# Sum of all the Boundary Nodes of a Binary Tree

Given a binary tree, the task is to print the sum of all the boundary nodes of the tree.

Examples:

```Input:
1
/   \
2     3
/ \   / \
4   5 6   7
Output: 28

Input:
1
/   \
2     3
\    /
4  5
\
6
/ \
7   8
Output: 36

```

Approach: We have already discussed the Boundary Traversal of a Binary tree. Here we will find the sum of the boundary nodes of the given binary tree in four steps:

• Sum up all the nodes of the left boundary,
• Sum up all the leaf nodes of the left sub-tree,
• Sum up all the leaf nodes of the right sub-tree and
• Sum up all the nodes of the right boundary.

We will have to take care of one thing that nodes don’t add up again, i.e. the left most node is also the leaf node of the tree.

Below is the implementation of the above approach:

 `// C++ implementation of the approach` `#include ` `using` `namespace` `std;`   `// A binary tree node has data,` `// pointer to left child` `// and a pointer to right child` `struct` `Node {` `    ``int` `data;` `    ``struct` `Node* left;` `    ``struct` `Node* right;` `};`   `// Utility function to create a node` `Node* newNode(``int` `data)` `{` `    ``Node* temp = ``new` `Node;`   `    ``temp->left = NULL;` `    ``temp->right = NULL;` `    ``temp->data = data;`   `    ``return` `temp;` `}`   `// Function to sum up all the left boundary nodes` `// except the leaf nodes` `void` `LeftBoundary(Node* root, ``int``& sum_of_boundary_nodes)` `{` `    ``if` `(root) {` `        ``if` `(root->left) {` `            ``sum_of_boundary_nodes += root->data;` `            ``LeftBoundary(root->left, sum_of_boundary_nodes);` `        ``}` `        ``else` `if` `(root->right) {` `            ``sum_of_boundary_nodes += root->data;` `            ``LeftBoundary(root->right, sum_of_boundary_nodes);` `        ``}` `    ``}` `}`   `// Function to sum up all the right boundary nodes` `// except the leaf nodes` `void` `RightBoundary(Node* root, ``int``& sum_of_boundary_nodes)` `{` `    ``if` `(root) {` `        ``if` `(root->right) {` `            ``RightBoundary(root->right, sum_of_boundary_nodes);` `            ``sum_of_boundary_nodes += root->data;` `        ``}` `        ``else` `if` `(root->left) {` `            ``RightBoundary(root->left, sum_of_boundary_nodes);` `            ``sum_of_boundary_nodes += root->data;` `        ``}` `    ``}` `}`   `// Function to sum up all the leaf nodes` `// of a binary tree` `void` `Leaves(Node* root, ``int``& sum_of_boundary_nodes)` `{` `    ``if` `(root) {` `        ``Leaves(root->left, sum_of_boundary_nodes);`   `        ``// Sum it up if it is a leaf node` `        ``if` `(!(root->left) && !(root->right))` `            ``sum_of_boundary_nodes += root->data;`   `        ``Leaves(root->right, sum_of_boundary_nodes);` `    ``}` `}`   `// Function to return the sum of all the` `// boundary nodes of the given binary tree` `int` `sumOfBoundaryNodes(``struct` `Node* root)` `{` `    ``if` `(root) {`   `        ``// Root node is also a boundary node` `        ``int` `sum_of_boundary_nodes = root->data;`   `        ``// Sum up all the left nodes` `        ``// in TOP DOWN manner` `        ``LeftBoundary(root->left, sum_of_boundary_nodes);`   `        ``// Sum up all the` `        ``// leaf nodes` `        ``Leaves(root->left, sum_of_boundary_nodes);` `        ``Leaves(root->right, sum_of_boundary_nodes);`   `        ``// Sum up all the right nodes` `        ``// in BOTTOM UP manner` `        ``RightBoundary(root->right, sum_of_boundary_nodes);`   `        ``// Return the sum of` `        ``// all the boundary nodes` `        ``return` `sum_of_boundary_nodes;` `    ``}`   `    ``return` `0;` `}`   `// Driver code` `int` `main()` `{` `    ``Node* root = newNode(10);` `    ``root->left = newNode(2);` `    ``root->right = newNode(5);` `    ``root->left->left = newNode(8);` `    ``root->left->right = newNode(14);` `    ``root->right->left = newNode(11);` `    ``root->right->right = newNode(3);` `    ``root->left->right->left = newNode(12);` `    ``root->right->left->right = newNode(1);` `    ``root->right->left->left = newNode(7);`   `    ``cout << sumOfBoundaryNodes(root);`   `    ``return` `0;` `}`

