$3.(50$ points$)$ Consider the following program:

class M $\{$

public static void main$($String $[]$ argv$)\{$

M obj $=$ new M$()$;

if $($argv$.$length $>0)$

obj.m$($argv$[0],$ argv.length$)$; $\}$

public void m$($String arg, int i$)\{$

int q $=1$;

A o $=$ null;

Impossible nothing $=$ new Impossible$()$;

if $($i $==0)$ q $=4$; q$++$; switch $($arg$.$length$())\{$

case $0$: q $/=2$; break;

case $1$: o $=$ new A$()$; new B$()$; q $=25$; break;

case $2$: o $=$ new A$()$; q $=$ q $*100$; $//$ no break

default: o $=$ new B$()$; break; $\}$

if $($arg$.$length$()>0)\{$ o$.$m$()$;

$\}$ else $\{$

System.out.println$("$zero$")$;

$\}$

nothing.happened$()$;

$\}$

$\}$

class A $\{$

public void m$()\{$

System.out.println$("$a$")$;

$\}$

$\}$

class B extends A $\{$

public void m$()\{$ System.out.println$("$b$")$;

$\}$

$\}$

class Impossible$\{$

public void happened$()\{$

$//"2$b$||!2$b$?",$ whatever the answer nothing happens here

$\}$

$\}$

a$)$ Using the minimal number of nodes $($hint: $11),$ draw a Control Flow Graph $($CFG$)$ for method

M$.$m$()$ and include it in your submission. The CFG should be at the level of basic blocks. See the lecture slides on CFG for examples.

$($b$)$ List the sets of Test Requirements $($TRs$)$ with respect to the CFG you drew in part $($a$)$ for each of the following coverages: node coverage; edge coverage; edge$-$pair coverage; and prime path$3$coverage. In other words, write four sets: TRNC $,$ TREC $,$ TREPC $,$ and TRPPC $.$ If there are infeasible test requirements, list them separately and explain why they are infeasible.

$($c$)$ Create test sets for method M$.$m$()$ that achieve each of the following coverages: $(1)$ node

coverage but not edge coverage; $(2)$ edge coverage but not edge$-$pair coverage; $(3)$ edge$-$pair

coverage but not prime path coverage; and $(4)$ prime path coverage. In other words, you will

write four test sets $($groups of test cases$)$ in total. One test set satisfies $(1),$ one satisfies $(2),$ one

satisfies $(3),$ and the last satisfies $(4),$ if possible. If it is not possible to write a test set to satisfy

$(1),(2),(3),$ or $(4),$ explain why. For each test case written, explain which TRs are satisfied by

that test. Consider feasible test requirements only for this part.