CSIS-385 Quiz 9: Algorithms and Graph Theory, Quizzes of Algorithms and Programming

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CSIS-385: Quiz 9 Name____________________________________

1. We have actually learned two ways to compute the shortest path from a single source: (1) Dijkstra’s algorithm or (2) you can do a Breadth First Search from the source vertex. However, Breath First Search will only produce a shortest path for which types of graphs (Circle one). a. Complete Graphs b. Directed Graphs c. Un-weighted Graphs d. Directed Acyclic Graphs
2. Trees are actually graphs. Thus, you could run Dijkstra’s algorithm on a tree to find the shortest distance from a node to any other node. Explain why this would be pointless.
4. If you worked for the Census Bureau and you had to implement an algorithm for sorting all U.S. residents (300 million) by their Social Security number 9 digits, which algorithm would be the fastest theoretically? The log 2 (300,000,000) = 28.16. Your computer has 8GB of RAM and a 9 digit integer can be sorted using 4 bytes. a. Quick Sort b. Radix Sort c. Counting Sort d. Bubble Sort Briefly explain your answer for partial credit:
5. Would your answer change if the government switched to a 16 digit Social Security number? a. Yes b. No Briefly explain your answer for partial credit.
6. Would your answer change if your algorithm had to be implemented on a computer with 512MB of Ram a. Yes b. No Briefly explain your answer for partial credit.
7. Given the following graph, show the last five update steps of Prim’s algorithm:

1 2 9 5 4 17 16 10 4 3 3 7 5 2 start