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Print path between any two nodes in a Binary Tree | Set 2
• Last Updated : 24 Feb, 2021

Given a Binary Tree of distinct nodes and a pair of nodes. The task is to find and print the path between the two given nodes in the binary tree.
Examples:

Input: N1 = 7, N2 = 4

Output: 7 3 1 4

Approach: An approach to solve this problem has been discussed in this article. In this article, an even optimized recursive approach will be discussed.
In this recursive approach, below are the steps:

1. Find the first value recursively, once found add the value to the stack.
2. Now every node that is visited whether in backtracking or forward tracking, adds the values to the stack but if the node was added in the forward tracking then remove it in the backtracking and continue this until the second value is found or all nodes are visited.

For example: Consider the path between 7 and 9 is to be found in the above tree. We traverse the tree as DFS, once we find the value 7, we add it to the stack. Traversing path 0 -> 1 -> 3 -> 7.
Now while backtracking, add 3 and 1 to the stack. So as of now, the stack has [7, 3, 1], child 1 has a right child, so we first add it to the stack. Now, the stack contains [7, 3, 1, 4]. Visit the left child of 4, add it to the stack. The stack contains [7, 3, 1, 4, 8] now. Since there is no further node we would go back to the previous node and since 8 was already added to the stack so remove it. Now the node 4 has a right child, and we add it to the stack since this is the second value we were looking for there won’t be any further recursive calls. Finally, the stack contains [7, 3, 1, 4, 9].
Below is the implementation of the above approach:

## C++

 `// CPP implementation of the approach``#include ``using` `namespace` `std;` `// A binary tree node``class` `Node {`` ``public``:``  ``int` `value;``  ``Node *left, *right;` `  ``Node(``int` `value) {``    ``this``->value = value;``    ``left = NULL;``    ``right = NULL;``  ``}``};` `bool` `firstValueFound = ``false``;``bool` `secondValueFound = ``false``;``stack stk;``Node *root = NULL;` `// Function to find the path between``// two nodes in binary tree``void` `pathBetweenNode(Node *root, ``int` `v1, ``int` `v2) {``  ``// Base condition``  ``if` `(root == NULL) ``return``;` `  ``// If both the values are found then return``  ``if` `(firstValueFound && secondValueFound) ``return``;` `  ``// Starting the stack frame with``  ``// isAddedToStack = false flag``  ``bool` `isAddedToStack = ``false``;` `  ``// If one of the value is found then add the``  ``// value to the stack and make the isAddedToStack = true``  ``if` `(firstValueFound ^ secondValueFound) {``    ``stk.push(root);``    ``isAddedToStack = ``true``;``  ``}` `  ``// If none of the two values is found``  ``if` `(!