please help with calculate permutations method in java must be recursive, no iteration and do not change method header lmport Java.util.ArrayList;

no usages

public class PartitionCalculator $\backslash \{$

no usages

public static int numOfPartitions $($int N$)\backslash \{$

return countPartitions$($N$,$N$)$;$//$ default return statement

$\backslash \}$

$3$ usages

private static int countPartitions$($int n $,$ int max$)\backslash \{$

if $($n $==0)\backslash \{$

return $1$;

$\backslash \}$ else if $\backslash (($n$<mn>0</mn><mi>)</mi><mtext></mtext><mi>\backslash </mi><mi>)</mi><mtext></mtext><mi>\backslash </mi><mi>\{</mi>$

return $0$;

$\backslash \}$ else if $($max $==0)\backslash \{$

return $0$;

$\backslash \}$ else $\backslash \{$

return countPartitions$($n$,$ max: max $-1)+$ countPartitions$($ n: n $-$ max, max$)$;

$\backslash (\backslash \}\backslash )$

$\backslash \}$

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public static ArrayList calculatePartitions $($int N$)\backslash \{$

$//$ no loops recursion only

$//$ For example if we call calculatePartitions$(4),$ there are a total of $5$ of them, the returned list

$//$should contain the following partitions $($in any order$)$: $```$

no usages

public static ArrayList calculatePartitions $($int N$)\{$

$//$ no loops recursion only

$//$ For example if we call calculatePartitions$(4),$ there are a total of $5$ of them, the returned list

$//$should contain the following partitions $($in any order$)$:

$//1.[4]$

$//2.[3,1]\backslash$Leftrightarrow$[1,3]$

$//3.[2,2]$

$//4.[2,1,1]\backslash$Leftrightarrow$[1,2,1]\backslash$Leftrightarrow$[1,1,2]$

$//5.[1,1,1,1]$

return null;

$\}$

no usages

public static ArrayList calculateAllPermutations$($ArrayList partitions$)\{$

return partitions;

$\}$

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

$//$ Testing the function with example given in the problem

System.out.println$("$Number of partitions for $5$: $"+$ numOfPartitions$($ N: $5))$; $//$ Output: $7$

$\}$

$```$