# Find right sibling of a binary tree with parent pointers

Given a binary tree with parent pointers, find the right sibling of a given node(pointer to the node will be given), if it doesnâ€™t exist return null. Do it in O(1) space and O(n) time?

Examples:

```             1
/ \
2   3
/  \  \
4    6  5
/      \  \
7        9  8
/         \
10         12
Input : Given above tree with parent pointer and node 10
Output : 12 ```

Approach: The idea is to find out the first right child of the nearest ancestor which is neither the current node nor the parent of the current node, keep track of the level in those while going up. then, iterate through that node first left child, if the left is not there then, right child and if the level becomes 0, then, this is the next right sibling of the given node.
In the above case, if the given node is 7, we will end up with 6 to find the right child which doesn’t have any child.

In this case, we need to recursively call for the right sibling with the current level, so that we case reach 8.

Implementation:

## C++

 `// C program to print right sibling of a node` `#include `   `// A Binary Tree Node` `struct` `Node {` `    ``int` `data;` `    ``Node *left, *right, *parent;` `};`   `// A utility function to create a new Binary` `// Tree Node` `Node* newNode(``int` `item, Node* parent)` `{` `    ``Node* temp = ``new` `Node;` `    ``temp->data = item;` `    ``temp->left = temp->right = NULL;` `    ``temp->parent = parent;` `    ``return` `temp;` `}`   `// Method to find right sibling` `Node* findRightSibling(Node* node, ``int` `level)` `{` `    ``if` `(node == NULL || node->parent == NULL)` `        ``return` `NULL;`   `    ``// GET Parent pointer whose right child is not` `    ``// a parent or itself of this node. There might` `    ``// be case when parent has no right child, but,` `    ``// current node is left child of the parent` `    ``// (second condition is for that).` `    ``while` `(node->parent->right == node` `           ``|| (node->parent->right == NULL` `               ``&& node->parent->left == node)) {` `        ``if` `(node->parent == NULL` `            ``|| node->parent->parent == NULL)` `            ``return` `NULL;`   `        ``node = node->parent;` `        ``level--;` `    ``}`   `    ``// Move to the required child, where right sibling` `    ``// can be present` `    ``node = node->parent->right;`   `    ``if` `(node == NULL)` `        ``return` `NULL;` `    ``// find right sibling in the given subtree(from current` `    ``// node), when level will be 0` `    ``while` `(level < 0) {`   `        ``// Iterate through subtree` `        ``if` `(node->left != NULL)` `            ``node = node->left;` `        ``else` `if` `(node->right != NULL)` `            ``node = node->right;` `        ``else`   `            ``// if no child are there, we cannot have right` `            ``// sibling in this path` `            ``break``;`   `        ``level++;` `    ``}`   `    ``if` `(level == 0)` `        ``return` `node;`   `    ``// This is the case when we reach 9 node in the tree,` `    ``// where we need to again recursively find the right` `    ``// sibling` `    ``return` `findRightSibling(node, level);` `}`   `// Driver Program to test above functions` `int` `main()` `{` `    ``Node* root = newNode(1, NULL);` `    ``root->left = newNode(2, root);` `    ``root->right = newNode(3, root);` `    ``root->left->left = newNode(4, root->left);` `    ``root->left->right = newNode(6, root->left);` `    ``root->left->left->left = newNode(7, root->left->left);` `    ``root->left->left->left->left = newNode(10, root->left->left->left);` `    ``root->left->right->right = newNode(9, root->left->right);` `    ``root->right->right = newNode(5, root->right);` `    ``root->right->right->right = newNode(8, root->right->right);` `    ``root->right->right->right->right = newNode(12, root->right->right->right);`   `    ``// passing 10` `    ``Node* res = findRightSibling(root->left->left->left->left, 0);` `    ``if` `(res == NULL)` `        ``printf``(``"No right sibling"``);` `    ``else` `        ``printf``(``"%d"``, res->data);`   `    ``return` `0;` `}`

