Data Structures and Algorithms

Questions and information are in the attachment. There is a total of 4 questions to answer.First question is about Depth First Search algorithm.Second question is about Breadth First Search algorithm.The third question is about LCS.and also there is the fourth question.
cse310_2018s_hw05.pdf

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CSE310 HW05, Thursday, 04/19/2018, Due: Thursday, 04/26/2018
Please note that you have to typeset your assignment using either LATEX or Microsoft
Word, and produce a PDF file for submission. Hand-written assignment (or photo of
it) will not be graded. You need to submit an electronic version (in PDF form) on the
blackboard. You should name your file using the format CSE310-HW05-LastNameFirstName.
1. (20 points) Figure 1 shows a directed graph G. Assume that the adjacency list lists the
edges in alphabetical order.
B
A
E
G
D
C
H
F
Figure 1: Graph for P1.
(a) Apply depth first search (DFS) to graph G, and show the discovery and finish times
of each vertex. In the main-loop of DFS, check the vertices in alphabetical
order. You can write the results on the graph in Figure 1.
(b) Draw the DFS tree obtained.
(c) Draw the transpose graph GT of the graph in Figure 1. The vertices are given for your
convenience.
B
A
E
G
D
C
F
1
H
(d) Apply DFS to GT to compute the strongly connected components. You need to show
the strongly connected components and indicate the order they are computed.
2. (10 points) This problem assumes an undirected graph obtained by ignoring the directions
of the graph in Figure 1. Assume that we perform breadth first search (BFS) on this graph,
starting at vertex A.
(a) Show the set of vertices L0 , L1 , L2 , L3 .
(b) Draw the resulting BFS tree.
3. (10 points) You are given two sequences X = AST U and Y = ASU T Z. Use dynamic
programming to compute the LCS of X and Y .
(a) Fill out the 20 entries in the following table. For each of the entries, you need to show
both the value and the arrow.
j
0
i
0
0
1
A
0
2
S
0
3
T
0
4
U
0
1
2
3
4
5
A
S
U
T
Z
0
0
0
0
0
(b) What is the LCS computed according to the table?
4. (10 points) We want to use dynamic programming to compute the optimal ordering for computing the chain of 6 matrices: A1 A2 A3 A4 A5 A6 , where Ai has pi-1 rows and pi columns.
Suppose that p0 = 10, p1 = 5, p2 = 20, p3 = 6, p4 = 30, p5 = 7, p6 = 100.
(a) Compute the entries m[i, j] and s[i, j] as shown in the lecture slides.
(b) Add parenthesise to show the optimal ordering.
2

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