$($python$)$# Hw$6$ BST: Implement a Node class for Binary Search Tree

class Node:

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

self.value $=$ value

self.left $=$ left

self.right $=$ right

# Return the smallest $($most left$)$ value of the BST

def min$($self$)$:

node $=$ self

while node and node.left:

node $=$ node.left

return node

# Task $1$: Return the largest $($most right$)$ value of the BST

def max$($self$)$:

# Print all elements in a list through pre order recursively

def preorder$\_$traversal$($self$)$:

self.$\_\_$listOfNodes $=[]$

self.$\_\_$preorderTraversal$($self$)$

print$($self$.\_\_$listOfNodes$)$

# Task $2$ Fullfill the inorder traversal function

def inorder$\_$traversal$($self$)$:

# Task $3$ Fullfill the postorder traversal function

def postorder$\_$traversal$($self$)$:

# Pre$-$Order Traversal of the Binary Search Tree

def $\_\_$preorderTraversal$($self$,$ node$)$:

if node $!=$ None:

self.$\_\_$listOfNodes.append$($node$.$value$)$

self.$\_\_$preorderTraversal$($node$.$left$)$

self.$\_\_$preorderTraversal$($node$.$right$)$

# In$-$Order Traversal of the Binary Search Tree

def $\_\_$inorderTraversal$($self$,$ node$)$:

#Post$-$Order Traversal of the Binary Search Tree

def $\_\_$postorderTraversal$($self$,$ node$)$:

# Insert value into node by following BST properties

def insert$($self$,$ value, node$=$None, root$=$True$)$:

if root:

node $=$ self

if node is None:

return Node$($value$)$

if value $<$ node.value:

node.left $=$ self.insert$($value$,$ node.left, False$)$

elif value $>$ node.value:

node.right $=$ self.insert$($value$,$ node.right, False$)$

else:

# Duplicate value, ignore it

return node

return node

# Task $4$ Create a function to do binary Search, return True$/$False

def search$($self$,$ value$)$:

# Task $5$ Run the following code to prove your program

val $=$ int$($input$("$Enter the first value $($root$)$ of your Binary Search Tree:"$))$

tree $=$ Node$($val$)$

while value $!=$"stop":

tree.insert$($int$($val$))$

value $=$ input$("$Enter another value of your Binary Search Tree:"$)$

print$("$In$-$order traversal:"$)$

tree.inorder$\_$traversal$()$

print$("$Pre$-$order traversal:"$)$

tree.preorder$\_$traversal$()$

print$("$post$-$order traversal:"$)$

tree.postorder$\_$traversal$()$

val $=$ int$($input$("$Enter the value to search in the BST: $"))$

print$($tree$.$search$($value$))$

print$("$The minimum is$",$ tree.min$().$value$)$

print$("$The maximum is$",$ tree.max$().$value$)$