# Inorder Successor of a node in Binary Tree

Given a binary tree and a node, we need to write a program to find inorder successor of this node.

Inorder Successor of a node in binary tree is the next node in Inorder traversal of the Binary Tree. Inorder Successor is NULL for the last node in Inoorder traversal. In the above diagram, inorder successor of node 4 is 2 and node 5 is 1.

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

We have already discussed how to find the inorder successor of a node in Binary Search Tree. We can not use the same approach to find the inorder successor in general Binary trees.

We need to take care of 3 cases for any node to find its inorder successor as described below:

1. Right child of node is not NULL. If the right child of the node is not NULL then the inorder successor of this node will be the leftmost node in it’s right subtree.
2. Right Child of the node is NULL. If the right child of node is NULL. Then we keep finding the parent of the given node x, say p such that p->left = x. For example in the above given tree, inorder successor of node 5 will be 1. First parent of 5 is 2 but 2->left != 5. So next parent of 2 is 1, now 1->left = 2. Therefore, inorder successor of 5 is 1.
Below is the algorithm for this case:

• Suppose the given node is x. Start traversing the tree from root node to find x recursively.
• If root == x, stop recursion otherwise find x recursively for left and right subtrees.
• Now after finding the node x, recur­sion will back­track to the root. Every recursive call will return the node itself to the calling function, we will store this in a temporary node say temp.Now, when it back­tracked to its par­ent which will be root now, check whether root.left = temp, if not , keep going up
• .

3. If node is the rightmost node. If the node is the rightmost node in the given tree. For example, in the above tree node 6 is the right most node. In this case, there will be no inorder successor of this node. i.e. Inorder Successor of the rightmost node in a tree is NULL.

Below is the implementation of above approach:

