Sum of all nodes in a binary tree

Give an algorithm for finding the sum of all elements in a binary tree.

In the above binary tree sum = 106.

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

The idea is to recursively, call left subtree sum, right subtree sum and add their values to current node’s data.

C++

/* Program to print sum of all the elements of a binary tree */
#include <iostream> 
using namespace std; 
  
struct Node { 
    int key; 
    Node* left, *right; 
}; 
  
/* utility that allocates a new Node with the given key  */
Node* newNode(int key) 
{ 
    Node* node = new Node; 
    node->key = key; 
    node->left = node->right = NULL; 
    return (node); 
} 
  
/* Function to find sum of all the elements*/
int addBT(Node* root) 
{ 
    if (root == NULL) 
        return 0; 
    return (root->key + addBT(root->left) + addBT(root->right)); 
} 
  
/* Driver program to test above functions*/
int main() 
{ 
    Node* root = newNode(1); 
    root->left = newNode(2); 
    root->right = newNode(3); 
    root->left->left = newNode(4); 
    root->left->right = newNode(5); 
    root->right->left = newNode(6); 
    root->right->right = newNode(7); 
    root->right->left->right = newNode(8); 
  
    int sum = addBT(root); 
    cout << "Sum of all the elements is: " << sum << endl; 
  
    return 0; 
} 

Java

// Java Program to print sum of 
// all the elements of a binary tree 
class GFG 
{ 
static class Node  
{  
    int key;  
    Node left, right;  
} 
  
/* utility that allocates a new  
   Node with the given key */
static Node newNode(int key)  
{  
    Node node = new Node();  
    node.key = key;  
    node.left = node.right = null;  
    return (node);  
}  
  
/* Function to find sum  
   of all the elements*/
static int addBT(Node root)  
{  
    if (root == null)  
        return 0;  
    return (root.key + addBT(root.left) +  
                       addBT(root.right));  
}  
  
// 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.left = newNode(6);  
    root.right.right = newNode(7);  
    root.right.left.right = newNode(8);  
  
    int sum = addBT(root);  
    System.out.println("Sum of all the elements is: " + sum);  
}  
} 
  
// This code is contributed by Arnab Kundu 

Python3

# Python3 Program to print sum of all  
# the elements of a binary tree  
  
# Binary Tree Node  
  
""" utility that allocates a new Node  
with the given key """
class newNode:  
  
    # Construct to create a new node  
    def __init__(self, key):  
        self.key = key 
        self.left = None
        self.right = None
          
# Function to find sum of all the element  
def addBT(root):  
    if (root == None): 
        return 0
    return (root.key + addBT(root.left) + 
                       addBT(root.right))  
  
# Driver Code  
if __name__ == '__main__': 
    root = newNode(1)  
    root.left = newNode(2)  
    root.right = newNode(3)  
    root.left.left = newNode(4)  
    root.left.right = newNode(5)  
    root.right.left = newNode(6)  
    root.right.right = newNode(7)  
    root.right.left.right = newNode(8)  
  
    sum = addBT(root)  
  
    print("Sum of all the nodes is:", sum) 
  
# This code is contributed by 
# Shubham Singh(SHUBHAMSINGH10) 

C#

using System; 
  
// C# Program to print sum of  
// all the elements of a binary tree  
public class GFG 
{ 
public class Node 
{ 
    public int key; 
    public Node left, right; 
} 
  
/* utility that allocates a new   
   Node with the given key */
public static Node newNode(int key) 
{ 
    Node node = new Node(); 
    node.key = key; 
    node.left = node.right = null; 
    return (node); 
} 
  
/* Function to find sum   
   of all the elements*/
public static int addBT(Node root) 
{ 
    if (root == null) 
    { 
        return 0; 
    } 
    return (root.key + addBT(root.left) + addBT(root.right)); 
} 
  
// 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.left = newNode(6); 
    root.right.right = newNode(7); 
    root.right.left.right = newNode(8); 
  
    int sum = addBT(root); 
    Console.WriteLine("Sum of all the elements is: " + sum); 
} 
} 
  
// This code is contributed by Shrikant13 

Output:

Sum of all the elements is: 36

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