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Print path between any two nodes in a Binary Tree | Set 2

  • Difficulty Level : Expert
  • Last Updated : 24 Jun, 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 
 

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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 <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);
  }
 
  // 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<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




// 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);
        }
 
        // 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<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




# 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<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);
        }
 
        // 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<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

Javascript




<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);
        }
  
        // Ccopy 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>
Output: 
7 3 1 4

 




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