## C++

 `// CPP program to find inorder successor of a node ` `#include ` `using` `namespace` `std; ` ` `  `// A Binary Tree Node ` `struct` `Node ` `{ ` `    ``int` `data; ` `    ``struct` `Node *left, *right; ` `}; ` ` `  `// Temporary node for case 2 ` `Node* temp = ``new` `Node; ` ` `  `// Utility function to create a new tree node ` `Node* newNode(``int` `data) ` `{ ` `    ``Node *temp = ``new` `Node; ` `    ``temp->data = data; ` `    ``temp->left = temp->right = NULL; ` `    ``return` `temp; ` `} ` ` `  `// function to find left most node in a tree ` `Node* leftMostNode(Node* node) ` `{ ` `    ``while` `(node != NULL && node->left != NULL) ` `        ``node = node->left; ` `    ``return` `node; ` `} ` ` `  `// function to find right most node in a tree ` `Node* rightMostNode(Node* node) ` `{ ` `    ``while` `(node != NULL && node->right != NULL) ` `        ``node = node->right; ` `    ``return` `node; ` `} ` ` `  `// recursive function to find the Inorder Scuccessor ` `// when the right child of node x is NULL ` `Node* findInorderRecursive(Node* root, Node* x ) ` `{ ` `    ``if` `(!root) ` `        ``return` `NULL; ` ` `  `    ``if` `(root==x || (temp = findInorderRecursive(root->left,x)) || ` `                   ``(temp = findInorderRecursive(root->right,x))) ` `    ``{ ` `        ``if` `(temp) ` `        ``{ ` `            ``if` `(root->left == temp) ` `            ``{ ` `                ``cout << ``"Inorder Successor of "` `<< x->data; ` `                ``cout << ``" is "``<< root->data << ``"\n"``; ` `                ``return` `NULL; ` `            ``} ` `        ``} ` ` `  `        ``return` `root; ` `    ``} ` ` `  `    ``return` `NULL; ` `} ` ` `  `// function to find inorder successor of  ` `// a node ` `void` `inorderSuccesor(Node* root, Node* x) ` `{ ` `    ``// Case1: If right child is not NULL ` `    ``if` `(x->right != NULL) ` `    ``{ ` `        ``Node* inorderSucc = leftMostNode(x->right); ` `        ``cout<<``"Inorder Successor of "``<data<<``" is "``; ` `        ``cout<data<<``"\n"``; ` `    ``} ` ` `  `    ``// Case2: If right child is NULL ` `    ``if` `(x->right == NULL) ` `    ``{     ` `        ``int` `f = 0; ` `         `  `        ``Node* rightMost = rightMostNode(root); ` ` `  `        ``// case3: If x is the right most node ` `        ``if` `(rightMost == x) ` `            ``cout << ``"No inorder successor! Right most node.\n"``; ` `        ``else` `            ``findInorderRecursive(root, x); ` `    ``} ` `} ` ` `  `// Driver program to test above functions ` `int` `main() ` `{ ` `    ``// Let's construct the binary tree  ` `    ``// as shown in above diagram ` ` `  `    ``Node* root = newNode(1); ` `    ``root->left = newNode(2); ` `    ``root->right = newNode(3); ` `    ``root->left->left = newNode(4); ` `    ``root->left->right = newNode(5); ` `    ``root->right->right = newNode(6); ` ` `  `    ``// Case 1  ` `    ``inorderSuccesor(root, root->right); ` ` `  `    ``// case 2 ` `    ``inorderSuccesor(root, root->left->left); ` ` `  `    ``// case 3 ` `    ``inorderSuccesor(root, root->right->right); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find inorder successor of a node  ` `class` `Solution ` `{ ` `// A Binary Tree Node  ` ` ``static` `class` `Node ` `{  ` `    ``int` `data;  ` `     ``Node left, right;  ` `}  ` ` `  `// Temporary node for case 2  ` `static` `Node temp = ``new` `Node(); ` ` `  `// Utility function to create a new tree node  ` `static` `Node newNode(``int` `data)  ` ` ``{ ` `    ``Node temp = ``new` `Node();  ` `    ``temp.data = data;  ` `    ``temp.left = temp.right = ``null``;  ` `    ``return` `temp;  ` `}  ` ` `  `// function to find left most node in a tree  ` `static` `Node leftMostNode(Node node)  ` ` ``{ ` `    ``while` `(node != ``null` `&& node.left != ``null``)  ` `        ``node = node.left;  ` `    ``return` `node;  ` `}  ` ` `  `// function to find right most node in a tree  ` `static` `Node rightMostNode(Node node)  ` ` ``{ ` `    ``while` `(node != ``null` `&& node.right != ``null``)  ` `        ``node = node.right;  ` `    ``return` `node;  ` `}  ` ` `  `// recursive function to find the Inorder Scuccessor  ` `// when the right child of node x is null  ` `static` `Node findInorderRecursive(Node root, Node x )  ` ` ``{ ` `    ``if` `(root==``null``)  ` `        ``return` `null``;  ` ` `  `    ``if` `(root==x || (temp = findInorderRecursive(root.left,x))!=``null` `||  ` `                ``(temp = findInorderRecursive(root.right,x))!=``null``)  ` `    ``{  ` `        ``if` `(temp!=``null``)  ` `        ``{  ` `            ``if` `(root.left == temp)  ` `            ``{  ` `                ``System.out.print( ``"Inorder Successor of "``+x.data);  ` `                ``System.out.print( ``" is "``+ root.data + ``"\n"``);  ` `                ``return` `null``;  ` `            ``}  ` `        ``}  ` ` `  `        ``return` `root;  ` `    ``}  ` ` `  `    ``return` `null``;  ` `}  ` ` `  `// function to find inorder successor of  ` `// a node  ` `static` `void` `inorderSuccesor(Node root, Node x)  ` ` ``{ ` `    ``// Case1: If right child is not null  ` `    ``if` `(x.right != ``null``)  ` `    ``{  ` `        ``Node inorderSucc = leftMostNode(x.right);  ` `        ``System.out.print(``"Inorder Successor of "``+x.data+``" is "``);  ` `        ``System.out.print(inorderSucc.data+``"\n"``);  ` `    ``}  ` ` `  `    ``// Case2: If right child is null  ` `    ``if` `(x.right == ``null``)  ` `    ``{      ` `        ``int` `f = ``0``;  ` `         `  `        ``Node rightMost = rightMostNode(root); ` ` `  `        ``// case3: If x is the right most node  ` `        ``if` `(rightMost == x)  ` `            ``System.out.print(``"No inorder successor! Right most node.\n"``);  ` `        ``else` `            ``findInorderRecursive(root, x);  ` `    ``}  ` `}  ` ` `  `// Driver program to test above functions  ` `public` `static` `void` `main(String args[]) ` `{  ` `    ``// Let's con the binary tree  ` `    ``// as shown in above diagram  ` ` `  `    ``Node root = newNode(``1``);  ` `    ``root.left = newNode(``2``);  ` `    ``root.right = newNode(``3``);  ` `    ``root.left.left = newNode(``4``);  ` `    ``root.left.right = newNode(``5``);  ` `    ``root.right.right = newNode(``6``);  ` ` `  `    ``// Case 1  ` `    ``inorderSuccesor(root, root.right);  ` ` `  `    ``// case 2  ` `    ``inorderSuccesor(root, root.left.left);  ` ` `  `    ``// case 3  ` `    ``inorderSuccesor(root, root.right.right);  ` ` `  `}  ` `} ` `//contributed by Arnab Kundu `