(firstValueFound && secondValueFound)) {``    ``pathBetweenNode(root->left, v1, v2);``  ``}` `  ``// Ccopy of current state of firstValueFound``  ``// and secondValueFound flag``  ``bool` `localFirstValueFound = firstValueFound;``  ``bool` `localSecondValueFound = secondValueFound;` `  ``// If the first value is found``  ``if` `(root->value == v1) firstValueFound = ``true``;` `  ``// If the second value is found``  ``if` `(root->value == v2) secondValueFound = ``true``;` `  ``bool` `localAdded = ``false``;` `  ``// If one of the value is found and the value``  ``// was not added to the stack yet or there was``  ``// only one value found and now both the values``  ``// are found and was not added to``  ``// the stack then add it``  ``if` `(((firstValueFound ^ secondValueFound) ||``       ``((localFirstValueFound ^ localSecondValueFound) &&``        ``(firstValueFound && secondValueFound))) &&``      ``!isAddedToStack) {``    ``localAdded = ``true``;``    ``stk.push(root);``  ``}` `  ``// If none of the two values is found yet``  ``if` `(!(firstValueFound && secondValueFound)) {``    ``pathBetweenNode(root->right, v1, v2);``  ``}` `  ``if` `((firstValueFound ^ secondValueFound) && !isAddedToStack && !localAdded)``    ``stk.push(root);` `  ``if` `((firstValueFound ^ secondValueFound) && isAddedToStack) stk.pop();``}` `// Function to find the path between``// two nodes in binary tree``stack pathBetweenNode(``int` `v1, ``int` `v2)``{``  ` `  ``// Global root``  ``pathBetweenNode(::root, v1, v2);` `  ``// If both the values are found``  ``// then return the stack``  ``if` `(firstValueFound && secondValueFound)``  ``{``    ` `    ``// Global Stack Object``    ``return` `::stk;``  ``}` `  ``// If none of the two values is``  ``// found then return empty stack``  ``stack stk;``  ``return` `stk;``}` `// Recursive function to print the``// contents of a stack in reverse``void` `print(stack stk)``{``  ` `  ``// If the stack is empty``  ``if` `(stk.empty()) ``return``;` `  ``// Get the top value``  ``int` `value = stk.top()->value;``  ``stk.pop();` `  ``// Recursive call``  ``print(stk);` `  ``// Print the popped value``  ``cout << value << ``" "``;``}` `// Driver code``int` `main(``int` `argc, ``char` `const` `*argv[])``{``  ``root = ``new` `Node(0);``  ``root->left = ``new` `Node(1);``  ``root->right = ``new` `Node(2);``  ``root->left->left = ``new` `Node(3);``  ``root->left->right = ``new` `Node(4);``  ``root->right->left = ``new` `Node(5);``  ``root->right->right = ``new` `Node(6);``  ``root->left->left->left = ``new` `Node(7);``  ``root->left->right->left = ``new` `Node(8);``  ``root->left->right->right = ``new` `Node(9);` `  ``// Find and print the path``  ``stack stck = pathBetweenNode(7, 4);``  ``print(stck);``}` `// This code is contributed by sanjeev2552`

