# Find the in-order successor of a given node in a binary search tree

#### Note:

We can do in-order traversal, which will give us a sorted array and then find the in-order successor very easily.

- But the time complexity of in-order traversal in
**O(n).**

Where as finding the in-order successor is very frequently used operation. Hence, we need to find better solution.

- We will show the solution which will run in
**O(log(n)).**

We will assume the BST is constructed in a way that each node has a reference to its parent.

#### Case I : Node has a right subtree

In that case we need to find the left most node in its right subtree which is also the min (lowest) node in its right subtree.

#### Case II : Node does not have a right subtree

#### Pseudo code

```
inorderSuccessor (node n) {
if (n has a right subtree) {
return leftmost child of right subtree;
} else {
while (n is a right child of n.parent) {
n = n.parent; // Climb up
}
return n.parent; // Deepest ancestor in the path from root, for which the node would be in the left sub-tree
}
}
```

#### Solution

If we have a BST in which each node has a reference to its parent node then the following solution can give us the inOrderSuccessor of the given node.

- CTCI_6_4.6