## Python3

 `""" Python3 code for inorder succesor  ` `and predecessor of tree """` ` `  `# A Binary Tree Node  ` `# Utility function to create a new tree node  ` `class` `newNode:  ` ` `  `    ``# Constructor to create a new node  ` `    ``def` `__init__(``self``, data):  ` `        ``self``.data ``=` `data  ` `        ``self``.left ``=` `None` `        ``self``.right ``=` `None` ` `  `# function to find left most node in a tree  ` `def` `leftMostNode(node): ` ` `  `    ``while` `(node !``=` `None` `and` `node.left !``=` `None``): ` `        ``node ``=` `node.left  ` `    ``return` `node  ` ` `  `# function to find right most node in a tree  ` `def` `rightMostNode(node): ` `    ``while` `(node !``=` `None` `and` `node.right !``=` `None``): ` `        ``node ``=` `node.right  ` `    ``return` `node ` ` `  `# recursive function to find the Inorder Scuccessor  ` `# when the right child of node x is None  ` `def` `findInorderRecursive(root, x ): ` ` `  `    ``if` `(``not` `root): ` `        ``return` `None` `    ``if` `(root ``=``=` `x ``or` `(findInorderRecursive(root.left, x)) ``or` `                     ``(findInorderRecursive(root.right, x))): ` `        ``if` `findInorderRecursive(root.right, x): ` `            ``temp``=``findInorderRecursive(root.right, x) ` `        ``else``: ` `            ``temp``=``findInorderRecursive(root.left, x) ` `        ``if` `(temp):  ` `         `  `            ``if` `(root.left ``=``=` `temp):  ` `             `  `                ``print``(``"Inorder Successor of"``,  ` `                            ``x.data, end ``=` `"") ` `                ``print``(``" is"``, root.data)  ` `                ``return` `None`  `        ``return` `root  ` `    ``return` `None` ` `  `# function to find inorder successor  ` `# of a node  ` `def` `inorderSuccesor(root, x): ` `     `  `    ``# Case1: If right child is not None  ` `    ``if` `(x.right !``=` `None``) : ` `        ``inorderSucc ``=` `leftMostNode(x.right)  ` `        ``print``(``"Inorder Successor of"``, x.data, ` `                             ``"is"``, end ``=` `" "``)  ` `        ``print``(inorderSucc.data)  ` `         `  `    ``# Case2: If right child is None  ` `    ``if` `(x.right ``=``=` `None``): ` `        ``f ``=` `0` `        ``rightMost ``=` `rightMostNode(root)  ` ` `  `        ``# case3: If x is the right most node  ` `        ``if` `(rightMost ``=``=` `x): ` `            ``print``(``"No inorder successor!"``, ` `                       ``"Right most node."``)  ` `        ``else``: ` `            ``findInorderRecursive(root, x) ` `     `  `# Driver Code ` `if` `__name__ ``=``=` `'__main__'``:  ` ` `  `    ``root ``=` `newNode(``1``)  ` `    ``root.left ``=` `newNode(``2``)  ` `    ``root.right ``=` `newNode(``3``)  ` `    ``root.left.left ``=` `newNode(``4``)  ` `    ``root.left.right ``=` `newNode(``5``)  ` `    ``root.right.right ``=` `newNode(``6``)  ` ` `  `    ``# Case 1  ` `    ``inorderSuccesor(root, root.right)  ` ` `  `    ``# case 2  ` `    ``inorderSuccesor(root, root.left.left) ` ` `  `    ``# case 3  ` `    ``inorderSuccesor(root, root.right.right) ` ` `  `# This code is contributed ` `# by SHUBHAMSINGH10 `

