# Find the maximum sum leaf to root path in a Binary Tree

Given a Binary Tree, find the maximum sum path from a leaf to root. For example, in the following tree, there are three leaf to root paths 8->-2->10, -4->-2->10 and 7->10. The sums of these three paths are 16, 4 and 17 respectively. The maximum of them is 17 and the path for maximum is 7->10.

```                  10
/
-2        7
/
8     -4
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Solution
1) First find the leaf node that is on the maximum sum path. In the following code getTargetLeaf() does this by assigning the result to *target_leaf_ref.
2) Once we have the target leaf node, we can print the maximum sum path by traversing the tree. In the following code, printPath() does this.

The main function is maxSumPath() that uses above two functions to get the complete solution.

## C++

 `// CPP program to find maximum sum leaf to root ` `// path in Binary Tree ` `#include ` `using` `namespace` `std; ` ` `  `/* A tree node structure */` `class` `node { ` `public``: ` `    ``int` `data; ` `    ``node* left; ` `    ``node* right; ` `}; ` ` `  `// A utility function that prints all nodes ` `// on the path from root to target_leaf ` `bool` `printPath(node* root, ` `               ``node* target_leaf) ` `{ ` `    ``// base case ` `    ``if` `(root == NULL) ` `        ``return` `false``; ` ` `  `    ``// return true if this node is the target_leaf ` `    ``// or target leaf is present in one of its ` `    ``// descendants ` `    ``if` `(root == target_leaf || printPath(root->left, target_leaf) ||  ` `                               ``printPath(root->right, target_leaf)) { ` `        ``cout << root->data << ``" "``; ` `        ``return` `true``; ` `    ``} ` ` `  `    ``return` `false``; ` `} ` ` `  `// This function Sets the target_leaf_ref to refer ` `// the leaf node of the maximum path sum. Also, ` `// returns the max_sum using max_sum_ref ` `void` `getTargetLeaf(node* Node, ``int``* max_sum_ref, ` `                   ``int` `curr_sum, node** target_leaf_ref) ` `{ ` `    ``if` `(Node == NULL) ` `        ``return``; ` ` `  `    ``// Update current sum to hold sum of nodes on path ` `    ``// from root to this node ` `    ``curr_sum = curr_sum + Node->data; ` ` `  `    ``// If this is a leaf node and path to this node has ` `    ``// maximum sum so far, then make this node target_leaf ` `    ``if` `(Node->left == NULL && Node->right == NULL) { ` `        ``if` `(curr_sum > *max_sum_ref) { ` `            ``*max_sum_ref = curr_sum; ` `            ``*target_leaf_ref = Node; ` `        ``} ` `    ``} ` ` `  `    ``// If this is not a leaf node, then recur down ` `    ``// to find the target_leaf ` `    ``getTargetLeaf(Node->left, max_sum_ref, curr_sum, ` `                  ``target_leaf_ref); ` `    ``getTargetLeaf(Node->right, max_sum_ref, curr_sum, ` `                  ``target_leaf_ref); ` `} ` ` `  `// Returns the maximum sum and prints the nodes on max ` `// sum path ` `int` `maxSumPath(node* Node) ` `{ ` `    ``// base case ` `    ``if` `(Node == NULL) ` `        ``return` `0; ` ` `  `    ``node* target_leaf; ` `    ``int` `max_sum = INT_MIN; ` ` `  `    ``// find the target leaf and maximum sum ` `    ``getTargetLeaf(Node, &max_sum, 0, &target_leaf); ` ` `  `    ``// print the path from root to the target leaf ` `    ``printPath(Node, target_leaf); ` ` `  `    ``return` `max_sum; ``// return maximum sum ` `} ` ` `  `/* Utility function to create a new Binary Tree node */` `node* newNode(``int` `data) ` `{ ` `    ``node* temp = ``new` `node; ` `    ``temp->data = data; ` `    ``temp->left = NULL; ` `    ``temp->right = NULL; ` `    ``return` `temp; ` `} ` ` `  `/* Driver function to test above functions */` `int` `main() ` `{ ` `    ``node* root = NULL; ` ` `  `    ``/* Constructing tree given in the above figure */` `    ``root = newNode(10); ` `    ``root->left = newNode(-2); ` `    ``root->right = newNode(7); ` `    ``root->left->left = newNode(8); ` `    ``root->left->right = newNode(-4); ` ` `  `    ``cout << ``"Following are the nodes on the maximum "` `            ````"sum path "````; ` `    ``int` `sum = maxSumPath(root); ` `    ``cout << ````" Sum of the nodes is "``` `<< sum; ` `    ``return` `0; ` `} ` ` `  `// This code is contributed by rathbhupendra `

