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# Common nodes in the inorder sequence of a tree between given two nodes in O(1) space

Given a binary tree consisting of distinct values and two numbers K1 and K2, the task is to find all nodes that lie between them in the inorder sequence of the tree.
Examples:

Input:
1
/   \
12    11
/       /   \
3    4     13
\      /
15   9
k1 = 12
k2 = 15
Output:
1 4
Explanation:
Inorder sequence is 3 12 1 4 15 11 9 13
The common nodes between 12 and 15 in the inorder sequence of the tree are {1, 4}.
Input:
5
/   \
21    77
/  \      \
61   16    36
\     /
10  3
/
23
k1 = 23
k2 = 3
Output:
10 5 77
Explanation:
Inorder sequence is 61 21 16 23 10 5 77 3 36
The common nodes between 23 and 3 in the inorder sequence of the tree are {10, 5, 77}.

Approach:
In order to solve this problem, we are using the Morris Inorder Traversal of a Binary Tree to avoid the use of any extra space. We are keeping a flag to set when either of K1 or K2 is found. Once found, print every node that appears in the inorder sequence until the other node is found.
Below is the implementation of the above approach:

## C++

 `// C++ Program to find``// the common nodes``// between given two nodes``// in the inorder sequence``// of the binary tree` `#include ``using` `namespace` `std;` `// Definition of Binary``// Tree Structure``struct` `tNode {``    ``int` `data;``    ``struct` `tNode* left;``    ``struct` `tNode* right;``};` `// Helper function to allocate``// memory to create new nodes``struct` `tNode* newtNode(``int` `data)``{``    ``struct` `tNode* node = ``new` `tNode;``    ``node->data = data;``    ``node->left = NULL;``    ``node->right = NULL;` `    ``return` `(node);``}` `// Flag to set if``// either of K1 or``// K2 is found``int` `flag = 0;` `// Function to traverse the``// binary tree without recursion``// and without stack using``// Morris Traversal``void` `findCommonNodes(``struct` `tNode* root,``                     ``int` `K1, ``int` `K2)``{``    ``struct` `tNode *current, *pre;` `    ``if` `(root == NULL)``        ``return``;` `    ``current = root;``    ``while` `(current != NULL) {` `        ``if` `(current->left == NULL) {` `            ``if` `(current->data == K1 || current->data == K2) {``                ``if` `(flag) {``                    ``return``;``                ``}``                ``else` `{``                    ``flag = 1;``                ``}``            ``}``            ``else` `if` `(flag) {``                ``cout << current->data << ``" "``;``            ``}``            ``current = current->right;``        ``}``        ``else` `{` `            ``// Find the inorder predecessor``            ``// of current``            ``pre = current->left;``            ``while` `(pre->right != NULL``                   ``&& pre->right != current)``                ``pre = pre->right;` `            ``// Make current as the right``            ``// child of its inorder``            ``// predecessor``            ``if` `(pre->right == NULL) {``                ``pre->right = current;``                ``current = current->left;``            ``}` `            ``// Revert the changes made``            ``// to restore the original tree``            ``// i.e., fix the right child``            ``// of predecessor``            ``else` `{``                ``pre->right = NULL;``                ``if` `(current->data == K1 || current->data == K2) {``                    ``if` `(flag) {``                        ``return``;``                    ``}``                    ``else` `{``                        ``flag = 1;``                    ``}``                ``}``                ``else` `if` `(flag) {``                    ``cout << current->data << ``" "``;``                ``}``                ``current = current->right;``            ``} ``// End of if condition pre->right == NULL``        ``} ``// End of if condition current->left == NULL``    ``} ``// End of while``}` `// Driver code``int` `main()``{``    ``struct` `tNode* root = newtNode(1);``    ``root->left = newtNode(12);``    ``root->right = newtNode(11);``    ``root->left->left = newtNode(3);``    ``root->right->left = newtNode(4);``    ``root->right->right = newtNode(13);``    ``root->right->left->right = newtNode(15);``    ``root->right->right->left = newtNode(9);` `    ``int` `K1 = 12, K2 = 15;` `    ``findCommonNodes(root, K1, K2);` `    ``return` `0;``}`

