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# Inorder Successor in Binary Tree

Algorithms - Inorder Successor in Binary Tree

Objective: Given a Binary tree (Not a Binary Search Tree ), find the inorder successor of a node.

What is Inorder Successor: Inorder successor of a node is the next node in the inorder traversal of the tree. For the last node in a tree, inorder successor will be NULL

Input: A binary tree, a node x

Output: Inorder successor of node x.

Example:

Approach:

NOTE: since it's not a binary search tree, we cannot use binary search technique to reach to the node. we need to travel all the nodes in order to find the node for which we need to find the inorder successor.

How to search for a path of any node in binary tree.

There will be 3 cases to solve this problem

Say the node for which inorder successor needs to be find is x.

Case 1 : If the x has a right child then its inorder successor will the left most element in the right sub tree of x.

1. Start from the root and compare it with x, if matched then we have found the node.
2. else go left and right.
3. recursively do step 2 and 3 till you find the node x.
4. Now when you have found the node, stop the recursion.
5. Now recursion will backtrack to the root, every recursive call will return the node itself (say it will be stored in n) so when it backtracked to its parent which will be root now, check whether parent.left = n, if not , keep going up.

Case 3: if x is the right most node in the tree then its inorder successor will be NULL.

Code:

```Tree : d b i j x e a f c g
The In Order Successor for 'x' is e
The In Order Successor for 'a' is f
InOrder Successor of g is NULL
```