## C

 `// C program to find maximum sum leaf to root ` `// path in Binary Tree ` `#include ` `#include ` `#include ` `#include ` ` `  `/* A tree node structure */` `struct` `node { ` `    ``int` `data; ` `    ``struct` `node* left; ` `    ``struct` `node* right; ` `}; ` ` `  `// A utility function that prints all nodes ` `// on the path from root to target_leaf ` `bool` `printPath(``struct` `node* root, ` `               ``struct` `node* target_leaf) ` `{ ` `    ``// base case ` `    ``if` `(root == NULL) ` `        ``return` `false``; ` ` `  `    ``// return true if this node is the target_leaf ` `    ``// or target leaf is present in one of its ` `    ``// descendants ` `    ``if` `(root == target_leaf || printPath(root->left, target_leaf) ||  ` `                               ``printPath(root->right, target_leaf)) { ` `        ``printf``(``"%d "``, root->data); ` `        ``return` `true``; ` `    ``} ` ` `  `    ``return` `false``; ` `} ` ` `  `// This function Sets the target_leaf_ref to refer ` `// the leaf node of the maximum path sum. Also, ` `// returns the max_sum using max_sum_ref ` `void` `getTargetLeaf(``struct` `node* node, ``int``* max_sum_ref, ` `                   ``int` `curr_sum, ``struct` `node** target_leaf_ref) ` `{ ` `    ``if` `(node == NULL) ` `        ``return``; ` ` `  `    ``// Update current sum to hold sum of nodes on path ` `    ``// from root to this node ` `    ``curr_sum = curr_sum + node->data; ` ` `  `    ``// If this is a leaf node and path to this node has ` `    ``// maximum sum so far, then make this node target_leaf ` `    ``if` `(node->left == NULL && node->right == NULL) { ` `        ``if` `(curr_sum > *max_sum_ref) { ` `            ``*max_sum_ref = curr_sum; ` `            ``*target_leaf_ref = node; ` `        ``} ` `    ``} ` ` `  `    ``// If this is not a leaf node, then recur down ` `    ``// to find the target_leaf ` `    ``getTargetLeaf(node->left, max_sum_ref, curr_sum, ` `                  ``target_leaf_ref); ` `    ``getTargetLeaf(node->right, max_sum_ref, curr_sum, ` `                  ``target_leaf_ref); ` `} ` ` `  `// Returns the maximum sum and prints the nodes on max ` `// sum path ` `int` `maxSumPath(``struct` `node* node) ` `{ ` `    ``// base case ` `    ``if` `(node == NULL) ` `        ``return` `0; ` ` `  `    ``struct` `node* target_leaf; ` `    ``int` `max_sum = INT_MIN; ` ` `  `    ``// find the target leaf and maximum sum ` `    ``getTargetLeaf(node, &max_sum, 0, &target_leaf); ` ` `  `    ``// print the path from root to the target leaf ` `    ``printPath(node, target_leaf); ` ` `  `    ``return` `max_sum; ``// return maximum sum ` `} ` ` `  `/* Utility function to create a new Binary Tree node */` `struct` `node* newNode(``int` `data) ` `{ ` `    ``struct` `node* temp = (``struct` `node*)``malloc``(``sizeof``(``struct` `node)); ` `    ``temp->data = data; ` `    ``temp->left = NULL; ` `    ``temp->right = NULL; ` `    ``return` `temp; ` `} ` ` `  `/* Driver function to test above functions */` `int` `main() ` `{ ` `    ``struct` `node* root = NULL; ` ` `  `    ``/* Constructing tree given in the above figure */` `    ``root = newNode(10); ` `    ``root->left = newNode(-2); ` `    ``root->right = newNode(7); ` `    ``root->left->left = newNode(8); ` `    ``root->left->right = newNode(-4); ` ` `  `    ``printf``(``"Following are the nodes on the maximum "` `           ````"sum path "````); ` `    ``int` `sum = maxSumPath(root); ` `    ``printf``(````" Sum of the nodes is %d "````, sum); ` ` `  `    ``getchar``(); ` `    ``return` `0; ` `} `

