I need to write some Methods $($See TODO$)$ in a junit program that tests another class.

import java.util.LinkedList;

import java.util.Arrays;

import static org.junit.jupiter.api.Assertions.$*$;

import org.junit.jupiter.api.Test;

class PermutationTest $\{$

PermutationVariation p$1$;

PermutationVariation p$2$;

public int n$1$;

public int n$2$;

int cases$=0$;

void initialize$()\{$

n$1=4$;

n$2=6$;

Cases c$=$ new Cases$()$;

p$1=$ c$.$switchforTesting$($cases$,$ n$1)$;

p$2=$ c$.$switchforTesting$($cases$,$ n$2)$;

$\}$

private int factorial$($int n$)\{$

int result $=1$;

for $($int i $=2$; i $<=$ n; i$++)\{$

result $*=$ i;

$\}$

return result;

$\}$

$//$TODO test the constructor of the permutation class, the variable original needs to be initialized in the constructor with the given length, and no number is allowed to be used twice. allDerangements needs to be initialized with an empty list

@Test

void testPermutation$()\{$

initialize$()$;

assertNotNull$($p$1.$original$)$;

assertEquals$($n$1,$ p$1.$original.length$)$;

assertTrue$($Arrays$.$stream$($p$1.$original$).$distinct$().$count$()==$ n$1)$;

assertNotNull$($p$1.$allDerangements$)$;

assertTrue$($p$1.$allDerangements.isEmpty$())$;

$\}$

$//$TODO needs to test the derangement method of the permutation class, this method developes all the fixed point free permutations and saves them in allDerangements. This test meeds tp determine whether the number of derangements is correct and if they're actually derangements $($if its actually permutations in the next one$)$

@Test

void testDerangements$()\{$

initialize$()$;

fixConstructor$()$;

p$1.$derangements$()$;

assertNotNull$($p$1.$allDerangements$)$;

assertTrue$($p$1.$allDerangements.isEmpty$())$;

$//$ Check if all are derangements

for $($int$[]$ arr : p$1.$allDerangements$)\{$

for $($int i $=0$; i $<$ arr.length; i$++)\{$

assertNotEquals$($i$,$ arr$[$i$])$;

$\}$

$\}$

$//$ Check the count of derangements

double expectedCount $=$ factorial$($n$1)/$ Math.E;

assertEquals$($expectedCount$,$ p$1.$allDerangements.size$())$;

$\}$

$//$TODO test whether all of the in the derangement method developed sequences are actually permutations of the original array "orriginal", if there were no permutations calculated, this test should not work

@Test

void testsameElements$()\{$

initialize$()$;

fixConstructor$()$;

p$1.$derangements$()$;

for $($int$[]$ derangement : p$1.$allDerangements$)\{$

int$[]$ sortedDerangement $=$ Arrays.copyOf$($derangement$,$ derangement.length$)$;

Arrays.sort$($sortedDerangement$)$;

assertArrayEquals$($p$1.$original, sortedDerangement$)$;

$\}$

$\}$

void setCases$($int c$)\{$

this.cases$=$c;

$\}$

public void fixConstructor$()\{$

$//$in case there is something wrong with the constructor

p$1.$allDerangements$=$new LinkedList$()$;

for$($int i$=0$;i$()$;

for$($int i$=0$;i$()$;

$\}$

public void derangements$()\{$

backtracking$($new LinkedList$())$;

$\}$

public void backtracking$($LinkedList candidate$)\{$

int$[]$ o$=$this.original;

if $($candidate$.$size$()==$ o$.$length$)\{$

int$[]$ finalist$=$new int$[$o$.$length$]$;

for$($int i$=0$;i