## Java

 `// Java implementation of the approach``import` `java.util.Stack;` `public` `class` `GFG {` `    ``// A binary tree node``    ``private` `static` `class` `Node {``        ``public` `Node left;``        ``public` `int` `value;``        ``public` `Node right;` `        ``public` `Node(``int` `value)``        ``{``            ``this``.value = value;``            ``left = ``null``;``            ``right = ``null``;``        ``}``    ``}` `    ``private` `boolean` `firstValueFound = ``false``;``    ``private` `boolean` `secondValueFound = ``false``;``    ``private` `Stack stack = ``new` `Stack();``    ``private` `Node root = ``null``;` `    ``public` `GFG(Node root)``    ``{``        ``this``.root = root;``    ``}` `    ``// Function to find the path between``    ``// two nodes in binary tree``    ``public` `Stack pathBetweenNode(``int` `v1, ``int` `v2)``    ``{``        ``pathBetweenNode(``this``.root, v1, v2);` `        ``// If both the values are found``        ``// then return the stack``        ``if` `(firstValueFound && secondValueFound) {``            ``return` `stack;``        ``}` `        ``// If none of the two values is``        ``// found then return empty stack``        ``return` `new` `Stack();``    ``}` `    ``// Function to find the path between``    ``// two nodes in binary tree``    ``private` `void` `pathBetweenNode(Node root, ``int` `v1, ``int` `v2)``    ``{``        ``// Base condition``        ``if` `(root == ``null``)``            ``return``;` `        ``// If both the values are found then return``        ``if` `(firstValueFound && secondValueFound)``            ``return``;` `        ``// Starting the stack frame with``        ``// isAddedToStack = false flag``        ``boolean` `isAddedToStack = ``false``;` `        ``// If one of the value is found then add the``        ``// value to the stack and make the isAddedToStack = true``        ``if` `(firstValueFound ^ secondValueFound) {``            ``stack.add(root);``            ``isAddedToStack = ``true``;``        ``}` `        ``// If none of the two values is found``        ``if` `(!(firstValueFound && secondValueFound)) {``            ``pathBetweenNode(root.left, v1, v2);``        ``}` `        ``// Ccopy of current state of firstValueFound``        ``// and secondValueFound flag``        ``boolean` `localFirstValueFound = firstValueFound;``        ``boolean` `localSecondValueFound = secondValueFound;` `        ``// If the first value is found``        ``if` `(root.value == v1)``            ``firstValueFound = ``true``;` `        ``// If the second value is found``        ``if` `(root.value == v2)``            ``secondValueFound = ``true``;` `        ``boolean` `localAdded = ``false``;` `        ``// If one of the value is found and the value``        ``// was not added to the stack yet or there was``        ``// only one value found and now both the values``        ``// are found and was not added to``        ``// the stack then add it``        ``if` `(((firstValueFound ^ secondValueFound)``             ``|| ((localFirstValueFound ^ localSecondValueFound)``                 ``&& (firstValueFound && secondValueFound)))``            ``&& !isAddedToStack) {``            ``localAdded = ``true``;``            ``stack.add(root);``        ``}` `        ``// If none of the two values is found yet``        ``if` `(!(firstValueFound && secondValueFound)) {``            ``pathBetweenNode(root.right, v1, v2);``        ``}` `        ``if` `((firstValueFound ^ secondValueFound)``            ``&& !isAddedToStack && !localAdded)``            ``stack.add(root);` `        ``if` `((firstValueFound ^ secondValueFound)``            ``&& isAddedToStack)``            ``stack.pop();``    ``}` `    ``// Recursive function to print the``    ``// contents of a stack in reverse``    ``private` `static` `void` `print(Stack stack)``    ``{` `        ``// If the stack is empty``        ``if` `(stack.isEmpty())``            ``return``;` `        ``// Get the top value``        ``int` `value = stack.pop().value;` `        ``// Recursive call``        ``print(stack);` `        ``// Print the popped value``        ``System.out.print(value + ``" "``);``    ``}` `    ``// Driver code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``Node root = ``new` `Node(``0``);``        ``root.left = ``new` `Node(``1``);``        ``root.right = ``new` `Node(``2``);``        ``root.left.left = ``new` `Node(``3``);``        ``root.left.right = ``new` `Node(``4``);``        ``root.right.left = ``new` `Node(``5``);``        ``root.right.right = ``new` `Node(``6``);``        ``root.left.left.left = ``new` `Node(``7``);``        ``root.left.right.left = ``new` `Node(``8``);``        ``root.left.right.right = ``new` `Node(``9``);` `        ``// Find and print the path``        ``GFG pathBetweenNodes = ``new` `GFG(root);``        ``Stack stack``            ``= pathBetweenNodes.pathBetweenNode(``7``, ``4``);``        ``print(stack);``    ``}``}`

