Problem Description

Given two integer matrices, A and B$,$ you are asked to write a program to perform matrix addition $($A $+$ B$).$

Both matrices will have the same number of rows and columns.

You need to divide A and B into four equal $($or close to equal$)$ size submatrices $($I will refer to them as A$00,$ A$01,$ A$10,$ A$11$ and B$00,$ B$01,$ B$10,$ B$11)$

If the original matrices have R rows and C columns, then each submatrix should have dimensions close to $($R$/2)$ x $($C$/2).$ In other words, each submatrix should be about one$-$quarter the size of the original matrices.

You need to create four Java threads. Each thread performs addition on one pair of the submatrices. For example, thread $0$ performs addition on A$00$ and B$00,$ thread $1$ performs addition on A$01$ and B$01,...$ etc.

The final result should be stored in a matrix C of size R x C$.$

You must divide the two$-$dimensional array into the form such as: A$=[($A$\_00$&A$\_01$@A$\_10$&A$\_11)].$ Same for B and C$.$

Using the above example, if

A $=231251$

$312224$

$123272$

$361513$

Then the upper left corner is

A$\_00=231$

$312$

One of your threads is responsible for adding

A$\_00+$ B$\_00=$C$\_00$

Same as

$231+654=885$

$312332643$

List of classes that you will write:

Main $$ contains the main method.

ThreadOperation $$ extends Thread and performs submatrix addition

Instructions for Part $1$

For part $1$ you need to create both of the above classes.

In the main method of Main, instantiate four ThreadOperation objects, start them, and join them. Each ThreadOperation will take as input $($through the constructor$)$ two matrices and a quadrant indicator. The indicator could be a String, an int, an enum or a set of indexes. It$$s up to you.

In Main.java, write a static method named print$2$dArray that takes a two$-$dimensional array as input and prints it out with the rows and columns lined up$.$ You must use System.out.printf.

Instantiate a test $2$d array with any values you like in main and use it to verify that print$2$dArray works.

The filename should be given through the command prompt and passed into main via String$[]$ args

Open and connect to the file using a Scanner.

Read in the number of rows and columns and save these in local variables in main.

Read in the first and second matrices $($two$-$dimensional arrays$)$ from the file. I recommend writing a method to accomplish this task and calling the method twice $($once for each matrix$).$ Consider using this method header:

public static int$[][]$ matrixFromFile$($int rows, int columns, Scanner file$\_$reader$)$

NOTE: if you are using a static scanner or an object$-$oriented approach then you may not need to pass these arguments to the method.

Information on the file format

the first line has two numbers, R and C $($R rows, C columns$),$ the size of both matrices A and B

the next R lines each has C elements for one of the rows of A

the next R lines each has C elements for one of the rows of B

Example:

$46$

$231251$

$312224$

$123272$

$361513$

$654143$

$332211$

$754325$

$218484$

For the above example, $4$ is the number of rows, $6$ is the number of columns. The first matrix values are highlighted in green and the second matrix is highlighted in red. The result of the sum should be as follow:

$885394$

$644435$

$877597$

$579997$

Example: The upper left quadrants of the corresponding matrices $($highlighted in yellow$)$ will be added together

$46$

$231251$

$312224$

$123272$

$361513$

$654143$

$332211$

$754325$

$218484$

For your convenience, three test cases are provided: matrix$1.$txt$,$ matrix$2.$txt$,$ and matrix$3.$txt$.$

One of the goals is to minimize the resource usage, such as memory and processor cycles. Explain how multi$-$threaded code accomplishes this goal in your document. YOU MUST ANSWER THIS QUESTION IN A COMMENT AT THE TOP OF YOUR Main CLASS. Tell me about blocking on I$/$O$,$ multicore machines, how sluggish humans are, etcetera, and then tell me how multi$-$threading helps. Compare threads to processes and tell me the advantages of multi$-$threading. It doesn$$t have to be long. Three sentences will suffice if they are good sentences.

UML Diagram for Matrix Addition Part $1$

Main

$+$ print$2$dArray$($matrix: int$[][])$ : void

ThreadOperation

$-$ A : int$[][]$

$-$ B : int$[][]$

$-$ quadrant : String

$<>$ThreadOperation$($A : int$[][],$ B : int$[][],$ quadrant : String$)$

$+$ run$()$ : void

Compilation and Execution

test your program as follows:

javac $*.$java

java Main matrix$1.$txt

WE USE THIS AS A BASE

$/*$

This code is provided to give you a

starting place. It should be modified.

No further imports are needed.

$*/$

import java.io$.$IOException;

import java.io$.$File;

import java.util.Scanner;

public class Main

$\{$

public static void main$($String$[]$ args$)$

$\{$

System.out.println$()$;

$\}$

$\}$

TEST USING

$46$

$231251$

$312224$

$123272$

$361513$

$654143$

$332211$

$754325$

$218484$