## Java

 `// Java program to print right sibling of a node` `public` `class` `Right_Sibling {`   `    ``// A Binary Tree Node` `    ``static` `class` `Node {` `        ``int` `data;` `        ``Node left, right, parent;`   `        ``// Constructor` `        ``public` `Node(``int` `data, Node parent)` `        ``{` `            ``this``.data = data;` `            ``left = ``null``;` `            ``right = ``null``;` `            ``this``.parent = parent;` `        ``}` `    ``};`   `    ``// Method to find right sibling` `    ``static` `Node findRightSibling(Node node, ``int` `level)` `    ``{` `        ``if` `(node == ``null` `|| node.parent == ``null``)` `            ``return` `null``;`   `        ``// GET Parent pointer whose right child is not` `        ``// a parent or itself of this node. There might` `        ``// be case when parent has no right child, but,` `        ``// current node is left child of the parent` `        ``// (second condition is for that).` `        ``while` `(node.parent.right == node` `               ``|| (node.parent.right == ``null` `                   ``&& node.parent.left == node)) {` `            ``if` `(node.parent == ``null``)` `                ``return` `null``;`   `            ``node = node.parent;` `            ``level--;` `        ``}`   `        ``// Move to the required child, where right sibling` `        ``// can be present` `        ``node = node.parent.right;`   `        ``// find right sibling in the given subtree(from current` `        ``// node), when level will be 0` `        ``while` `(level < ``0``) {`   `            ``// Iterate through subtree` `            ``if` `(node.left != ``null``)` `                ``node = node.left;` `            ``else` `if` `(node.right != ``null``)` `                ``node = node.right;` `            ``else`   `                ``// if no child are there, we cannot have right` `                ``// sibling in this path` `                ``break``;`   `            ``level++;` `        ``}`   `        ``if` `(level == ``0``)` `            ``return` `node;`   `        ``// This is the case when we reach 9 node in the tree,` `        ``// where we need to again recursively find the right` `        ``// sibling` `        ``return` `findRightSibling(node, level);` `    ``}`   `    ``// Driver Program to test above functions` `    ``public` `static` `void` `main(String args[])` `    ``{` `        ``Node root = ``new` `Node(``1``, ``null``);` `        ``root.left = ``new` `Node(``2``, root);` `        ``root.right = ``new` `Node(``3``, root);` `        ``root.left.left = ``new` `Node(``4``, root.left);` `        ``root.left.right = ``new` `Node(``6``, root.left);` `        ``root.left.left.left = ``new` `Node(``7``, root.left.left);` `        ``root.left.left.left.left = ``new` `Node(``10``, root.left.left.left);` `        ``root.left.right.right = ``new` `Node(``9``, root.left.right);` `        ``root.right.right = ``new` `Node(``5``, root.right);` `        ``root.right.right.right = ``new` `Node(``8``, root.right.right);` `        ``root.right.right.right.right = ``new` `Node(``12``, root.right.right.right);`   `        ``// passing 10` `        ``System.out.println(findRightSibling(root.left.left.left.left, ``0``).data);` `    ``}` `}` `// This code is contributed by Sumit Ghosh`

## Python3

 `# Python3 program to print right sibling` `# of a node `   `# A class to create a new Binary ` `# Tree Node ` `class` `newNode: ` `    ``def` `__init__(``self``, item, parent): ` `        ``self``.data ``=` `item ` `        ``self``.left ``=` `self``.right ``=` `None` `        ``self``.parent ``=` `parent `   `# Method to find right sibling ` `def` `findRightSibling(node, level):` `    ``if` `(node ``=``=` `None` `or` `node.parent ``=``=` `None``): ` `        ``return` `None`      `    ``# GET Parent pointer whose right child is not ` `    ``# a parent or itself of this node. There might ` `    ``# be case when parent has no right child, but, ` `    ``# current node is left child of the parent ` `    ``# (second condition is for that). ` `    ``while` `(node.parent.right ``=``=` `node ``or` `          ``(node.parent.right ``=``=` `None` `and` `           ``node.parent.left ``=``=` `node)): ` `        ``if` `(node.parent ``=``=` `None``): ` `            ``return` `None`   `        ``node ``=` `node.parent ` `        ``level ``-``=` `1`   `    ``# Move to the required child, where ` `    ``# right sibling can be present ` `    ``node ``=` `node.parent.right `   `    ``# find right sibling in the given subtree` `    ``# (from current node), when level will be 0 ` `    ``while` `(level < ``0``):`   `        ``# Iterate through subtree ` `        ``if` `(node.left !``=` `None``): ` `            ``node ``=` `node.left ` `        ``else` `if` `(node.right !