# Inorder Successor in Binary Search Tree without Using Parent link

Objective: Given 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 search tree, a node x

Output: Inorder successor of node x.

Example:

InOrder Successor example

Approach:

Time Complexity : O(h) , h – height of the 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.

InOrder Successor – Case 1

Case 2: If the x doesn’t have a right child then its inorder successor will the one of its ancestors, use the binary search technique to find the node x, start from the root, if root is bigger than the x then go left, if root is less than x, go right. while traveling whenever you go left , store the node and call it successor.

InOrder Successor – use binray search techique – Case 2

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

Complete Code:

Output:

```Tree : 3 5 7 10 17 15
InOrder Successor of 7 is 10
InOrder Successor of 10 is 17
```

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If you find anything incorrect or you feel that there is any better approach to solve the above problem, please write comment.
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