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Fundamentals of Algorithms (CS502)
Assignment # 02
Fall 2018
Total Marks = 20

Lectures Covered: This assignment covers Lectures # 19 to 28.

Instructions:
Please read the following instructions carefully before solving & submitting the assignment:
1.      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.
3.      The 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).
5.      Zero marks will be awarded to the assignment if the Student ID is not mentioned in the assignment file.

For any query about the assignment, contact only at CS502@vu.edu.pk
Please 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;
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.
Note: Show all intermediate steps (i.e. computations)

Question # 2:                                                             10 (5+5) Marks
A)     List down In and Out- Degrees of vertices of the 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)?