Print path between any two nodes in a Binary Tree | Set 2
Last Updated :
12 Jul, 2025
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:
- Find the first value recursively, once found add the value to the stack.
- 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 <bits/stdc++.h>
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<Node *> 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);
}
// Copy 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<Node *> 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<Node *> stk;
return stk;
}
// Recursive function to print the
// contents of a stack in reverse
void print(stack<Node *> 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<Node *> stck = pathBetweenNode(7, 4);
print(stck);
}
// This code is contributed by sanjeev2552
// 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<Node> stack = new Stack<Node>();
private Node root = null;
public GFG(Node root)
{
this.root = root;
}
// Function to find the path between
// two nodes in binary tree
public Stack<Node> 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<Node>();
}
// 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);
}
// Copy 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<Node> 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<Node> stack
= pathBetweenNodes.pathBetweenNode(7, 4);
print(stack);
}
}
# 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)
# Copy 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# 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<Node> stack = new Stack<Node>();
private Node root = null;
public GFG(Node root)
{
this.root = root;
}
// Function to find the path between
// two nodes in binary tree
public Stack<Node> 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<Node>();
}
// 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);
}
// Copy 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<Node> 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<Node> stack
= pathBetweenNodes.pathBetweenNode(7, 4);
print(stack);
}
}
// This code is contributed by Arnab Kundu
<script>
// JavaScript implementation of the approach
// A binary tree node
class Node {
constructor(value) {
this.left = null;
this.right = null;
this.value = value;
}
}
let firstValueFound = false;
let secondValueFound = false;
let stack = [];
let root = null;
// Function to find the path between
// two nodes in binary tree
function path_BetweenNode(root, v1, 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
let 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)) {
path_BetweenNode(root.left, v1, v2);
}
// Copy of current state of firstValueFound
// and secondValueFound flag
let localFirstValueFound = firstValueFound;
let 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;
let 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)) {
path_BetweenNode(root.right, v1, v2);
}
if ((firstValueFound ^ secondValueFound)
&& !isAddedToStack && !localAdded)
stack.push(root);
if ((firstValueFound ^ secondValueFound)
&& isAddedToStack)
stack.pop();
}
// Function to find the path between
// two nodes in binary tree
function pathBetweenNode(v1, v2)
{
path_BetweenNode(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 [];
}
// Recursive function to print the
// contents of a stack in reverse
function print(stack)
{
// If the stack is empty
if (stack.length == 0)
return;
// Get the top value
let value = stack[stack.length - 1].value;
stack.pop();
// Recursive call
print(stack);
// Print the popped value
document.write(value + " ");
}
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 = pathBetweenNode(7, 4);
print(stack);
</script>
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