 `// Java implementation of the approach ` `class` `GFG` `{` `    ``static` `int` `sum_of_boundary_nodes=``0``;`   `// A binary tree node has data, ` `// pointer to left child ` `static` `class` `Node` `{ ` `    ``int` `data; ` `    ``Node left; ` `    ``Node right; ` `}; `   `// Utility function to create a node ` `static` `Node newNode(``int` `data) ` `{ ` `    ``Node temp = ``new` `Node(); `   `    ``temp.left = ``null``; ` `    ``temp.right = ``null``; ` `    ``temp.data = data; `   `    ``return` `temp; ` `} `   `// Function to sum up all the left boundary nodes ` `// except the leaf nodes ` `static` `void` `LeftBoundary(Node root) ` `{ ` `    ``if` `(root != ``null``)` `    ``{ ` `        ``if` `(root.left != ``null``)` `        ``{ ` `            ``sum_of_boundary_nodes += root.data; ` `            ``LeftBoundary(root.left); ` `        ``} ` `        ``else` `if` `(root.right != ``null``)` `        ``{ ` `            ``sum_of_boundary_nodes += root.data; ` `            ``LeftBoundary(root.right); ` `        ``} ` `    ``} ` `} `   `// Function to sum up all the right boundary nodes ` `// except the leaf nodes ` `static` `void` `RightBoundary(Node root) ` `{ ` `    ``if` `(root != ``null``)` `    ``{ ` `        ``if` `(root.right != ``null``)` `        ``{ ` `            ``RightBoundary(root.right); ` `            ``sum_of_boundary_nodes += root.data; ` `        ``} ` `        ``else` `if` `(root.left != ``null``)` `        ``{ ` `            ``RightBoundary(root.left); ` `            ``sum_of_boundary_nodes += root.data; ` `        ``} ` `    ``} ` `} `   `// Function to sum up all the leaf nodes ` `// of a binary tree ` `static` `void` `Leaves(Node root) ` `{ ` `    ``if` `(root != ``null``)` `    ``{ ` `        ``Leaves(root.left); `   `        ``// Sum it up if it is a leaf node ` `        ``if` `((root.left == ``null``) && (root.right == ``null``)) ` `            ``sum_of_boundary_nodes += root.data; `   `        ``Leaves(root.right); ` `    ``} ` `} `   `// Function to return the sum of all the ` `// boundary nodes of the given binary tree ` `static` `int` `sumOfBoundaryNodes( Node root) ` `{ ` `    ``if` `(root != ``null``) ` `    ``{ `   `        ``// Root node is also a boundary node ` `        ``sum_of_boundary_nodes = root.data; `   `        ``// Sum up all the left nodes ` `        ``// in TOP DOWN manner ` `        ``LeftBoundary(root.left); `   `        ``// Sum up all the ` `        ``// leaf nodes ` `        ``Leaves(root.left); ` `        ``Leaves(root.right); `   `        ``// Sum up all the right nodes ` `        ``// in BOTTOM UP manner ` `        ``RightBoundary(root.right); `   `        ``// Return the sum of ` `        ``// all the boundary nodes ` `        ``return` `sum_of_boundary_nodes; ` `    ``} `   `    ``return` `0``; ` `} `   `// Driver code ` `public` `static` `void` `main(String args[])` `{ ` `    ``Node root = newNode(``10``); ` `    ``root.left = newNode(``2``); ` `    ``root.right = newNode(``5``); ` `    ``root.left.left = newNode(``8``); ` `    ``root.left.right = newNode(``14``); ` `    ``root.right.left = newNode(``11``); ` `    ``root.right.right = newNode(``3``); ` `    ``root.left.right.left = newNode(``12``); ` `    ``root.right.left.right = newNode(``1``); ` `    ``root.right.left.left = newNode(``7``); `   `    ``System.out.println(sumOfBoundaryNodes(root)); ` `}` `} `   `// This code is contributed by andrew1234`

