CS557AL Homework-5
Student’s Name: _____________________________________
All work must be your own. Turn in an electronic format (PDF or MS Word file) and any supporting programs (source code and test cases). Show your work in detail.
NOTE: No extensions or late submissions for anything other than major emergency.
Q1 [15 pts.]: [The depth-first search tree] Solve Problem 7.4a from the Baase’s textbook (page 376).
Find the depth-first search tree for the graph used in Example 7.6 (see Figure 7.28, below) with B as the starting vertex under the assumption about the adjacency-list order:
- Each adjacency list is in alphabetical order
Q2 [15 pts.]: [The breadth-first search tree] Solve Problem 7.5b from the Baase’s textbook (page 376).
Find the breath-first search tree and breath-first distances for the graph used in Example 7.7 (see Figure 7.28, above) with B as the starting vertex under the assumption about the adjacency-list order:
- Each adjacency list is in reverse alphabetical order.
Q3 [25 pts.]: [Prim’s minimum spanning tree algorithm] Solve Problem 8.6b from the Baase’s textbook (page 416).
Execute Prim’s minimum spanning tree algorithm by hand on the graph in Figure 8.4(a) [see above], showing how the data structures evolve. Clearly indicate which edges become part of the minimum spinning tree and in what order.
- Start at vertex I.
Q4 [25 pts.]: [Dijkstra’s shortest-path algorithm] Solve Problem 8.15c from the Baase’s textbook (page 419).
Here is the adjacency list (with edge weights in parentheses) for the digraph shown in Figure 8.13 [see above]:
A: B(4.0), F(2.0)
B: A(1.0), C(3.0), D(4.0)
C: A(6.0), B(3.0), D(7.0)
D: A(6.0), E(2.0)
E: D(5.0)
F: D(2.0), E(3.0)
- Execute Dijkstra’s shortest-path algorithm by hand on this graph, showing how the data structures evolve, with the starting node s = D. Clearly indicate which edges become part of the shortest-path tree and in what order.
Q5 [20 pts.]: Show the Huffman tree and Encoding Table that results from the following distribution (frequency) of punctuation characters and digits: colon (59), space (113), newline (40), comma (25), 1 (121), 2 (67), 3 (34), 5 (211), 6 (93).
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