In Binary Tree, Inorder successor of a node is the next node in Inorder traversal of the Binary Tree. Inorder Successor is NULL for the last node in Inorder traversal.
In Binary Search Tree, Inorder Successor of an input node can also be defined as the node with the smallest key greater than the key of input node. So, it is sometimes important to find next node in sorted order.

This algoritham is divided into two parts, on the basis of right subtree of the input node being empty or not.

Steps 

 1)If right subtree of node is not NULL, then succ lies in right subtree. Do following. Go to right subtree and return the node with minimum key value in right subtree.

2) If right subtree of node is NULL, then successor  is one of the ancestors. Do following. Travel up using the parent pointer until you see a node which is left child of it%u2019s parent. The parent of such a node is the successor.

Program:

# A binary tree node
class Node:

# Constructor to create a new node
def __init__(self, key):
self.data = key
self.left = None
self.right = None

def inOrderSuccessor(root, n):

# Step 1 of the above algorithm
if n.right is not None:
return minValue(n.right)

# Step 2 of the above algorithm
p = n.parent
while( p is not None):
if n != p.right :
break
n = p
p = p.parent
return p

# Given a non-empty binary search tree, return the minimum data value found in that tree. Note that the entire tree doesn't need to be searched
def minValue(node):
current = node

# loop down to find the leftmost leaf
while(current is not None):
if current.left is None:
break
current = current.left

return current


# Given a binary search tree and a number, inserts a new node with the given number in the correct place in the tree. Returns the new root pointer which the
#caller should then use( the standard trick to avoid
# using reference parameters)
def insert( node, data):

# 1) If tree is empty then return a new singly node
if node is None:
return Node(data)
else:

# 2) Otherwise, recur down the tree
if data <= node.data:
temp = insert(node.left, data)
node.left = temp
temp.parent = node
else:
temp = insert(node.right, data)
node.right = temp
temp.parent = node

# return the unchanged node pointer
return node


# Driver progam to test above function

root = None

# Creating the tree given in the above diagram
root = insert(root, 20)
root = insert(root, 8);
root = insert(root, 22);
root = insert(root, 4);
root = insert(root, 12);
root = insert(root, 10);
root = insert(root, 14);
temp = root.left.right.right

succ = inOrderSuccessor( root, temp)
if succ is not None:
print ("\nInorder Successor of %d is %d " %(temp.data , succ.data) )
else:
print ("\nInorder Successor doesn't exist")

Output:

Inorder Successor of 14 is 20 

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