 `# Python3 implementation of the approach` ` `  `# A binary tree node has data,` `# pointer to left child` `# and a pointer to right child` `class` `Node:` `    `  `    ``def` `__init__(``self``):` `        `  `        ``self``.left ``=` `None` `        ``self``.right ``=` `None` `        `  `sum_of_boundary_nodes ``=` `0`   `# Utility function to create a node` `def` `newNode(data):`   `    ``temp ``=` `Node()` `    ``temp.data ``=` `data;` `    ``return` `temp;`   `# Function to sum up all the ` `# left boundary nodes except` `# the leaf nodes` `def` `LeftBoundary(root):` `    `  `    ``global` `sum_of_boundary_nodes` `    `  `    ``if` `(root !``=` `None``):` `        ``if` `(root.left !``=` `None``):` `            ``sum_of_boundary_nodes ``+``=` `root.data;` `            ``LeftBoundary(root.left);` `        `  `        ``elif` `(root.right !``=` `None``):` `            ``sum_of_boundary_nodes ``+``=` `root.data;` `            ``LeftBoundary(root.right);`   `# Function to sum up all the right ` `# boundary nodes except the leaf nodes` `def` `RightBoundary(root):` `    `  `    ``global` `sum_of_boundary_nodes` `    `  `    ``if` `(root !``=` `None``):` `        ``if` `(root.right !``=` `None``):` `            ``RightBoundary(root.right);` `            ``sum_of_boundary_nodes ``+``=` `root.data;` `        `  `        ``elif` `(root.left !``=` `None``):` `            ``RightBoundary(root.left);` `            ``sum_of_boundary_nodes ``+``=` `root.data;` `        `  `# Function to sum up all the leaf nodes` `# of a binary tree` `def` `Leaves(root):` `    `  `    ``global` `sum_of_boundary_nodes` `    `  `    ``if` `(root !``=` `None``):` `        ``Leaves(root.left);` ` `  `        ``# Sum it up if it is a leaf node` `        ``if` `((root.left ``=``=` `None``) ``and` `           ``(root.right ``=``=` `None``)):` `            ``sum_of_boundary_nodes ``+``=` `root.data;` ` `  `        ``Leaves(root.right);` `    `  `# Function to return the sum of all the` `# boundary nodes of the given binary tree` `def` `sumOfBoundaryNodes(root):` `    `  `    ``global` `sum_of_boundary_nodes` `    `  `    ``if` `(root !``=` `None``):` `        `  `        ``# Root node is also a boundary node` `        ``sum_of_boundary_nodes ``=` `root.data;` ` `  `        ``# Sum up all the left nodes` `        ``# in TOP DOWN manner` `        ``LeftBoundary(root.left);` ` `  `        ``# Sum up all the` `        ``# leaf nodes` `        ``Leaves(root.left);` `        ``Leaves(root.right);` ` `  `        ``# Sum up all the right nodes` `        ``# in BOTTOM UP manner` `        ``RightBoundary(root.right);` ` `  `        ``# Return the sum of` `        ``# all the boundary nodes` `        ``return` `sum_of_boundary_nodes;` `    `  `    ``return` `0``;`   `# Driver code` `if` `__name__``=``=``"__main__"``:` `    `  `    ``root ``=` `newNode(``10``);` `    ``root.left ``=` `newNode(``2``);` `    ``root.right ``=` `newNode(``5``);` `    ``root.left.left ``=` `newNode(``8``);` `    ``root.left.right ``=` `newNode(``14``);` `    ``root.right.left ``=` `newNode(``11``);` `    ``root.right.right ``=` `newNode(``3``);` `    ``root.left.right.left ``=` `newNode(``12``);` `    ``root.right.left.right ``=` `newNode(``1``);` `    ``root.right.left.left ``=` `newNode(``7``);` ` `  `    ``print``(sumOfBoundaryNodes(root));`   `# This code is contributed by rutvik_56`