## C#

 `// C# program to find inorder ` `// successor of a node  ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `// A Binary Tree Node  ` `public` `class` `Node ` `{ ` `    ``public` `int` `data; ` `    ``public` `Node left, right; ` `} ` ` `  `// Temporary node for case 2  ` `public` `static` `Node temp = ``new` `Node(); ` ` `  `// Utility function to create  ` `// a new tree node  ` `public` `static` `Node newNode(``int` `data) ` `{ ` `    ``Node temp = ``new` `Node(); ` `    ``temp.data = data; ` `    ``temp.left = temp.right = ``null``; ` `    ``return` `temp; ` `} ` ` `  `// function to find left most ` `// node in a tree  ` `public` `static` `Node leftMostNode(Node node) ` `{ ` `    ``while` `(node != ``null` `&&  ` `        ``node.left != ``null``) ` `    ``{ ` `        ``node = node.left; ` `    ``} ` `    ``return` `node; ` `} ` ` `  `// function to find right most  ` `// node in a tree  ` `public` `static` `Node rightMostNode(Node node) ` `{ ` `    ``while` `(node != ``null` `&& ` `        ``node.right != ``null``) ` `    ``{ ` `        ``node = node.right; ` `    ``} ` `    ``return` `node; ` `} ` ` `  `// recursive function to find the  ` `// Inorder Scuccessor when the right ` `// child of node x is null  ` `public` `static` `Node findInorderRecursive(Node root,  ` `                                        ``Node x) ` `{ ` `    ``if` `(root == ``null``) ` `    ``{ ` `        ``return` `null``; ` `    ``} ` ` `  `    ``if` `(root == x || ` `    ``(temp = findInorderRecursive(root.left, x)) != ``null` `||  ` `    ``(temp = findInorderRecursive(root.right, x)) != ``null``) ` `    ``{ ` `        ``if` `(temp != ``null``) ` `        ``{ ` `            ``if` `(root.left == temp) ` `            ``{ ` `                ``Console.Write(``"Inorder Successor of "` `+ x.data); ` `                ``Console.Write(``" is "` `+ root.data + ``"\n"``); ` `                ``return` `null``; ` `            ``} ` `        ``} ` ` `  `        ``return` `root; ` `    ``} ` ` `  `    ``return` `null``; ` `} ` ` `  `// function to find inorder successor  ` `// of a node  ` `public` `static` `void` `inorderSuccesor(Node root, Node x) ` `{ ` `    ``// Case1: If right child is not null  ` `    ``if` `(x.right != ``null``) ` `    ``{ ` `        ``Node inorderSucc = leftMostNode(x.right); ` `        ``Console.Write(``"Inorder Successor of "` `+  ` `                            ``x.data + ``" is "``); ` `        ``Console.Write(inorderSucc.data + ``"\n"``); ` `    ``} ` ` `  `    ``// Case2: If right child is null  ` `    ``if` `(x.right == ``null``) ` `    ``{ ` `        ``int` `f = 0; ` ` `  `        ``Node rightMost = rightMostNode(root); ` ` `  `        ``// case3: If x is the right most node  ` `        ``if` `(rightMost == x) ` `        ``{ ` `            ``Console.Write(``"No inorder successor! "` `+  ` `                            ``"Right most node.\n"``); ` `        ``} ` `        ``else` `        ``{ ` `            ``findInorderRecursive(root, x); ` `        ``} ` `    ``} ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main(``string``[] args) ` `{ ` `    ``// Let's con the binary tree  ` `    ``// as shown in above diagram  ` `    ``Node root = newNode(1); ` `    ``root.left = newNode(2); ` `    ``root.right = newNode(3); ` `    ``root.left.left = newNode(4); ` `    ``root.left.right = newNode(5); ` `    ``root.right.right = newNode(6); ` ` `  `    ``// Case 1  ` `    ``inorderSuccesor(root, root.right); ` ` `  `    ``// case 2  ` `    ``inorderSuccesor(root, root.left.left); ` ` `  `    ``// case 3  ` `    ``inorderSuccesor(root, root.right.right); ` `} ` `} ` ` `  `// This code is contributed by Shrikant13 `