## Python3

 `# Python3 implementation of``# the above approach` `# A binary tree node``class` `Node:` `    ``def` `__init__(``self``, value):` `        ``self``.left ``=` `None``        ``self``.right ``=` `None``        ``self``.value ``=` `value` `firstValueFound ``=` `False``secondValueFound ``=` `False``stack ``=` `[]``root ``=` `None` `# Function to find the path``# between two nodes in binary``# tree``def` `pathBetweennode(v1, v2):` `    ``global` `firstValueFound, secondValueFound``    ``pathBetweenNode(root, v1, v2)` `    ``# If both the values are found``    ``# then return the stack``    ``if` `(firstValueFound ``and``        ``secondValueFound):``        ``return` `stack` `    ``# If none of the two values is``    ``# found then return empty stack``    ``return` `[]` `# Function to find the path``# between two nodes in binary``# tree``def` `pathBetweenNode(root,``                    ``v1, v2):``    ``global` `firstValueFound, secondValueFound``    ` `    ``# Base condition``    ``if` `(root ``=``=` `None``):``        ``return` `    ``# If both the values are found``    ``# then return``    ``if` `(firstValueFound ``and``        ``secondValueFound):``        ``return` `    ``# Starting the stack frame with``    ``# isAddedToStack = false flag``    ``isAddedToStack ``=` `False` `    ``# If one of the value is found``    ``# then add the value to the``    ``# stack and make the isAddedToStack = true``    ``if` `(firstValueFound ^ secondValueFound):``        ``stack.append(root)``        ``isAddedToStack ``=` `True` `    ``# If none of the two values``    ``# is found``    ``if` `(``not` `(firstValueFound ``and``             ``secondValueFound)):``        ``pathBetweenNode(root.left,``                        ``v1, v2)` `    ``# Ccopy of current state of``    ``# firstValueFound and``    ``# secondValueFound flag``    ``localFirstValueFound ``=` `firstValueFound``    ``localSecondValueFound ``=` `secondValueFound` `    ``# If the first value is found``    ``if` `(root.value ``=``=` `v1):``        ``firstValueFound ``=` `True` `    ``# If the second value is found``    ``if` `(root.value ``=``=` `v2):``        ``secondValueFound ``=` `True` `    ``localAdded ``=` `False` `    ``# If one of the value is found``    ``# and the value was not added``    ``# to the stack yet or there was``    ``# only one value found and now``    ``# both the values are found and``    ``# was not added to the stack``    ``# then add it``    ``if` `(((firstValueFound ^``          ``secondValueFound) ``or``        ``((localFirstValueFound ^``          ``localSecondValueFound) ``and``         ``(firstValueFound ``and``          ``secondValueFound))) ``and``          ``not` `isAddedToStack):``        ``localAdded ``=` `True``        ``stack.append(root)` `    ``# If none of the two values``    ``# is found yet``    ``if` `(``not` `(firstValueFound ``and``             ``secondValueFound)):``        ``pathBetweenNode(root.right,``                        ``v1, v2)` `    ``if` `((firstValueFound ^``         ``secondValueFound) ``and``         ``not` `isAddedToStack ``and``         ``not` `localAdded):``        ``stack.append(root)` `    ``if` `((firstValueFound ^``         ``secondValueFound) ``and``         ``isAddedToStack):``        ``stack.pop()` `# Recursive function to print``# the contents of a stack in``# reverse``def` `pri(stack):` `    ``# If the stack is empty``    ``if` `(``len``(stack) ``=``=` `0``):``        ``return` `    ``# Get the top value``    ``value ``=` `stack.pop().value` `    ``# Recursive call``    ``pri(stack)` `    ``# Print the popped value``    ``print``(value, end ``=` `" "``)` `# Driver code``if` `__name__ ``=``=` `"__main__"``:` `    ``root ``=` `Node(``0``)``    ``root.left ``=` `Node(``1``)``    ``root.right ``=` `Node(``2``)``    ``root.left.left ``=` `Node(``3``)``    ``root.left.right ``=` `Node(``4``)``    ``root.right.left ``=` `Node(``5``)``    ``root.right.right ``=` `Node(``6``)``    ``root.left.left.left ``=` `Node(``7``)``    ``root.left.right.left ``=` `Node(``8``)``    ``root.left.right.right ``=` `Node(``9``)` `    ``# Find and print the path``    ``stack ``=` `pathBetweennode(``7``, ``4``)``    ``pri(stack)` `# This code is contributed by Rutvik_56`

