'''
inorder()function time complexity : O(n)
insert() function time complexity : O(n)
delete() function time complexity : O(n)
'''
# Python program to delete operation
# in binary search tree(BST)
# A Binary Tree Node
class Node:
# Constructor to create a new node
def __init__(self, key):
self.val = key
self.left = None
self.right = None
# A function to do inorder traversal
def inorder(root):
if root is not None:
inorder(root.left)
print(root.val, end=' ')
inorder(root.right)
# A function to insert a new node
def insert(root, key):
# if the tree is empty, return a new node
if root is None:
return Node(key)
# otherwise recur down the tree
if root.val < key:
root.right = insert(root.right, key)
else:
root.left = insert(root.left, key)
return root
# A function min key value found in that tree
def minValueNode(root):
while root.left is not None:
root = root.left
return root
# Given a binary search tree and a key, this function
# delete the key and returns the new root
def deleteNode(root, key):
# Base case
if root is None:
return root
# if the key to be deleted is smaller than the root's
# key then it lies in left subtree
if root.val > key:
root.left = deleteNode(root.left, key)
# if the key to be delete is greater then the root's key
# then it lies in right subtree
elif root.val < key:
root.right = deleteNode(root.right, key)
else:
# Node with only child or no child
if root.left is None:
temp = root.right
root = None
return temp
elif root.right is None:
temp = root.left
root = None
return temp
# Node with two children Get teh inorder successor
# smallest in the right subtree
temp = minValueNode(root.right)
# Copy the inorder successor's content to this node
root.val = temp.val
# Delete the inorder successor
root.right = deleteNode(root.right, temp.val)
return root
# Driver program to test above functions
if __name__ == '__main__':
""" Let us create following BST
50
/ \
30 70
/ \ / \
20 40 60 80
/
55
inorder traversal->[20, 30, 40, 50, 55, 60, 70, 80]
"""
root = None
root = insert(root, 80)
root = insert(root, 50)
root = insert(root, 30)
root = insert(root, 55)
root = insert(root, 20)
root = insert(root, 40)
root = insert(root, 70)
root = insert(root, 60)
print("Inorder traversal of the given tree")
inorder(root)
print("\n\nDelete->50")
root = deleteNode(root, 50)
print("Inorder traversal of the modified tree")
inorder(root)
print("\n\nDelete->20")
root = deleteNode(root, 20)
print("Inorder traversal of the modified tree")
inorder(root)
print("\n\nDelete->30")
root = deleteNode(root, 70)
print("Inorder traversal of the modified tree")
inorder(root)