting algorithms are designed to be fast, and efficient. To be able to sort a list of data as quickly as possible, using as little memory as possible. To measure or classify an algorithm according to these two criteria, we measure the algorithm’s computational complexity. The computational complexity of a sorting algorithm is it’s worst, average and best behavior. Sorting algorithms are generally classified by their computational complexity of element comparisons, against the size of the list.
Leron and Dubinsky's paper referred to above and papers resulting from their research contain the bulk of literature that I reviewed. In this paper, they summarize their