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.



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

C++

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/* 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;
}

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Java

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// 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

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Python3

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# 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)

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C#

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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

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Output:

Sum of all the elements is: 36

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