 `// C# implementation of the approach` `using` `System;` `class` `GFG` `{` `static` `int` `sum_of_boundary_nodes = 0;`   `// A binary tree node has data, ` `// pointer to left child ` `public` `class` `Node` `{ ` `    ``public` `int` `data; ` `    ``public` `Node left; ` `    ``public` `Node right; ` `}; `   `// Utility function to create a node ` `static` `Node newNode(``int` `data) ` `{ ` `    ``Node temp = ``new` `Node(); `   `    ``temp.left = ``null``; ` `    ``temp.right = ``null``; ` `    ``temp.data = data; `   `    ``return` `temp; ` `} `   `// Function to sum up all the left boundary ` `// nodes except the leaf nodes ` `static` `void` `LeftBoundary(Node root) ` `{ ` `    ``if` `(root != ``null``)` `    ``{ ` `        ``if` `(root.left != ``null``)` `        ``{ ` `            ``sum_of_boundary_nodes += root.data; ` `            ``LeftBoundary(root.left); ` `        ``} ` `        `  `        ``else` `if` `(root.right != ``null``)` `        ``{ ` `            ``sum_of_boundary_nodes += root.data; ` `            ``LeftBoundary(root.right); ` `        ``} ` `    ``} ` `} `   `// Function to sum up all the right boundary ` `// nodes except the leaf nodes ` `static` `void` `RightBoundary(Node root) ` `{ ` `    ``if` `(root != ``null``)` `    ``{ ` `        ``if` `(root.right != ``null``)` `        ``{ ` `            ``RightBoundary(root.right); ` `            ``sum_of_boundary_nodes += root.data; ` `        ``} ` `        ``else` `if` `(root.left != ``null``)` `        ``{ ` `            ``RightBoundary(root.left); ` `            ``sum_of_boundary_nodes += root.data; ` `        ``} ` `    ``} ` `} `   `// Function to sum up all the leaf nodes ` `// of a binary tree ` `static` `void` `Leaves(Node root) ` `{ ` `    ``if` `(root != ``null``)` `    ``{ ` `        ``Leaves(root.left); `   `        ``// Sum it up if it is a leaf node ` `        ``if` `((root.left == ``null``) &&` `            ``(root.right == ``null``)) ` `            ``sum_of_boundary_nodes += root.data; `   `        ``Leaves(root.right); ` `    ``} ` `} `   `// Function to return the sum of all the ` `// boundary nodes of the given binary tree ` `static` `int` `sumOfBoundaryNodes(Node root) ` `{ ` `    ``if` `(root != ``null``) ` `    ``{ `   `        ``// Root node is also a boundary node ` `        ``sum_of_boundary_nodes = root.data; `   `        ``// Sum up all the left nodes ` `        ``// in TOP DOWN manner ` `        ``LeftBoundary(root.left); `   `        ``// Sum up all the ` `        ``// leaf nodes ` `        ``Leaves(root.left); ` `        ``Leaves(root.right); `   `        ``// Sum up all the right nodes ` `        ``// in BOTTOM UP manner ` `        ``RightBoundary(root.right); `   `        ``// Return the sum of ` `        ``// all the boundary nodes ` `        ``return` `sum_of_boundary_nodes; ` `    ``} ` `    ``return` `0; ` `} `   `// Driver code ` `public` `static` `void` `Main(String []args)` `{ ` `    ``Node root = newNode(10); ` `    ``root.left = newNode(2); ` `    ``root.right = newNode(5); ` `    ``root.left.left = newNode(8); ` `    ``root.left.right = newNode(14); ` `    ``root.right.left = newNode(11); ` `    ``root.right.right = newNode(3); ` `    ``root.left.right.left = newNode(12); ` `    ``root.right.left.right = newNode(1); ` `    ``root.right.left.left = newNode(7); `   `    ``Console.WriteLine(sumOfBoundaryNodes(root)); ` `}` `} `   `// This code is contributed by Princi Singh`

Output:
```48

```

Time Complexity: O(N) where N is the number of nodes in the binary tree.

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