# Sum of nodes on the longest path from root to leaf node

Given a binary tree containing n nodes. The problem is to find the sum of all nodes on the longest path from root to leaf node. If two or more paths compete for the longest path, then the path having maximum sum of nodes is being considered.

Examples:

```Input : Binary tree:
4
/
2   5
/  /
7  1 2  3
/
6
Output : 13

4
/
2   5
/  /
7  1 2  3
/
6

The highlighted nodes (4, 2, 1, 6) above are
part of the longest root to leaf path having
sum = (4 + 2 + 1 + 6) = 13
```

Approach: Recursively find the length and sum of nodes of each root to leaf path and accordingly update the maximum sum.

Algorithm:

```sumOfLongRootToLeafPath(root, sum, len, maxLen, maxSum)
if root == NULL
if maxLen < len
maxLen = len
maxSum = sum
else if maxLen == len && maxSum is less than sum
maxSum = sum
return

sumOfLongRootToLeafPath(root-left, sum + root-data,
len + 1, maxLen, maxSum)
sumOfLongRootToLeafPath(root-right, sum + root-data,
len + 1, maxLen, maxSum)

sumOfLongRootToLeafPathUtil(root)
if (root == NULL)
return 0

Declare maxSum = Minimum Integer
Declare maxLen = 0
sumOfLongRootToLeafPath(root, 0, 0, maxLen, maxSum)
return maxSum
```

## C++

 `// C++ implementation to find the sum of nodes ` `// on the longest path from root to leaf node ` `#include ` ` `  `using` `namespace` `std; ` ` `  `// Node of a binary tree ` `struct` `Node { ` `    ``int` `data; ` `    ``Node* left, *right; ` `}; ` ` `  `// function to get a new node ` `Node* getNode(``int` `data) ` `{ ` `    ``// allocate memory for the node ` `    ``Node* newNode = (Node*)``malloc``(``sizeof``(Node)); ` ` `  `    ``// put in the data ` `    ``newNode->data = data; ` `    ``newNode->left = newNode->right = NULL; ` `    ``return` `newNode; ` `} ` ` `  `// function to find the sum of nodes on the ` `// longest path from root to leaf node ` `void` `sumOfLongRootToLeafPath(Node* root, ``int` `sum, ` `                      ``int` `len, ``int``& maxLen, ``int``& maxSum) ` `{ ` `    ``// if true, then we have traversed a ` `    ``// root to leaf path ` `    ``if` `(!root) { ` `        ``// update maximum length and maximum sum ` `        ``// according to the given conditions ` `        ``if` `(maxLen < len) { ` `            ``maxLen = len; ` `            ``maxSum = sum; ` `        ``} ``else` `if` `(maxLen == len && maxSum < sum) ` `            ``maxSum = sum; ` `        ``return``; ` `    ``} ` ` `  `    ``// recur for left subtree ` `    ``sumOfLongRootToLeafPath(root->left, sum + root->data, ` `                            ``len + 1, maxLen, maxSum); ` ` `  `    ``// recur for right subtree ` `    ``sumOfLongRootToLeafPath(root->right, sum + root->data, ` `                            ``len + 1, maxLen, maxSum); ` `} ` ` `  `// utility function to find the sum of nodes on ` `// the longest path from root to leaf node ` `int` `sumOfLongRootToLeafPathUtil(Node* root) ` `{ ` `    ``// if tree is NULL, then sum is 0 ` `    ``if` `(!root) ` `        ``return` `0; ` ` `  `    ``int` `maxSum = INT_MIN, maxLen = 0; ` ` `  `    ``// finding the maximum sum 'maxSum' for the ` `    ``// maximum length root to leaf path ` `    ``sumOfLongRootToLeafPath(root, 0, 0, maxLen, maxSum); ` ` `  `    ``// required maximum sum ` `    ``return` `maxSum; ` `} ` ` `  `// Driver program to test above ` `int` `main() ` `{ ` `    ``// binary tree formation ` `    ``Node* root = getNode(4);         ``/*        4        */` `    ``root->left = getNode(2);         ``/*       /        */` `    ``root->right = getNode(5);        ``/*      2   5      */` `    ``root->left->left = getNode(7);   ``/*     / /      */` `    ``root->left->right = getNode(1);  ``/*    7  1 2  3    */` `    ``root->right->left = getNode(2);  ``/*      /          */` `    ``root->right->right = getNode(3); ``/*     6           */` `    ``root->left->right->left = getNode(6); ` ` `  `    ``cout << ``"Sum = "` `         ``<< sumOfLongRootToLeafPathUtil(root); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation to find the sum of nodes ` `// on the longest path from root to leaf node ` `public` `class` `GFG  ` `{                         ` `    ``// Node of a binary tree ` `    ``static` `class` `Node { ` `        ``int` `data; ` `        ``Node left, right; ` `         `  `        ``Node(``int` `data){ ` `            ``this``.data = data; ` `            ``left = ``null``; ` `            ``right = ``null``; ` `        ``} ` `    ``} ` `    ``static` `int` `maxLen; ` `    ``static` `int` `maxSum; ` `     `  `    ``// function to find the sum of nodes on the ` `    ``// longest path from root to leaf node ` `    ``static` `void` `sumOfLongRootToLeafPath(Node root, ``int` `sum, ` `                                         ``int` `len) ` `    ``{ ` `        ``// if true, then we have traversed a ` `        ``// root to leaf path ` `        ``if` `(root == ``null``) { ` `            ``// update maximum length and maximum sum ` `            ``// according to the given conditions ` `            ``if` `(maxLen < len) { ` `                ``maxLen = len; ` `                ``maxSum = sum; ` `            ``} ``else` `if` `(maxLen == len && maxSum < sum) ` `                ``maxSum = sum; ` `            ``return``; ` `        ``} ` `         `  `         `  `        ``// recur for left subtree ` `        ``sumOfLongRootToLeafPath(root.left, sum + root.data, ` `                                ``len + ``1``); ` `         `  `        ``sumOfLongRootToLeafPath(root.right, sum + root.data, ` `                                ``len + ``1``); ` `         `  `    ``} ` `      `  `    ``// utility function to find the sum of nodes on ` `    ``// the longest path from root to leaf node ` `    ``static` `int` `sumOfLongRootToLeafPathUtil(Node root) ` `    ``{ ` `        ``// if tree is NULL, then sum is 0 ` `        ``if` `(root == ``null``) ` `            ``return` `0``; ` `      `  `        ``maxSum = Integer.MIN_VALUE; ` `        ``maxLen = ``0``; ` `      `  `        ``// finding the maximum sum 'maxSum' for the ` `        ``// maximum length root to leaf path ` `        ``sumOfLongRootToLeafPath(root, ``0``, ``0``); ` `      `  `        ``// required maximum sum ` `        ``return` `maxSum; ` `    ``} ` `      `  `    ``// Driver program to test above ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``// binary tree formation ` `        ``Node root = ``new` `Node(``4``);         ``/*        4        */` `        ``root.left = ``new` `Node(``2``);         ``/*       /        */` `        ``root.right = ``new` `Node(``5``);        ``/*      2   5      */` `        ``root.left.left = ``new` `Node(``7``);    ``/*     / /      */` `        ``root.left.right = ``new` `Node(``1``);   ``/*    7  1 2  3    */` `        ``root.right.left = ``new` `Node(``2``);   ``/*      /          */` `        ``root.right.right = ``new` `Node(``3``);  ``/*     6           */` `        ``root.left.right.left = ``new` `Node(``6``); ` `      `  `        ``System.out.println( ``"Sum = "` `             ``+ sumOfLongRootToLeafPathUtil(root)); ` `    ``} ` `} ` `// This code is contributed by Sumit Ghosh `