## C#

 `// C# implementation of the approach``using` `System;``using` `System.Collections;``using` `System.Collections.Generic;` `class` `GFG``{` `    ``// A binary tree node``    ``public` `class` `Node``    ``{``        ``public` `Node left;``        ``public` `int` `value;``        ``public` `Node right;` `        ``public` `Node(``int` `value)``        ``{``            ``this``.value = value;``            ``left = ``null``;``            ``right = ``null``;``        ``}``    ``}` `    ``private` `Boolean firstValueFound = ``false``;``    ``private` `Boolean secondValueFound = ``false``;``    ``private` `Stack stack = ``new` `Stack();``    ``private` `Node root = ``null``;` `    ``public` `GFG(Node root)``    ``{``        ``this``.root = root;``    ``}` `    ``// Function to find the path between``    ``// two nodes in binary tree``    ``public` `Stack pathBetweenNode(``int` `v1, ``int` `v2)``    ``{``        ``pathBetweenNode(``this``.root, v1, v2);` `        ``// If both the values are found``        ``// then return the stack``        ``if` `(firstValueFound && secondValueFound)``        ``{``            ``return` `stack;``        ``}` `        ``// If none of the two values is``        ``// found then return empty stack``        ``return` `new` `Stack();``    ``}` `    ``// Function to find the path between``    ``// two nodes in binary tree``    ``private` `void` `pathBetweenNode(Node root, ``int` `v1, ``int` `v2)``    ``{``        ``// Base condition``        ``if` `(root == ``null``)``            ``return``;` `        ``// If both the values are found then return``        ``if` `(firstValueFound && secondValueFound)``            ``return``;` `        ``// Starting the stack frame with``        ``// isAddedToStack = false flag``        ``Boolean isAddedToStack = ``false``;` `        ``// If one of the value is found then add the``        ``// value to the stack and make the isAddedToStack = true``        ``if` `(firstValueFound ^ secondValueFound)``        ``{``            ``stack.Push(root);``            ``isAddedToStack = ``true``;``        ``}` `        ``// If none of the two values is found``        ``if` `(!(firstValueFound && secondValueFound))``        ``{``            ``pathBetweenNode(root.left, v1, v2);``        ``}` `        ``// Ccopy of current state of firstValueFound``        ``// and secondValueFound flag``        ``Boolean localFirstValueFound = firstValueFound;``        ``Boolean localSecondValueFound = secondValueFound;` `        ``// If the first value is found``        ``if` `(root.value == v1)``            ``firstValueFound = ``true``;` `        ``// If the second value is found``        ``if` `(root.value == v2)``            ``secondValueFound = ``true``;` `        ``Boolean localAdded = ``false``;` `        ``// If one of the value is found and the value``        ``// was not added to the stack yet or there was``        ``// only one value found and now both the values``        ``// are found and was not added to``        ``// the stack then add it``        ``if` `(((firstValueFound ^ secondValueFound)``            ``|| ((localFirstValueFound ^ localSecondValueFound)``            ``&& (firstValueFound && secondValueFound)))``            ``&& !isAddedToStack)``        ``{``            ``localAdded = ``true``;``            ``stack.Push(root);``        ``}` `        ``// If none of the two values is found yet``        ``if` `(!(firstValueFound && secondValueFound))``        ``{``            ``pathBetweenNode(root.right, v1, v2);``        ``}` `        ``if` `((firstValueFound ^ secondValueFound)``            ``&& !isAddedToStack && !localAdded)``            ``stack.Push(root);` `        ``if` `((firstValueFound ^ secondValueFound)``            ``&& isAddedToStack)``            ``stack.Pop();``    ``}` `    ``// Recursive function to print the``    ``// contents of a stack in reverse``    ``private` `static` `void` `print(Stack stack)``    ``{` `        ``// If the stack is empty``        ``if` `(stack.Count==0)``            ``return``;` `        ``// Get the top value``        ``int` `value = stack.Pop().value;` `        ``// Recursive call``        ``print(stack);` `        ``// Print the Popped value``        ``Console.Write(value + ``" "``);``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main(String []args)``    ``{``        ``Node root = ``new` `Node(0);``        ``root.left = ``new` `Node(1);``        ``root.right = ``new` `Node(2);``        ``root.left.left = ``new` `Node(3);``        ``root.left.right = ``new` `Node(4);``        ``root.right.left = ``new` `Node(5);``        ``root.right.right = ``new` `Node(6);``        ``root.left.left.left = ``new` `Node(7);``        ``root.left.right.left = ``new` `Node(8);``        ``root.left.right.right = ``new` `Node(9);` `        ``// Find and print the path``        ``GFG pathBetweenNodes = ``new` `GFG(root);``        ``Stack stack``            ``= pathBetweenNodes.pathBetweenNode(7, 4);``        ``print(stack);``    ``}``}` `// This code is contributed by Arnab Kundu`
Output:
`7 3 1 4`

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