Sum of all odd nodes in the path connecting two given nodes

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Given a binary tree and two nodes of that binary tree. Find the sum of all nodes with odd values in the path connecting the two given nodes.

For Example: In the above binary tree, sum of all odd nodes in the path between the nodes $5$ and $6$ will be 5 + 1 + 3 = 9.

Source : Amazon Interview Experience on Campus

Approach : The idea is to first find the path between the two given nodes of the binary tree using the concept as discussed in: Print path between any two nodes.
Once, we have the path between the two given nodes, calculate sum of all the odd valued nodes in that path and print it.

Below is the implementation of the above approach:

C++

// C++ program to find sum of all odd nodes 
// in the path connecting two given nodes
 
#include<bits/stdc++.h>
using namespace std;
 
// Binary Tree node
struct Node
{
    int data;
    struct Node* left;
    struct Node* right;
};
 
// Utility function to create a 
// new Binary Tree node
struct Node* newNode(int data)
{
    struct Node* node = new Node;
    node->data = data;
    node->left = NULL;
    node->right = NULL;
     
    return node;
}
 
// Function to check if there is a path from root 
// to the given node. It also populates 
// 'arr' with the given path 
bool getPath(Node* root, vector<int>& arr, int x) 
{ 
    // if root is NULL 
    // there is no path 
    if (!root) 
        return false; 
 
    // push the node's value in 'arr' 
    arr.push_back(root->data); 
 
    // if it is the required node 
    // return true 
    if (root->data == x) 
        return true; 
 
    // else check whether the required node lies 
    // in the left subtree or right subtree of 
    // the current node 
    if (getPath(root->left, arr, x) || getPath(root->right, arr, x)) 
        return true; 
 
    // required node does not lie either in the 
    // left or right subtree of the current node 
    // Thus, remove current node's value from 
    // 'arr'and then return false 
    arr.pop_back(); 
    return false; 
} 
 
// Function to get the sum of odd nodes in the 
// path between any two nodes in a binary tree 
int sumOddNodes(Node* root, int n1, int n2) 
{ 
    // vector to store the path of 
    // first node n1 from root 
    vector<int> path1; 
 
    // vector to store the path of 
    // second node n2 from root 
    vector<int> path2; 
 
    getPath(root, path1, n1); 
    getPath(root, path2, n2); 
 
    int intersection = -1; 
 
    // Get intersection point 
    int i = 0, j = 0; 
    while (i != path1.size() || j != path2.size()) { 
 
        // Keep moving forward until no intersection 
        // is found 
        if (i == j && path1[i] == path2[j]) { 
            i++; 
            j++; 
        } 
        else { 
            intersection = j - 1; 
            break; 
        } 
    } 
     
    int sum = 0;
     
    // calculate sum of ODD nodes from the path 
    for (int i = path1.size() - 1; i > intersection; i--) 
        if(path1[i]%2)
            sum += path1[i];
 
    for (int i = intersection; i < path2.size(); i++) 
        if(path2[i]%2)
            sum += path2[i];
             
    return sum;        
} 
 
// Driver Code
int main()
{
    struct Node* root = newNode(1);
     
    root->left = newNode(2);
    root->right = newNode(3);
    root->left->left = newNode(4);
    root->left->right = newNode(5);
    root->right->right = newNode(6);
     
    int node1 = 5; 
    int node2 = 6; 
     
    cout<<sumOddNodes(root, node1, node2); 
     
    return 0;
} 

Java

// Java program to find sum of all odd nodes 
// in the path connecting two given nodes 
 
import java.util.*;
class solution
{
 
// Binary Tree node 
static class Node 
{ 
    int data; 
     Node left; 
     Node right; 
} 
 
// Utility function to create a 
// new Binary Tree node 
 static Node newNode(int data) 
{ 
     Node node = new Node(); 
    node.data = data; 
    node.left = null; 
    node.right = null; 
     
    return node; 
} 
 
// Function to check if there is a path from root 
// to the given node. It also populates 
// 'arr' with the given path 
static boolean getPath(Node root, Vector<Integer> arr, int x) 
{ 
    // if root is null 
    // there is no path 
    if (root==null) 
        return false; 
 
    // push the node's value in 'arr' 
    arr.add(root.data); 
 
    // if it is the required node 
    // return true 
    if (root.data == x) 
        return true; 
 
    // else check whether the required node lies 
    // in the left subtree or right subtree of 
    // the current node 
    if (getPath(root.left, arr, x) || getPath(root.right, arr, x)) 
        return true; 
 
    // required node does not lie either in the 
    // left or right subtree of the current node 
    // Thus, remove current node's value from 
    // 'arr'and then return false 
    arr.remove(arr.size()-1); 
    return false; 
} 
 
// Function to get the sum of odd nodes in the 
// path between any two nodes in a binary tree 
static int sumOddNodes(Node root, int n1, int n2) 
{ 
    // vector to store the path of 
    // first node n1 from root 
    Vector<Integer> path1= new Vector<Integer>(); 
 
