6) Consider the matrix chain A3A4A5, where A3 has dimension 5 × 20, A4 has dimen

Question

6) Consider the matrix chain A3A4A5, where A3 has dimension 5 × 20, A4 has dimension 20 × 80 and A5 has dimension 80 × 4. Which of the following parenthesizations require the minimum number of scalar multiplications?

      
((A3A4)A5)

      
(A3(A4A5))

      
This chain of matrices cannot be parenthesized because the sequence of matrices is incompatible.

      
All parenthesizations have the same number of scalar multiplications.

7)Let S = {a1, a2, ..., a10} be a set with n = 10 activities. The start time and finish time of each activity is shown below:

    si   fi
a1   9   11
a2   8   12
a3   13   17
a4   4   9
a5   1   3
a6   14   16
a7   10   15
a8   6   9
a9   4   7
a10   2   4
The objective is to find a maximum-size subset of mutually compatible activities. Apply the function GREEDY-ACTIVITY-SELECTOR learned in class. What is the subset of activity returned? Write the activities in the correct order in which they are selected by the algorithm.

Explanation / Answer

Multiple QUestion : Answering 6th

((A3A4)A5) = 5*20*80 + 5*80*4 = 9600
(A3(A4A5)) = 20*80*4 + 5*20*4 = 6800

answer : (A3(A4A5))

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