# Sum of all nodes in a binary tree

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

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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++

`/* Program to print sum of all the elements of a binary tree */` `#include <bits/stdc++.h>` `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` |

## Javascript

`<script>` `// Javascript Program to print sum of` `// all the elements of a binary tree` `class Node` `{ ` ` ` `constructor(key)` ` ` `{` ` ` `this` `.key=key;` ` ` `this` `.left=` `this` `.right=` `null` `;` ` ` `}` `}` `/* Function to find sum` ` ` `of all the elements*/` `function` `addBT(root)` `{` ` ` `if` `(root == ` `null` `)` ` ` `return` `0;` ` ` `return` `(root.key + addBT(root.left) +` ` ` `addBT(root.right));` `}` `// Driver Code` `let root = ` `new` `Node(1);` `root.left = ` `new` `Node(2);` `root.right = ` `new` `Node(3);` `root.left.left = ` `new` `Node(4);` `root.left.right = ` `new` `Node(5);` `root.right.left = ` `new` `Node(6);` `root.right.right = ` `new` `Node(7);` `root.right.left.right = ` `new` `Node(8);` `let sum = addBT(root);` `document.write(` `"Sum of all the elements is: "` `+ sum);` `// This code is contributed by avanitrachhadiya2155` `</script>` |

**Output**

Sum of all the elements is: 36

**Method 2 – **Another way to solve this problem is by using **Level Order Traversal. **Every time when a Node is deleted from the queue, add it to the sum variable.

## C++

`#include <bits/stdc++.h>` `#include <iostream>` `using` `namespace` `std;` `struct` `Node {` ` ` `int` `key;` ` ` `struct` `Node *left, *right;` `};` `// Utility function to create a new node` `Node* newNode(` `int` `key)` `{` ` ` `Node* temp = ` `new` `Node;` ` ` `temp->key = key;` ` ` `temp->left = temp->right = NULL;` ` ` `return` `(temp);` `}` `/*Function to find sum of all elements*/` `int` `sumBT(Node* root)` `{` ` ` `//sum variable to track the sum of` ` ` `//all variables.` ` ` `int` `sum = 0;` ` ` ` ` `queue<Node*> q;` ` ` `//Pushing the first level.` ` ` `q.push(root);` ` ` `//Pushing elements at each level from` ` ` `//the tree.` ` ` `while` `(!q.empty()) {` ` ` `Node* temp = q.front();` ` ` `q.pop();` ` ` ` ` `//After popping each element from queue` ` ` `//add its data to the sum variable.` ` ` `sum += temp->key;` ` ` `if` `(temp->left) {` ` ` `q.push(temp->left);` ` ` `}` ` ` `if` `(temp->right) {` ` ` `q.push(temp->right);` ` ` `}` ` ` `}` ` ` `return` `sum;` `}` `// Driver program` `int` `main()` `{` ` ` `// Let us create Binary Tree shown in above example` ` ` `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);` ` ` `cout << ` `"Sum of all elements in the binary tree is: "` ` ` `<< sumBT(root);` `}` `//This code is contributed by Sarthak Delori` |

**Output**

Sum of all elements in the binary tree is: 36

Time Complexity: O(n)

Auxiliary Space: O(n)

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