Output:

```Inorder Successor of 3 is 6
Inorder Successor of 4 is 2
No inorder successor! Right most node.
```

Another approach:
We will do a reverse inorder traversal and keep the track of current visited node. Once we found the element, last tracked element would be our answer.

Below is the implementation of above approach:

## Java

 `// Java program to find inorder successor of a node. ` ` `  `class` `Node { ` `    ``int` `data; ` `    ``Node left, right; ` ` `  `    ``Node(``int` `data) { ` `        ``this``.data = data; ` `        ``left = ``null``; right = ``null``; ` `    ``} ` `} ` ` `  `// class to find inorder successor of  ` `// a node  ` `class` `InorderSuccessor { ` `    ``Node root; ` `     `  `    ``// to change previous node ` `    ``static` `class` `PreviousNode { ` `        ``Node pNode; ` `        ``PreviousNode() { ` `            ``pNode = ``null``; ` `        ``} ` `    ``} ` `     `  `    ``// function to find inorder successor of  ` `    ``// a node  ` `    ``private` `void` `inOrderSuccessorOfBinaryTree(Node root,  ` `                    ``PreviousNode pre, ``int` `searchNode)  ` `    ``{ ` `        ``// Case1: If right child is not NULL  ` `        ``if``(root.right != ``null``)  ` `        ``inOrderSuccessorOfBinaryTree(root.right, pre, searchNode); ` `         `  `        ``// Case2: If root data is equal to search node ` `        ``if``(root.data == searchNode)  ` `        ``System.out.println(``"inorder successor of "` `+ searchNode + ``" is: "` `                            ``+ (pre.pNode != ``null` `? pre.pNode.data : ``"null"``)); ` `            ``pre.pNode = root; ` `             `  `        ``if``(root.left != ``null``)  ` `        ``inOrderSuccessorOfBinaryTree(root.left, pre, searchNode); ` `    ``} ` `     `  `    ``// Driver program to test above functions  ` `    ``public` `static` `void` `main(String[] args)  ` `    ``{ ` `        ``InorderSuccessor tree = ``new` `InorderSuccessor(); ` `         `  `        ``// Let's construct the binary tree  ` `        ``// as shown in above diagram  ` `        ``tree.root = ``new` `Node(``1``);  ` `        ``tree.root.left = ``new` `Node(``2``);  ` `        ``tree.root.right = ``new` `Node(``3``);  ` ` `  `        ``tree.root.left.left = ``new` `Node(``4``);  ` `        ``tree.root.left.right = ``new` `Node(``5``);  ` `        ``tree.root.right.right = ``new` `Node(``6``);  ` `         `  `        ``// Case 1 ` `        ``tree.inOrderSuccessorOfBinaryTree(tree.root,  ` `                                        ``new` `PreviousNode(), ``3``); ` `         `  `        ``// Case 2 ` `        ``tree.inOrderSuccessorOfBinaryTree(tree.root,  ` `                                           ``new` `PreviousNode(), ``4``); ` `         `  `        ``// Case 3 ` `        ``tree.inOrderSuccessorOfBinaryTree(tree.root,  ` `                                          ``new` `PreviousNode(), ``6``); ` `    ``} ` `} ` `// This code is contributed by Ashish Goyal.  `