## Java

 `// Java program to find the common nodes``// between given two nodes in the inorder``// sequence of the binary tree``import` `java.util.*;` `class` `GFG{` `// Definition of Binary Tree``static` `class` `tNode``{``    ``int` `data;``    ``tNode left;``    ``tNode right;``};` `// Helper function to allocate``// memory to create new nodes``static` `tNode newtNode(``int` `data)``{``    ``tNode node = ``new` `tNode();``    ``node.data = data;``    ``node.left = ``null``;``    ``node.right = ``null``;` `    ``return` `(node);``}` `// Flag to set if either``// of K1 or K2 is found``static` `int` `flag = ``0``;` `// Function to traverse the binary``// tree without recursion and``// without stack using``// Morris Traversal``static` `void` `findCommonNodes(tNode root,``                            ``int` `K1, ``int` `K2)``{``    ``tNode current, pre;` `    ``if` `(root == ``null``)``        ``return``;``    ``current = root;``    ` `    ``while` `(current != ``null``)``    ``{``        ``if` `(current.left == ``null``)``        ``{``            ``if` `(current.data == K1 ||``                ``current.data == K2)``            ``{``                ``if` `(flag == ``1``)``                ``{``                    ``return``;``                ``}``                ``else``                ``{``                    ``flag = ``1``;``                ``}``            ``}``            ``else` `if` `(flag == ``1``)``            ``{``                ``System.out.print(current.data + ``" "``);``            ``}``            ``current = current.right;``        ``}``        ``else``        ``{` `            ``// Find the inorder predecessor``            ``// of current``            ``pre = current.left;``            ``while` `(pre.right != ``null` `&&``                   ``pre.right != current)``            ``{``                ``pre = pre.right;``            ``}` `            ``// Make current as the right``            ``// child of its inorder``            ``// predecessor``            ``if` `(pre.right == ``null``)``            ``{``                ``pre.right = current;``                ``current = current.left;``            ``}` `            ``// Revert the changes made``            ``// to restore the original tree``            ``// i.e., fix the right child``            ``// of predecessor``            ``else``            ``{``                ``pre.right = ``null``;``                ``if` `(current.data == K1 ||``                    ``current.data == K2)``                ``{``                    ``if` `(flag == ``1``)``                    ``{``                        ``return``;``                    ``}``                    ``else``                    ``{``                        ``flag = ``1``;``                    ``}``                ``}``                ``else` `if` `(flag == ``1``)``                ``{``                    ``System.out.print(current.data + ``" "``);``                ``}``                ``current = current.right;``            ``} ``// End of if condition pre.right == null``        ``} ``// End of if condition current.left == null``    ``} ``// End of while``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ``tNode root = newtNode(``1``);``    ``root.left = newtNode(``12``);``    ``root.right = newtNode(``11``);``    ``root.left.left = newtNode(``3``);``    ``root.right.left = newtNode(``4``);``    ``root.right.right = newtNode(``13``);``    ``root.right.left.right = newtNode(``15``);``    ``root.right.right.left = newtNode(``9``);` `    ``int` `K1 = ``12``, K2 = ``15``;` `    ``findCommonNodes(root, K1, K2);``}``}` `// This code is contributed by Amit Katiyar`

## Python3

 `# Python3 program for the``# above approach``from` `collections ``import` `deque` `# A Tree node``class` `Node:``  ` `    ``def` `__init__(``self``, x):``      ` `        ``self``.data ``=` `x``        ``self``.left ``=` `None``        ``self``.right ``=` `None` `# Flag to set if``# either of K1 or``# K2 is found``flag ``=` `0` `# Function to traverse the``# binary tree without recursion``# and without stack using``# Morris Traversal``def` `findCommonNodes(root,``                    ``K1, K2):``  ` `    ``global` `flag``    ``current, pre ``=` `None``, ``None` `    ``if` `(root ``=``=` `None``):``        ``return` `    ``current ``=` `root``    ``while` `(current !``=` `None``):``        ``if` `(current.left ``=``=` `None``):``            ``if` `(current.data ``=``=` `K1 ``or``                ``current.data ``=``=` `K2):``                ``if` `(flag):``                    ``return` `                ``else``:``                    ``flag ``=` `1` `            ``elif` `(flag):``                ``print``(current.data,``                      ``end ``=` `" "``)``            ``else``:``                ``None` `            ``current ``=` `current.right` `        ``else``:` `            ``# Find the inorder``            ``# predecessor of current``            ``pre ``=` `current.left``            ``while` `(pre.right !``=` `None` `and``                   ``pre.right !``=` `current):``                ``pre ``=` `pre.right` `            ``# Make current as the right``            ``# child of its inorder``            ``# predecessor``            ``if` `(pre.right ``=``=` `None``):``                ``pre.right ``=` `current``                ``current ``=` `current.left` `            ``# Revert the changes made``            ``# to restore the original tree``            ``# i.e., fix the right child``            ``# of predecessor``            ``else``:``                ``pre.right ``=` `None``                ``if` `(current.data ``=``=` `K1 ``or``                    ``current.data ``=``=` `K2):``                    ``if` `(flag):``                        ``return``                    ``else``:``                        ``flag ``=` `1` `                ``elif` `(flag):``                    ``print``(current.data,``                          ``end ``=` `" "``)` `                ``current ``=` `current.right``             ``# End of if condition``            ``# pre.right == None``         ``# End of if condition``         ``#current.left == None``     ``# End of while` `# Driver code``if` `__name__ ``=``=` `'__main__'``:``  ` `    ``root ``=` `Node(``1``)``    ``root.left ``=` `Node(``12``)``    ``root.right ``=` `Node(``11``)``    ``root.left.left ``=` `Node(``3``)``    ``root.right.left ``=` `Node(``4``)``    ``root.right.right ``=` `Node(``13``)``    ``root.right.left.right ``=` `Node(``15``)``    ``root.right.right.left ``=` `Node(``9``)` `    ``K1 ``=` `12``    ``K2 ``=` `15` `    ``findCommonNodes(root, K1, K2)` `# This code is contributed by Mohit Kumar 29`