``=` `None``): ` `            ``node ``=` `node.right ` `        ``else``:`   `            ``# if no child are there, we cannot ` `            ``# have right sibling in this path ` `            ``break` `        `  `        ``level ``+``=` `1`   `    ``if` `(level ``=``=` `0``):` `        ``return` `node     `   `    ``# This is the case when we reach 9 node ` `    ``# in the tree, where we need to again ` `    ``# recursively find the right sibling ` `    ``return` `findRightSibling(node, level)`   `# Driver Code` `if` `__name__ ``=``=` `'__main__'``:` `    ``root ``=` `newNode(``1``, ``None``) ` `    ``root.left ``=` `newNode(``2``, root) ` `    ``root.right ``=` `newNode(``3``, root) ` `    ``root.left.left ``=` `newNode(``4``, root.left) ` `    ``root.left.right ``=` `newNode(``6``, root.left) ` `    ``root.left.left.left ``=` `newNode(``7``, root.left.left) ` `    ``root.left.left.left.left ``=` `newNode(``10``, root.left.left.left) ` `    ``root.left.right.right ``=` `newNode(``9``, root.left.right) ` `    ``root.right.right ``=` `newNode(``5``, root.right) ` `    ``root.right.right.right ``=` `newNode(``8``, root.right.right) ` `    ``root.right.right.right.right ``=` `newNode(``12``, root.right.right.right) `   `    ``# passing 10 ` `    ``res ``=` `findRightSibling(root.left.left.left.left, ``0``) ` `    ``if` `(res ``=``=` `None``): ` `        ``print``(``"No right sibling"``) ` `    ``else``:` `        ``print``(res.data)`   `# This code is contributed by PranchalK`

## C#

 `using` `System;`   `// C# program to print right sibling of a node` `public` `class` `Right_Sibling {`   `    ``// A Binary Tree Node` `    ``public` `class` `Node {` `        ``public` `int` `data;` `        ``public` `Node left, right, parent;`   `        ``// Constructor` `        ``public` `Node(``int` `data, Node parent)` `        ``{` `            ``this``.data = data;` `            ``left = ``null``;` `            ``right = ``null``;` `            ``this``.parent = parent;` `        ``}` `    ``}`   `    ``// Method to find right sibling` `    ``public` `static` `Node findRightSibling(Node node, ``int` `level)` `    ``{` `        ``if` `(node == ``null` `|| node.parent == ``null``) {` `            ``return` `null``;` `        ``}`   `        ``// GET Parent pointer whose right child is not` `        ``// a parent or itself of this node. There might` `        ``// be case when parent has no right child, but,` `        ``// current node is left child of the parent` `        ``// (second condition is for that).` `        ``while` `(node.parent.right == node` `               ``|| (node.parent.right == ``null` `                   ``&& node.parent.left == node)) {` `            ``if` `(node.parent == ``null` `                ``|| node.parent.parent == ``null``) {` `                ``return` `null``;` `            ``}`   `            ``node = node.parent;` `            ``level--;` `        ``}`   `        ``// Move to the required child, where right sibling` `        ``// can be present` `        ``node = node.parent.right;`   `        ``// find right sibling in the given subtree(from current` `        ``// node), when level will be 0` `        ``while` `(level < 0) {`   `            ``// Iterate through subtree` `            ``if` `(node.left != ``null``) {` `                ``node = node.left;` `            ``}` `            ``else` `if` `(node.right != ``null``) {` `                ``node = node.right;` `            ``}` `            ``else` `{`   `                ``// if no child are there, we cannot have right` `                ``// sibling in this path` `                ``break``;` `            ``}`   `            ``level++;` `        ``}`   `        ``if` `(level == 0) {` `            ``return` `node;` `        ``}`   `        ``// This is the case when we reach 9 node in the tree,` `        ``// where we need to again recursively find the right` `        ``// sibling` `        ``return` `findRightSibling(node, level);` `    ``}`   `    ``// Driver Program to test above functions` `    ``public` `static` `void` `Main(``string``[] args)` `    ``{` `        ``Node root = ``new` `Node(1, ``null``);` `        ``root.left = ``new` `Node(2, root);` `        ``root.right = ``new` `Node(3, root);` `        ``root.left.left = ``new` `Node(4, root.left);` `        ``root.left.right = ``new` `Node(6, root.left);` `        ``root.left.left.left = ``new` `Node(7, root.left.left);` `        ``root.left.left.left.left = ``new` `Node(10, root.left.left.left);` `        ``root.left.right.right = ``new` `Node(9, root.left.right);` `        ``root.right.right = ``new` `Node(5, root.right);` `        ``root.right.right.right = ``new` `Node(8, root.right.right);` `        ``root.right.right.right.right = ``new` `Node(12, root.right.right.right);`   `        ``// passing 10` `        ``Console.WriteLine(findRightSibling(root.left.left.left.left, 0).data);` `    ``}` `}`   `// This code is contributed by Shrikant13`

## Javascript

 ``

Output

`12`

Time Complexity: O(N)
Auxiliary Space: O(1)

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