    // vector to store the path of 
    // second node n2 from root 
    Vector<Integer> path2= new Vector<Integer>(); 
 
    getPath(root, path1, n1); 
    getPath(root, path2, n2); 
 
    int intersection = -1; 
 
    // Get intersection point 
    int i = 0, j = 0; 
    while (i != path1.size() || j != path2.size()) { 
 
        // Keep moving forward until no intersection 
        // is found 
        if (i == j && path1.get(i) == path2.get(j)) { 
            i++; 
            j++; 
        } 
        else { 
            intersection = j - 1; 
            break; 
        } 
    } 
     
    int sum = 0; 
     
    // calculate sum of ODD nodes from the path 
    for (i = path1.size() - 1; i > intersection; i--) 
        if(path1.get(i)%2!=0) 
            sum += path1.get(i); 
 
    for (i = intersection; i < path2.size(); i++) 
        if(path2.get(i)%2!=0) 
            sum += path2.get(i); 
             
    return sum;         
} 
 
// Driver Code 
public static void main(String args[]) 
{ 
     Node root = newNode(1); 
     
    root.left = newNode(2); 
    root.right = newNode(3); 
    root.left.left = newNode(4); 
    root.left.right = newNode(5); 
    root.right.right = newNode(6); 
     
    int node1 = 5; 
    int node2 = 6; 
     
    System.out.print(sumOddNodes(root, node1, node2)); 
     
} 
}

Python3

# Python3 program to find sum of all odd nodes 
# in the path connecting two given nodes 
 
# Binary Tree node 
class Node: 
    def __init__(self):
        self.data = 0
        self.left = None
        self.right = None
 
# Utility function to create a 
# Binary Tree node 
def newNode( data): 
 
    node = Node() 
    node.data = data 
    node.left = None
    node.right = None
     
    return node 
 
# Function to check if there is a path from root 
# to the given node. It also populates 
# 'arr' with the given path 
def getPath(root, arr, x): 
 
    # if root is None 
    # there is no path 
    if (root == None) :
        return False
 
    # push the node's value in 'arr' 
    arr.append(root.data) 
 
    # if it is the required node 
    # return True 
    if (root.data == x) :
        return True
 
    # else check whether the required node lies 
    # in the left subtree or right subtree of 
    # the current node 
    if (getPath(root.left, arr, x) or getPath(root.right, arr, x)) :
        return True
 
    # required node does not lie either in the 
    # left or right subtree of the current node 
    # Thus, remove current node's value from 
    # 'arr'and then return False 
    arr.pop() 
    return False
 
# Function to get the sum of odd nodes in the 
# path between any two nodes in a binary tree 
def sumOddNodes(root, n1, n2) :
 
    # vector to store the path of 
    # first node n1 from root 
    path1 = [] 
 
    # vector to store the path of 
    # second node n2 from root 
    path2 = [] 
 
    getPath(root, path1, n1) 
    getPath(root, path2, n2) 
 
    intersection = -1
 
    # Get intersection point 
    i = 0
    j = 0
    while (i != len(path1) or j != len(path2)): 
 
        # Keep moving forward until no intersection 
        # is found 
        if (i == j and path1[i] == path2[j]): 
            i = i + 1
            j = j + 1
         
        else :
            intersection = j - 1
            break
         
    sum = 0
     
    i = len(path1) - 1
     
    # calculate sum of ODD nodes from the path 
    while ( i > intersection ): 
        if(path1[i] % 2 != 0): 
            sum += path1[i]
        i = i - 1
         
    i = intersection
    while ( i < len(path2) ): 
        if(path2[i] % 2 != 0) :
            sum += path2[i]
        i = i + 1
             
    return sum       
 
# Driver Code 
 
root = newNode(1) 
     
root.left = newNode(2) 
root.right = newNode(3) 
root.left.left = newNode(4) 
root.left.right = newNode(5) 
root.right.right = newNode(6) 
     
node1 = 5
node2 = 6
     
print(sumOddNodes(root, node1, node2)) 
 
# This code is contributed by Arnab Kundu

C#

// C# program to find sum of all odd nodes 
// in the path connecting two given nodes 
using System;
using System.Collections.Generic;
 
class GFG
{
 
// Binary Tree node 
public class Node 
{ 
    public int data; 
    public Node left; 
    public Node right; 
} 
 
// Utility function to create a 
// new Binary Tree node 
static Node newNode(int data) 
{ 
    Node node = new Node(); 
    node.data = data; 
    node.left = null; 
    node.right = null; 
     
    return node; 
} 
 
// Function to check if there is a path from 
// root to the given node. It also populates 
// 'arr' with the given path 
static Boolean getPath(Node root, 
                       List<int> arr, int x) 
{ 
    // if root is null 
    // there is no path 
    if (root == null) 
        return false; 
 
    // push the node's value in 'arr' 
    arr.Add(root.data); 
 
    // if it is the required node 
    // return true 
    if (root.data == x) 
        return true; 
 
