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CSE 310 Homework3 Spring 2009
Due 9:30AM Monday, March 30
Name
Student ID
Instructions Follow instructions carefully, failure to do so will result in points being deducted. It is highly recommended that you typeset your homework using LATEX or Word. Staple this cover page to the front of your assignment for easier grading. Be sure to submit a hardcopy of your problem answers and your program analysis in class. Clearly label each problem and submit the answers in order. Put your program analysis to the end. In addition, submit your homework in- cluding the problem answers, all the program files and the program analysis via the webhandin (http://www.cse.unl.edu/~cse310/handin). Late homework policy specified in course syllabus will be strictly followed. Be sure to show sufficient work to justify your answer(s). Numerical and yes/no answers with no explanation will NOT be granted full points. If you are asked to prove something, you must give as formal, rigorous, and complete proof as possible. You are to work individually, and all work should be your own. The CSE academic dishonesty policy is in effect (http://cse.unl.edu/undergrads/academic integrity.php).
Problem Page Points Score 1 see below 10 2 see below 10 5.1.2 163 10 5.1.3 163 5 5.3.1(b) 176 5 5.4.2 181 10 Program Correctness 30 Style/Documentation 10 Analysis 10 Total 100
- A k-way merge operation: suppose you have k sorted arrays, each with n elements, and you want to combine them into a single sorted array of kn elements. A) Here is one strategy: using the merge procedure from Section 4.1, merge the first two arrays, then merge in the third, then merge in the fourth, and so on. What is the time efficiency of this algorithm, in terms of k and n?
B) Give a more efficient solution to this problem, using divide-and-conquer.
Program
Write a program (based on a graph traversal algorithm you’ve learned in this class) that, for a given undirected graph, outputs: (i) vertices of each connected component; (ii) a cycle or a message that the graph is acyclic (if there are more than one cycles in a graph, you are required to output just one of them).
Your program must be written in C++, execute correctly on the CSE unix environment, and com- pile using the g++ compiler using a makefile. The makefile should compile your program into an executable called graph inspector. Your main.cpp program should take input from a file via the command line (example: prompt:>graph inspector inputfile) with the following structure in the input file (you may assume that an input file will be well structured so you don’t have to error check the input).
Each line of the input file represents a graph. The first number in a line specifies the number of vertices in the graph. Then pairs of nodes define the edges.
An example of an input file is as follows:
5 (1,2) (3,4) (3,5) (4,5) 4 (1,2) (2,3) (1,4)
It specifies two graphs. The first graph has five vertices (1,2,3,4,5) and four edges. The second graph has four vertices (1,2,3,4) and three edges.
Proper output should look (something) like:
//////////////////////////////////////////////////// Graph1: Two connected components: {1 2} {3 4 5} Cycle detected: 3 - 4 - 5 - 3
Graph2: One connected component: {1 2 3 4} The graph is acyclic. ///////////////////////////////////////////////////
Points will be awarded based on the following categories:
- Correctness – Your code must compile and execute as expected. You must include a makefile that will compile your code into an executable called graph inspector.
- Style/Documentation – Your code should be readable, properly indented and spaced with sufficient comments to explain. Good naming style should be followed.
- Analysis – For this homework, your analysis should include two parts. First, you need to explain your design of the algorithms. Second, you analyze the algorithms and give time and space efficiencies as a conclusion. Discuss anything you think relevant, pitfalls that you faced, etc. Turn in your analysis as a hard copy with the rest of your assignment.