## Java

 `// Java program to find maximum sum leaf to root ` `// path in Binary Tree ` ` `  `// A Binary Tree node ` `class` `Node { ` `    ``int` `data; ` `    ``Node left, right; ` ` `  `    ``Node(``int` `item) ` `    ``{ ` `        ``data = item; ` `        ``left = right = ``null``; ` `    ``} ` `} ` ` `  `// A wrapper class is used so that max_no ` `// can be updated among function calls. ` `class` `Maximum { ` `    ``int` `max_no = Integer.MIN_VALUE; ` `} ` ` `  `class` `BinaryTree { ` `    ``Node root; ` `    ``Maximum max = ``new` `Maximum(); ` `    ``Node target_leaf = ``null``; ` ` `  `    ``// A utility function that prints all nodes on the ` `    ``// path from root to target_leaf ` `    ``boolean` `printPath(Node node, Node target_leaf) ` `    ``{ ` `        ``// base case ` `        ``if` `(node == ``null``) ` `            ``return` `false``; ` ` `  `        ``// return true if this node is the target_leaf or ` `        ``// target leaf is present in one of its descendants ` `        ``if` `(node == target_leaf || printPath(node.left, target_leaf) ` `            ``|| printPath(node.right, target_leaf)) { ` `            ``System.out.print(node.data + ``" "``); ` `            ``return` `true``; ` `        ``} ` ` `  `        ``return` `false``; ` `    ``} ` ` `  `    ``// This function Sets the target_leaf_ref to refer ` `    ``// the leaf node of the maximum path sum. Also, ` `    ``// returns the max_sum using max_sum_ref ` `    ``void` `getTargetLeaf(Node node, Maximum max_sum_ref, ` `                       ``int` `curr_sum) ` `    ``{ ` `        ``if` `(node == ``null``) ` `            ``return``; ` ` `  `        ``// Update current sum to hold sum of nodes on ` `        ``// path from root to this node ` `        ``curr_sum = curr_sum + node.data; ` ` `  `        ``// If this is a leaf node and path to this node ` `        ``// has maximum sum so far, the n make this node ` `        ``// target_leaf ` `        ``if` `(node.left == ``null` `&& node.right == ``null``) { ` `            ``if` `(curr_sum > max_sum_ref.max_no) { ` `                ``max_sum_ref.max_no = curr_sum; ` `                ``target_leaf = node; ` `            ``} ` `        ``} ` ` `  `        ``// If this is not a leaf node, then recur down ` `        ``// to find the target_leaf ` `        ``getTargetLeaf(node.left, max_sum_ref, curr_sum); ` `        ``getTargetLeaf(node.right, max_sum_ref, curr_sum); ` `    ``} ` ` `  `    ``// Returns the maximum sum and prints the nodes on ` `    ``// max sum path ` `    ``int` `maxSumPath() ` `    ``{ ` `        ``// base case ` `        ``if` `(root == ``null``) ` `            ``return` `0``; ` ` `  `        ``// find the target leaf and maximum sum ` `        ``getTargetLeaf(root, max, ``0``); ` ` `  `        ``// print the path from root to the target leaf ` `        ``printPath(root, target_leaf); ` `        ``return` `max.max_no; ``// return maximum sum ` `    ``} ` ` `  `    ``// driver function to test the above functions ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``BinaryTree tree = ``new` `BinaryTree(); ` `        ``tree.root = ``new` `Node(``10``); ` `        ``tree.root.left = ``new` `Node(-``2``); ` `        ``tree.root.right = ``new` `Node(``7``); ` `        ``tree.root.left.left = ``new` `Node(``8``); ` `        ``tree.root.left.right = ``new` `Node(-``4``); ` `        ``System.out.println(``"Following are the nodes "` `                           ``+ ``"on maximum sum path"``); ` `        ``int` `sum = tree.maxSumPath(); ` `        ``System.out.println(``""``); ` `        ``System.out.println(``"Sum of nodes is : "` `+ sum); ` `    ``} ` `} ` `// This code has been contributed by Mayank Jaiswal `

