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Fundamentals of
Algorithms (CS502)
Algorithms (CS502)
Assignment # 02
Fall 2018
Total
Marks = 20
Marks = 20
Deadline
= 25-01-2019
= 25-01-2019
Lectures Covered: This
assignment covers Lectures # 19 to 28.
assignment covers Lectures # 19 to 28.
Instructions:
Please read the following instructions carefully before solving
& submitting the assignment:
& submitting the assignment:
1.
The assignment will not be accepted after
due date.
The assignment will not be accepted after
due date.
2. Zero
marks will be awarded to the assignment that does not open or the file is
corrupt.
marks will be awarded to the assignment that does not open or the file is
corrupt.
3. The
assignment file must be an MS Word (.doc/.docx) file format; Assignment will
not be accepted in any other format.
assignment file must be an MS Word (.doc/.docx) file format; Assignment will
not be accepted in any other format.
4.
Zero marks will be awarded to the assignment
if copied (from other student or copied from handouts or Internet).
Zero marks will be awarded to the assignment
if copied (from other student or copied from handouts or Internet).
5.
Zero marks will be awarded to the assignment
if the Student ID is not mentioned in the assignment file.
Zero marks will be awarded to the assignment
if the Student ID is not mentioned in the assignment file.
Please
do not post queries related to assignment on MDB.
do not post queries related to assignment on MDB.
Question # 1: 10 Marks
Consider the following five matrices A, B, C, D and E
along with their dimensions;
along with their dimensions;
A B C D E
(6×5) (5×1) (1×7) (7×4) (4×2)
Determine
the Optimal Multiplication Order for
above matrices using Dynamic Programming
approach and also present the sequence (i.e. optimal order) in Binary Tree.
the Optimal Multiplication Order for
above matrices using Dynamic Programming
approach and also present the sequence (i.e. optimal order) in Binary Tree.
Note: Show all intermediate steps
(i.e. computations)
(i.e. computations)
Question # 2: 10
(5+5) Marks
(5+5) Marks
A) List down In and Out- Degrees of vertices of the
given directed graph.
given directed graph.
|
Vertex
|
In Degree
|
Out Degree
|
|
A
|
|
|
|
B
|
|
|
|
C
|
|
|
|
D
|
|
|
|
E
|
|
|
B) How many cycles are there in the given directed
graph, list all of them. Further, is there any Hamiltonian cycle in it (yes/no)?
graph, list all of them. Further, is there any Hamiltonian cycle in it (yes/no)?
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