## C#

 `// C# program to find inorder successor of a node. ` `using` `System; ` ` `  `class` `Node  ` `{ ` `    ``public` `int` `data; ` `    ``public` `Node left, right; ` ` `  `    ``public` `Node(``int` `data)  ` `    ``{ ` `        ``this``.data = data; ` `        ``left = ``null``; right = ``null``; ` `    ``} ` `} ` ` `  `// class to find inorder successor of  ` `// a node  ` `public` `class` `InorderSuccessor ` `{ ` `    ``Node root; ` `     `  `    ``// to change previous node ` `    ``class` `PreviousNode ` `    ``{ ` `        ``public` `Node pNode; ` `        ``public` `PreviousNode()  ` `        ``{ ` `            ``pNode = ``null``; ` `        ``} ` `    ``} ` `     `  `    ``// function to find inorder successor of  ` `    ``// a node  ` `    ``private` `void` `inOrderSuccessorOfBinaryTree(Node root,  ` `                    ``PreviousNode pre, ``int` `searchNode)  ` `    ``{ ` `        ``// Case1: If right child is not NULL  ` `        ``if``(root.right != ``null``)  ` `        ``inOrderSuccessorOfBinaryTree(root.right, ` `                                ``pre, searchNode); ` `         `  `        ``// Case2: If root data is equal to search node ` `        ``if``(root.data == searchNode) ` `        ``{ ` `            ``Console.Write(``"inorder successor of "` `+  ` `                            ``searchNode + ``" is: "``); ` `            ``if``(pre.pNode != ``null``) ` `                ``Console.WriteLine(pre.pNode.data); ` `            ``else` `                ``Console.WriteLine(``"null"``); ` `        ``} ` `            ``pre.pNode = root; ` `             `  `        ``if``(root.left != ``null``)  ` `            ``inOrderSuccessorOfBinaryTree(root.left, ` `                                ``pre, searchNode); ` `    ``} ` `     `  `    ``// Driver code  ` `    ``public` `static` `void` `Main(String[] args)  ` `    ``{ ` `        ``InorderSuccessor tree = ``new` `InorderSuccessor(); ` `         `  `        ``// Let's construct the binary tree  ` `        ``// as shown in above diagram  ` `        ``tree.root = ``new` `Node(1);  ` `        ``tree.root.left = ``new` `Node(2);  ` `        ``tree.root.right = ``new` `Node(3);  ` ` `  `        ``tree.root.left.left = ``new` `Node(4);  ` `        ``tree.root.left.right = ``new` `Node(5);  ` `        ``tree.root.right.right = ``new` `Node(6);  ` `         `  `        ``// Case 1 ` `        ``tree.inOrderSuccessorOfBinaryTree(tree.root,  ` `                                        ``new` `PreviousNode(), 3); ` `         `  `        ``// Case 2 ` `        ``tree.inOrderSuccessorOfBinaryTree(tree.root,  ` `                                        ``new` `PreviousNode(), 4); ` `         `  `        ``// Case 3 ` `        ``tree.inOrderSuccessorOfBinaryTree(tree.root,  ` `                                        ``new` `PreviousNode(), 6); ` `    ``} ` `} ` ` `  `// This code is contributed by PrinciRaj1992 `

Output:

```inorder successor of 3 is: 6
inorder successor of 4 is: 2
inorder successor of 6 is: null
```

Time Complexity: O( n ), where n is the number of nodes in the tree.
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