Implement the disjoint set data structure. You can choose any programming language that the grader can understand, but you might have to change the mandatory unit test and adapt the following layout.

$```$

class Element:

def $\_\_$init$\_\_($self$,$ nr$)$:

self.id $=$ nr

self.ptr $=$ self

self.length $=1$

def $\_\_$str$\_\_($self$)$:

return f$\text{'}\{$self$.$id$\}(\{$self$.$length$\})->\{$self$.$ptr$.$id$\}\text{'}$

def lookup$($self$)$:

$"""$returns the leader of the set self is in$.$ The set is

compacted, meaning that all nodes on the path to the

leader now point directly to the leader."""

def join$($self$,$ other$)$:

$"""$ joins the leader of the smaller set with the leader of the

larger set.

The length of the leader of the smaller set is $0."""$

$```$

The unit test is as follows:

$```$

def show$($eles$)$:

for ele in eles:

print$($ele$)$

print$()$

eles $=[$Element$($i$)$ for i in range$(20)]$

eles$[0].$join$($eles$[1])$

eles$[2].$join$($eles$[3])$

eles$[0].$join$($eles$[2])$

eles$[5].$join$($eles$[6])$

eles$[7].$join$($eles$[6])$

eles$[3].$join$($eles$[7])$

eles$[4].$join$($eles$[2])$

eles$[8].$join$($eles$[9])$

eles$[9].$join$($eles$[6])$

eles$[10].$join$($eles$[11])$

eles$[10].$join$($eles$[12])$

eles$[14].$join$($eles$[12])$

eles$[13].$join$($eles$[10])$

eles$[15].$join$($eles$[14])$

eles$[16].$join$($eles$[15])$

eles$[17].$join$($eles$[18])$

$```$

eles$[19].$join$($eles$[18])$

eles$[17].$join$($eles$[14])$

show$($eles$)$

and should give you the following output: