i have a data structures assignment in binary search trees please use my class methods and attributes and understand it then answer the questions kindly write for each function a main program to test it after implementing each function

note i have a remove function that delete any node and deals with all special cases this is the question :

Remove Min

$(20$ points$)$

Write a function removeMin$2($self$)$ that will remove the minimum and the second minimum from

the current tree $($if it exists$).$

and this is the class:

class BST:

class $\_$Node:

def $\_\_$init$\_\_($self$,$ data, left$=$None, right$=$None$)$:

self.$\_$data $=$ data

self.$\_$left $=$ left

self.$\_$right $=$ right

self.$\_$depth $=0$

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

return $\text{'}(\{0\})\text{'}.$format$($self$.\_$data$)$

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

self.$\_$root $=$ None

def clear$($self$)$:

self.$\_$root $=$ None

def isEmpty$($self$)$:

return self.$\_$root is None

def rootVal$($self$)$:

if not self.isEmpty$()$:

return self.$\_$root.$\_$data

else:

raise TypeError$("$None value"$)$

def rootNode$($self$)$:

return self.$\_$root

def insert$($self$,$ val$)$:

newNode $=$ self.$\_$Node$($val$,$ None, None$)$

if self.isEmpty$()$:

self.$\_$root $=$ newNode

return

p $=$ None

c $=$ self.$\_$root

while c is not None:

p $=$ c

if val $>$ c$.\_$data:

c $=$ c$.\_$right

elif val $<$ c$.\_$data:

c $=$ c$.\_$left

else:

return

if val $>$ p$.\_$data:

p$.\_$right $=$ newNode

else:

p$.\_$left $=$ newNode

def $\_\_$contains$\_\_($self$,$ val$)$:

c $=$ self.$\_$root

while c is not None:

if val $==$ c$.\_$data:

return True

if val $<$ c$.\_$data:

c $=$ c$.\_$left

else:

c $=$ c$.\_$right

return False

def minT$($self$)$:

if self.isEmpty$()$:

print$("$Empty$")$ # or raise exception

return

c $=$ self.$\_$root

while c$.\_$left is not None:

c $=$ c$.\_$left

return c$.\_$data

def remove$($self$,$ val$)$:

prev $=$ None

k $=$ self.$\_$root

while k is not None:

if k$.\_$data $==$ val:

break

elif k$.\_$data $>$ val:

prev $=$ k

k $=$ k$.\_$left

else:

prev $=$ k

k $=$ k$.\_$right

if k is None:

return False

if k$.\_$left is None or k$.\_$right is None:

self.$\_$delSingle$($k$,$ prev$)$

else:

self.$\_$delDouble$($k$)$

return True

def $\_$delSingle$($self$,$ ptr$,$ prev$)$:

if ptr is self.$\_$root:

if self.$\_$root.$\_$left is None:

self.$\_$root $=$ self.$\_$root.$\_$right

else:

self.$\_$root $=$ self.$\_$root.$\_$left

elif ptr is prev.$\_$left:

if ptr$.\_$left is None:

prev.$\_$left $=$ ptr$.\_$right

else:

prev.$\_$left $=$ ptr$.\_$left

else:

if ptr$.\_$left is None:

prev.$\_$right $=$ ptr$.\_$right

else:

prev.$\_$right $=$ ptr$.\_$left

def $\_$delDouble$($self$,$ c$)$: # predecessor

prev $=$ c

rep $=$ c$.\_$left

while rep.$\_$right is not None:

prev $=$ rep

rep $=$ rep.$\_$right

c$.\_$data $=$ rep.$\_$data

self.$\_$delSingle$($rep$,$ prev$)$