    // else check whether the required node lies 
    // in the left subtree or right subtree of 
    // the current node 
    if (getPath(root.left, arr, x) || 
        getPath(root.right, arr, x)) 
        return true; 
 
    // required node does not lie either in the 
    // left or right subtree of the current node 
    // Thus, Remove current node's value from 
    // 'arr'and then return false 
    arr.RemoveAt(arr.Count - 1); 
    return false; 
} 
 
// Function to get the sum of odd nodes in the 
// path between any two nodes in a binary tree 
static int sumOddNodes(Node root, int n1, int n2) 
{ 
    // List to store the path of 
    // first node n1 from root 
    List<int> path1 = new List<int>(); 
 
    // List to store the path of 
    // second node n2 from root 
    List<int> path2 = new List<int>(); 
 
    getPath(root, path1, n1); 
    getPath(root, path2, n2); 
 
    int intersection = -1;
 
    // Get intersection point 
    int i = 0, j = 0; 
    while (i < path1.Count || j < path2.Count)
    { 
         
        // Keep moving forward until 
        // no intersection is found 
        if ( i == j && path1[i] == path2[j])
        { 
            i++; 
            j++; 
        } 
        else
        { 
            intersection = j - 1; 
            break; 
        } 
    } 
    int sum = 0; 
     
    // calculate sum of ODD nodes from the path 
    for (i = path1.Count - 1; i > intersection; i--) 
        if(path1[i] % 2 != 0) 
            sum += path1[i]; 
 
    for (i = intersection; i < path2.Count; i++) 
        if(path2[i] % 2 != 0) 
            sum += path2[i]; 
             
    return sum;         
} 
 
// Driver Code 
public static void Main(String []args) 
{ 
    Node root = newNode(1); 
     
    root.left = newNode(2); 
    root.right = newNode(3); 
    root.left.left = newNode(4); 
    root.left.right = newNode(5); 
    root.right.right = newNode(6); 
     
    int node1 = 5; 
    int node2 = 6; 
     
    Console.Write(sumOddNodes(root, node1, node2)); 
} 
}
 
// This code is contributed by Arnub Kundu

Javascript

<script>
 
    // JavaScript program to find sum of all odd nodes 
    // in the path connecting two given nodes 
     
    // Binary Tree node 
    class Node
    {
        constructor(data) {
           this.left = null;
           this.right = null;
           this.data = data;
        }
    }
 
    // Utility function to create a 
    // new Binary Tree node 
    function newNode(data) 
    { 
          let node = new Node(data);
        return node; 
    } 
 
    // Function to check if there is a path from root 
    // to the given node. It also populates 
    // 'arr' with the given path 
    function getPath(root, arr, x) 
    { 
        // if root is null 
        // there is no path 
        if (root==null) 
            return false; 
 
        // push the node's value in 'arr' 
        arr.push(root.data); 
 
        // if it is the required node 
        // return true 
        if (root.data == x) 
            return true; 
 
        // else check whether the required node lies 
        // in the left subtree or right subtree of 
        // the current node 
        if (getPath(root.left, arr, x) || getPath(root.right, arr, x)) 
            return true; 
 
        // required node does not lie either in the 
        // left or right subtree of the current node 
        // Thus, remove current node's value from 
        // 'arr'and then return false 
        arr.pop(); 
        return false; 
    } 
 
    // Function to get the sum of odd nodes in the 
    // path between any two nodes in a binary tree 
    function sumOddNodes(root, n1, n2) 
    { 
        // vector to store the path of 
        // first node n1 from root 
        let path1= []; 
 
        // vector to store the path of 
        // second node n2 from root 
        let path2= []; 
 
        getPath(root, path1, n1); 
        getPath(root, path2, n2); 
 
        let intersection = -1; 
 
        // Get intersection point 
        let i = 0, j = 0; 
        while (i != path1.length || j != path2.length) { 
 
            // Keep moving forward until no intersection 
            // is found 
            if (i == j && path1[i] == path2[j]) { 
                i++; 
                j++; 
            } 
            else { 
                intersection = j - 1; 
                break; 
            } 
        } 
 
        let sum = 0; 
 
        // calculate sum of ODD nodes from the path 
        for (i = path1.length - 1; i > intersection; i--) 
            if(path1[i]%2!=0) 
                sum += path1[i]; 
 
        for (i = intersection; i < path2.length; i++) 
            if(path2[i]%2!=0) 
                sum += path2[i]; 
 
        return sum;         
    }
     
    let root = newNode(1); 
       
    root.left = newNode(2); 
    root.right = newNode(3); 
    root.left.left = newNode(4); 
    root.left.right = newNode(5); 
    root.right.right = newNode(6); 
       
    let node1 = 5; 
    let node2 = 6; 
       
    document.write(sumOddNodes(root, node1, node2)); 
 
</script>

Output

Complexity Analysis:

Time Complexity : O(n)
Auxiliary Space : O(n)

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