## C#

 `using` `System; ` ` `  `// C# program to find maximum sum leaf to root ` `// path in Binary Tree ` ` `  `// A Binary Tree node ` `public` `class` `Node { ` `    ``public` `int` `data; ` `    ``public` `Node left, right; ` ` `  `    ``public` `Node(``int` `item) ` `    ``{ ` `        ``data = item; ` `        ``left = right = ``null``; ` `    ``} ` `} ` ` `  `// A wrapper class is used so that max_no ` `// can be updated among function calls. ` `public` `class` `Maximum { ` `    ``public` `int` `max_no = ``int``.MinValue; ` `} ` ` `  `public` `class` `BinaryTree { ` `    ``public` `Node root; ` `    ``public` `Maximum max = ``new` `Maximum(); ` `    ``public` `Node target_leaf = ``null``; ` ` `  `    ``// A utility function that prints all nodes on the ` `    ``// path from root to target_leaf ` `    ``public` `virtual` `bool` `printPath(Node node, Node target_leaf) ` `    ``{ ` `        ``// base case ` `        ``if` `(node == ``null``) { ` `            ``return` `false``; ` `        ``} ` ` `  `        ``// return true if this node is the target_leaf or ` `        ``// target leaf is present in one of its descendants ` `        ``if` `(node == target_leaf || printPath(node.left, target_leaf) ` `            ``|| printPath(node.right, target_leaf)) { ` `            ``Console.Write(node.data + ``" "``); ` `            ``return` `true``; ` `        ``} ` ` `  `        ``return` `false``; ` `    ``} ` ` `  `    ``// This function Sets the target_leaf_ref to refer ` `    ``// the leaf node of the maximum path sum. Also, ` `    ``// returns the max_sum using max_sum_ref ` `    ``public` `virtual` `void` `getTargetLeaf(Node node, Maximum max_sum_ref, ` `                                      ``int` `curr_sum) ` `    ``{ ` `        ``if` `(node == ``null``) { ` `            ``return``; ` `        ``} ` ` `  `        ``// Update current sum to hold sum of nodes on ` `        ``// path from root to this node ` `        ``curr_sum = curr_sum + node.data; ` ` `  `        ``// If this is a leaf node and path to this node ` `        ``// has maximum sum so far, the n make this node ` `        ``// target_leaf ` `        ``if` `(node.left == ``null` `&& node.right == ``null``) { ` `            ``if` `(curr_sum > max_sum_ref.max_no) { ` `                ``max_sum_ref.max_no = curr_sum; ` `                ``target_leaf = node; ` `            ``} ` `        ``} ` ` `  `        ``// If this is not a leaf node, then recur down ` `        ``// to find the target_leaf ` `        ``getTargetLeaf(node.left, max_sum_ref, curr_sum); ` `        ``getTargetLeaf(node.right, max_sum_ref, curr_sum); ` `    ``} ` ` `  `    ``// Returns the maximum sum and prints the nodes on ` `    ``// max sum path ` `    ``public` `virtual` `int` `maxSumPath() ` `    ``{ ` `        ``// base case ` `        ``if` `(root == ``null``) { ` `            ``return` `0; ` `        ``} ` ` `  `        ``// find the target leaf and maximum sum ` `        ``getTargetLeaf(root, max, 0); ` ` `  `        ``// print the path from root to the target leaf ` `        ``printPath(root, target_leaf); ` `        ``return` `max.max_no; ``// return maximum sum ` `    ``} ` ` `  `    ``// driver function to test the above functions ` `    ``public` `static` `void` `Main(``string``[] args) ` `    ``{ ` `        ``BinaryTree tree = ``new` `BinaryTree(); ` `        ``tree.root = ``new` `Node(10); ` `        ``tree.root.left = ``new` `Node(-2); ` `        ``tree.root.right = ``new` `Node(7); ` `        ``tree.root.left.left = ``new` `Node(8); ` `        ``tree.root.left.right = ``new` `Node(-4); ` `        ``Console.WriteLine(``"Following are the nodes "` `                          ``+ ``"on maximum sum path"``); ` `        ``int` `sum = tree.maxSumPath(); ` `        ``Console.WriteLine(``""``); ` `        ``Console.WriteLine(``"Sum of nodes is : "` `+ sum); ` `    ``} ` `} ` ` `  `// This code is contributed by Shrikant13 `

Output:

```Following are the nodes on the maximum sum path
7 10
Sum of the nodes is 17
```

Time Complexity: Time complexity of the above solution is O(n) as it involves tree traversal two times.

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Tree Tree

code
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