Algorithms 3.Divide and Conquer(a) Multiply the following two matrices using Strassen's Multiplication(A*B).If you just show the steps without the computations you get 4 points;If you make errors in calculation you get 4 to 9 points.A=5 2B=[1 15 3(b) Give three examples of recursion that cannot be solved using the Mas-ters theorem formulas, and explain why they cannot be solved. Solvethe recursion for any one of them(c) Develop a divide and conquer algorithm to find the most frequently oc-curing number (mode) in a set of integers. Give the steps and computethe complexity of your methods Dynamic Programming(a) Find the grouping of the matrices that will minimize the number ofoperations to compute A1*A2*A3*A4. The sizes of the matrices areas follows;A1=2x1; A2=1x5; A3=5x2; A4=2x2If you just show the steps without the computations you get 4 points;If you make errors in calculation you get 4 to 9 points. Completelycorrect answer is 10 points.(b) For the problems given below, determine whether it is more efficient touse a divide and conquer strategy or a dynamic programming strategy.4.Give the recursion formula for each.Find the average of a given set of unsorted numbers.Find whether there is a subset of integers in a given set that addsi.ii.upto 8Given a set of numbers, can they set be partitioned into twogroups such that the sum of each group is equal; i.e 1,5,11,5 canbe partitioned to 1,5,5 and 11111.(c) State the difference between divide and conquer and dynamic pro-gramming.

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Multiply the following two matrices using Strassen's Multiplication (A*B). If you just show the steps without the computations you get 4 points; If you make errors in calculation you get 4 to 9 points. A= 5 2 2 3 B= 5 3

Multiply the following two matrices using Strassen's Multiplication (A*B). If you just show the steps without the computations you get 4 points; If you make errors in calculation you get 4 to 9 points. A= 5 2 2 3 B= 5 3

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ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

Algorithms

3.
Divide and Conquer
(a) Multiply the following two matrices using Strassen's Multiplication
(A*B).
If you just show the steps without the computations you get 4 points;
If you make errors in calculation you get 4 to 9 points.
A=
5 2
B=
[1 1
5 3
(b) Give three examples of recursion that cannot be solved using the Mas-
ters theorem formulas, and explain why they cannot be solved. Solve
the recursion for any one of them
(c) Develop a divide and conquer algorithm to find the most frequently oc-
curing number (mode) in a set of integers. Give the steps and compute
the complexity of your methods

Dynamic Programming
(a) Find the grouping of the matrices that will minimize the number of
operations to compute A1*A2*A3*A4. The sizes of the matrices are
as follows;
A1=2x1; A2=1x5; A3=5x2; A4=2x2
If you just show the steps without the computations you get 4 points;
If you make errors in calculation you get 4 to 9 points. Completely
correct answer is 10 points.
(b) For the problems given below, determine whether it is more efficient to
use a divide and conquer strategy or a dynamic programming strategy.
4.
Give the recursion formula for each.
Find the average of a given set of unsorted numbers.
Find whether there is a subset of integers in a given set that adds
i.
ii.
upto 8
Given a set of numbers, can they set be partitioned into two
groups such that the sum of each group is equal; i.e 1,5,11,5 can
be partitioned to 1,5,5 and 11
111.
(c) State the difference between divide and conquer and dynamic pro-
gramming.

Process or set of rules that allow for the solving of specific, well-defined computational problems through a specific series of commands. This topic is fundamental in computer science, especially with regard to artificial intelligence, databases, graphics, networking, operating systems, and security.

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