## Python3

 `# Python3 implementation to find the   ` `# Sum of nodes on the longest path  ` `# from root to leaf nodes ` ` `  `# function to get a new node  ` `class` `getNode: ` `    ``def` `__init__(``self``, data):  ` ` `  `        ``# put in the data  ` `        ``self``.data ``=` `data  ` `        ``self``.left ``=` `self``.right ``=` `None` ` `  `# function to find the Sum of nodes on the  ` `# longest path from root to leaf node  ` `def` `SumOfLongRootToLeafPath(root, ``Sum``, ``Len``, ` `                            ``maxLen, maxSum): ` `                                 `  `    ``# if true, then we have traversed a  ` `    ``# root to leaf path  ` `    ``if` `(``not` `root): ` `         `  `        ``# update maximum Length and maximum Sum  ` `        ``# according to the given conditions  ` `        ``if` `(maxLen[``0``] < ``Len``):  ` `            ``maxLen[``0``] ``=` `Len` `            ``maxSum[``0``] ``=` `Sum` `        ``elif` `(maxLen[``0``]``=``=` `Len` `and`  `              ``maxSum[``0``] < ``Sum``):  ` `            ``maxSum[``0``] ``=` `Sum` `        ``return` ` `  `    ``# recur for left subtree  ` `    ``SumOfLongRootToLeafPath(root.left, ``Sum` `+` `root.data,  ` `                            ``Len` `+` `1``, maxLen, maxSum)  ` ` `  `    ``# recur for right subtree  ` `    ``SumOfLongRootToLeafPath(root.right, ``Sum` `+` `root.data,  ` `                            ``Len` `+` `1``, maxLen, maxSum) ` ` `  `# utility function to find the Sum of nodes on  ` `# the longest path from root to leaf node  ` `def` `SumOfLongRootToLeafPathUtil(root): ` `     `  `    ``# if tree is NULL, then Sum is 0  ` `    ``if` `(``not` `root):  ` `        ``return` `0` ` `  `    ``maxSum ``=` `[``-``999999999999``] ` `    ``maxLen ``=` `[``0``]  ` ` `  `    ``# finding the maximum Sum 'maxSum' for  ` `    ``# the maximum Length root to leaf path  ` `    ``SumOfLongRootToLeafPath(root, ``0``, ``0``,  ` `                            ``maxLen, maxSum)  ` ` `  `    ``# required maximum Sum  ` `    ``return` `maxSum[``0``] ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `'__main__'``: ` `     `  `    ``# binary tree formation  ` `    ``root ``=` `getNode(``4``)         ``#     4      ` `    ``root.left ``=` `getNode(``2``)         ``#     /       ` `    ``root.right ``=` `getNode(``5``)     ``#     2 5      ` `    ``root.left.left ``=` `getNode(``7``) ``#     / /       ` `    ``root.left.right ``=` `getNode(``1``) ``# 7 1 2 3  ` `    ``root.right.left ``=` `getNode(``2``) ``#     /          ` `    ``root.right.right ``=` `getNode(``3``) ``#     6          ` `    ``root.left.right.left ``=` `getNode(``6``)  ` ` `  `    ``print``(``"Sum = "``, SumOfLongRootToLeafPathUtil(root)) ` `     `  `# This code is contributed by PranchalK `