## C#

 `// C# program to find the common nodes``// between given two nodes in the inorder``// sequence of the binary tree``using` `System;` `class` `GFG{` `// Definition of Binary Tree``class` `tNode``{``    ``public` `int` `data;``    ``public` `tNode left;``    ``public` `tNode right;``};` `// Helper function to allocate``// memory to create new nodes``static` `tNode newtNode(``int` `data)``{``    ``tNode node = ``new` `tNode();``    ``node.data = data;``    ``node.left = ``null``;``    ``node.right = ``null``;` `    ``return` `(node);``}` `// Flag to set if either``// of K1 or K2 is found``static` `int` `flag = 0;` `// Function to traverse the binary``// tree without recursion and``// without stack using``// Morris Traversal``static` `void` `findCommonNodes(tNode root,``                            ``int` `K1, ``int` `K2)``{``    ``tNode current, pre;` `    ``if` `(root == ``null``)``        ``return``;``    ``current = root;``    ` `    ``while` `(current != ``null``)``    ``{``        ``if` `(current.left == ``null``)``        ``{``            ``if` `(current.data == K1 ||``                ``current.data == K2)``            ``{``                ``if` `(flag == 1)``                ``{``                    ``return``;``                ``}``                ``else``                ``{``                    ``flag = 1;``                ``}``            ``}``            ``else` `if` `(flag == 1)``            ``{``                ``Console.Write(current.data + ``" "``);``            ``}``            ``current = current.right;``        ``}``        ``else``        ``{` `            ``// Find the inorder predecessor``            ``// of current``            ``pre = current.left;``            ``while` `(pre.right != ``null` `&&``                   ``pre.right != current)``            ``{``                ``pre = pre.right;``            ``}` `            ``// Make current as the right``            ``// child of its inorder``            ``// predecessor``            ``if` `(pre.right == ``null``)``            ``{``                ``pre.right = current;``                ``current = current.left;``            ``}` `            ``// Revert the changes made``            ``// to restore the original tree``            ``// i.e., fix the right child``            ``// of predecessor``            ``else``            ``{``                ``pre.right = ``null``;``                ``if` `(current.data == K1 ||``                    ``current.data == K2)``                ``{``                    ``if` `(flag == 1)``                    ``{``                        ``return``;``                    ``}``                    ``else``                    ``{``                        ``flag = 1;``                    ``}``                ``}``                ``else` `if` `(flag == 1)``                ``{``                    ``Console.Write(current.data + ``" "``);``                ``}``                ``current = current.right;``            ``} ``// End of if condition pre.right == null``        ``} ``// End of if condition current.left == null``    ``} ``// End of while``}` `// Driver code``public` `static` `void` `Main(String[] args)``{``    ``tNode root = newtNode(1);``    ``root.left = newtNode(12);``    ``root.right = newtNode(11);``    ``root.left.left = newtNode(3);``    ``root.right.left = newtNode(4);``    ``root.right.right = newtNode(13);``    ``root.right.left.right = newtNode(15);``    ``root.right.right.left = newtNode(9);` `    ``int` `K1 = 12, K2 = 15;` `    ``findCommonNodes(root, K1, K2);``}``}` `// This code is contributed by Amit Katiyar`

## Javascript

 ``

Output:

`1 4`

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

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