Combine the two permutations p$1$ and p$2$ into a result permutation p that represents the operation of first applying permutation p$2$ to the given array, followed by applying permutation p$1$ to this intermediate result.

public static int$[]$ chain$($int$[]$ p$1,$ int$[]$ p$2)\{$

int$[]$ p $=$ new int$[$p$1.$length$]$;

for $($int i $=0$; i $<$ p$1.$length; i$++)\{$

p$[$i$]=$ p$1[$p$2[$i$]]$;

$\}$

return p;

$\}$

$//$ Given the permutation perm, construct its inverse permutation that, when combined with perm, produces the identity permutation for which p$[$i$]==$ i for all positions i$.$

public static int$[]$ inverse$($int$[]$ perm$)\{$

int$[]$ inv $=$ new int$[$perm$.$length$]$;

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

inv$[$perm$[$i$]]=$ i;

$\}$

return inv;

$\}$

$//$ The square of the permutation is constructed by combining it with itself.

public static int$[]$ square$($int$[]$ perm$)\{$

return chain$($perm$,$ perm$)$;

$\}$

$//$ Compute the k$-$th power of the given permutation perm, that is$,$ the result of chaining perm with itself k times.

public static int$[]$ power$($int$[]$ perm, int k$)\{$

if $($k $==0)\{$

int$[]$ idenPerm $=$ new int$[$perm$.$length$]$;

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

idenPerm$[$i$]=$ i;

$\}$

return idenPerm;

$\}$ else if $($k $==1)\{$

return perm;

$\}$ else if $($k $==2)\{$

return square$($perm$)$;

$\}$ else if $($k $<0)\{$

return power$($inverse$($perm$),-$k$)$;

$\}$ else if $($k $\%2==0)\{$

int$[]$ tempPerm $=$ power$($perm$,$ k$/2)$;

return square$($tempPerm$)$;

$\}$ else $\{$

int$[]$ tempPerm $=$ power$($perm$,($k$-1)/2)$;

return chain$($perm$,$ square$($tempPerm$))$;

$\}$

$\}$

$//$ Main method for testing

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

int$[]$ perm$1=\{1,0,2,3\}$;

int$[]$ perm$2=\{1,3,6,0,5,2,4,7\}$;

int$[]$ perm$3=\{0,6,3,4,8,7,2,9,5,1\}$;

int$[]$ res$1=$ power$($perm$1,4)$;

int$[]$ res$2=$ power$($perm$2,98)$;

int$[]$ res$3=$ power$($perm$3,-397)$;

$//$ Print expected and actual results

System.out.println$("$Expected result for perm$1,4$: $\{0,1,2,3\}")$;

System.out.println$("$Actual result: $"+$ Arrays.toString$($res$1))$;

System.out.println$("$Expected result for perm$2,98$: $\{3,0,4,1,2,6,5,7\}")$;

System.out.println$("$Actual result: $"+$ Arrays.toString$($res$2))$;

System.out.println$("$Expected result for perm$3,-397$: $\{0,9,6,2,3,8,1,5,4,7\}")$;