## C#

 `using` `System; ` ` `  `// c# implementation to find the sum of nodes  ` `// on the longest path from root to leaf node  ` `public` `class` `GFG ` `{ ` `    ``// Node of a binary tree  ` `    ``public` `class` `Node ` `    ``{ ` `        ``public` `int` `data; ` `        ``public` `Node left, right; ` ` `  `        ``public` `Node(``int` `data) ` `        ``{ ` `            ``this``.data = data; ` `            ``left = ``null``; ` `            ``right = ``null``; ` `        ``} ` `    ``} ` `    ``public` `static` `int` `maxLen; ` `    ``public` `static` `int` `maxSum; ` ` `  `    ``// function to find the sum of nodes on the  ` `    ``// longest path from root to leaf node  ` `    ``public` `static` `void` `sumOfLongRootToLeafPath(Node root, ``int` `sum, ``int` `len) ` `    ``{ ` `        ``// if true, then we have traversed a  ` `        ``// root to leaf path  ` `        ``if` `(root == ``null``) ` `        ``{ ` `            ``// update maximum length and maximum sum  ` `            ``// according to the given conditions  ` `            ``if` `(maxLen < len) ` `            ``{ ` `                ``maxLen = len; ` `                ``maxSum = sum; ` `            ``} ` `            ``else` `if` `(maxLen == len && maxSum < sum) ` `            ``{ ` `                ``maxSum = sum; ` `            ``} ` `            ``return``; ` `        ``} ` ` `  ` `  `        ``// recur for left subtree  ` `        ``sumOfLongRootToLeafPath(root.left, sum + root.data, len + 1); ` ` `  `        ``sumOfLongRootToLeafPath(root.right, sum + root.data, len + 1); ` ` `  `    ``} ` ` `  `    ``// utility function to find the sum of nodes on  ` `    ``// the longest path from root to leaf node  ` `    ``public` `static` `int` `sumOfLongRootToLeafPathUtil(Node root) ` `    ``{ ` `        ``// if tree is NULL, then sum is 0  ` `        ``if` `(root == ``null``) ` `        ``{ ` `            ``return` `0; ` `        ``} ` ` `  `        ``maxSum = ``int``.MinValue; ` `        ``maxLen = 0; ` ` `  `        ``// finding the maximum sum 'maxSum' for the  ` `        ``// maximum length root to leaf path  ` `        ``sumOfLongRootToLeafPath(root, 0, 0); ` ` `  `        ``// required maximum sum  ` `        ``return` `maxSum; ` `    ``} ` ` `  `    ``// Driver program to test above  ` `    ``public` `static` `void` `Main(``string``[] args) ` `    ``{ ` `        ``// binary tree formation  ` `        ``Node root = ``new` `Node(4); ``//        4 ` `        ``root.left = ``new` `Node(2); ``//       / ` `        ``root.right = ``new` `Node(5); ``//      2   5 ` `        ``root.left.left = ``new` `Node(7); ``//     / / ` `        ``root.left.right = ``new` `Node(1); ``//    7  1 2  3 ` `        ``root.right.left = ``new` `Node(2); ``//      / ` `        ``root.right.right = ``new` `Node(3); ``//     6 ` `        ``root.left.right.left = ``new` `Node(6); ` ` `  `        ``Console.WriteLine(``"Sum = "` `+ sumOfLongRootToLeafPathUtil(root)); ` `    ``} ` `} ` ` `  `  ``// This code is contributed by Shrikant13 `

Output:

```Sum = 13
```

Time Complexity: O(n)

## tags:

Tree Traversal Traversal Tree