# Find if there is a pair in root to a leaf path with sum equals to root’s data

Given a binary tree, find if there is a pair in root to a leaf path such that sum of values in pair is equal to root’s data. For example, in below tree (2, 3) and (4, 1) are pairs with sum equals to root’s data. ## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

The idea is based on hashing and tree traversal. The idea is similar to method 2 of array pair sum problem.

• Create an empty hash table.
• Start traversing tree in Preorder fashion.
• If we reach a leaf node, we return false.
• For every visited node, check if root’s data minus current node’s data exists in hash table or not. If yes, return true. Else insert current node in hash table.
• Recursively check in left and right subtrees.
• Remove current node from hash table so that it doesn’t appear in other root to leaf paths.

Below is the implementation of above idea.

## C++

 `// C++ program to find if there is a pair in any root ` `// to leaf path with sum equals to root's key. ` `#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, *right; ` `}; ` ` `  `/* utility that allocates a new node with the ` `given data and NULL left and right pointers. */` `struct` `Node* newnode(``int` `data) ` `{ ` `    ``struct` `Node* node = ``new` `Node; ` `    ``node->data = data; ` `    ``node->left = node->right  = NULL; ` `    ``return` `(node); ` `} ` ` `  `// Function to print root to leaf path which satisfies the condition ` `bool` `printPathUtil(Node *node, unordered_set<``int``> &s, ``int` `root_data) ` `{ ` `    ``// Base condition ` `    ``if` `(node == NULL) ` `        ``return` `false``; ` ` `  `    ``// Check if current node makes a pair with any of the ` `    ``// existing elements in set. ` `    ``int` `rem = root_data - node->data; ` `    ``if` `(s.find(rem) != s.end()) ` `        ``return` `true``; ` ` `  `    ``// Insert current node in set ` `    ``s.insert(node->data); ` ` `  `    ``// If result returned by either left or right child is ` `    ``// true, return true. ` `    ``bool` `res = printPathUtil(node->left, s, root_data) || ` `               ``printPathUtil(node->right, s, root_data); ` ` `  `    ``// Remove current node from hash table ` `    ``s.erase(node->data); ` ` `  `    ``return` `res; ` `} ` ` `  `// A wrapper over printPathUtil() ` `bool` `isPathSum(Node *root) ` `{ ` `   ``// create an empty hash table  ` `   ``unordered_set<``int``> s; ` ` `  `   ``// Recursively check in left and right subtrees. ` `   ``return` `printPathUtil(root->left, s, root->data) || ` `          ``printPathUtil(root->right, s, root->data); ` `} ` ` `  `// Driver program to run the case ` `int` `main() ` `{ ` `    ``struct` `Node *root = newnode(8); ` `    ``root->left    = newnode(5); ` `    ``root->right   = newnode(4); ` `    ``root->left->left = newnode(9); ` `    ``root->left->right = newnode(7); ` `    ``root->left->right->left = newnode(1); ` `    ``root->left->right->right = newnode(12); ` `    ``root->left->right->right->right = newnode(2); ` `    ``root->right->right = newnode(11); ` `    ``root->right->right->left = newnode(3); ` `    ``isPathSum(root)? cout << ``"Yes"` `: cout << ``"No"``; ` `    ``return` `0; ` `} `

## Python3

 `# Python3 program to find if there is a  ` `# pair in any root to leaf path with sum  ` `# equals to root's key  ` ` `  `# A binary tree node has data, pointer to ` `# left child and a pointer to right child  ` ` `  `""" utility that allocates a new node with the  ` `given data and None left and right pointers. """` `class` `newnode:  ` `    ``def` `__init__(``self``, data):  ` `        ``self``.data ``=` `data  ` `        ``self``.left ``=` `self``.right ``=` `None` `         `  `# Function to prroot to leaf path which  ` `# satisfies the condition  ` `def` `printPathUtil(node, s, root_data) : ` ` `  `    ``# Base condition  ` `    ``if` `(node ``=``=` `None``) : ` `        ``return` `False` ` `  `    ``# Check if current node makes a pair  ` `    ``# with any of the existing elements in set.  ` `    ``rem ``=` `root_data ``-` `node.data  ` `    ``if` `rem ``in` `s:  ` `        ``return` `True` ` `  `    ``# Insert current node in set  ` `    ``s.add(node.data)  ` ` `  `    ``# If result returned by either left or  ` `    ``# right child is True, return True.  ` `    ``res ``=` `printPathUtil(node.left, s, root_data) ``or` ` ` `          ``printPathUtil(node.right, s, root_data)  ` ` `  `    ``# Remove current node from hash table  ` `    ``s.remove(node.data)  ` ` `  `    ``return` `res  ` ` `  `# A wrapper over printPathUtil()  ` `def` `isPathSum(root) : ` `     `  `    ``# create an empty hash table  ` `    ``s ``=` `set``() ` `     `  `    ``# Recursively check in left and right subtrees.  ` `    ``return` `printPathUtil(root.left, s, root.data) ``or` ` ` `           ``printPathUtil(root.right, s, root.data)  ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``root ``=` `newnode(``8``)  ` `    ``root.left ``=` `newnode(``5``)  ` `    ``root.right ``=` `newnode(``4``)  ` `    ``root.left.left ``=` `newnode(``9``)  ` `    ``root.left.right ``=` `newnode(``7``)  ` `    ``root.left.right.left ``=` `newnode(``1``)  ` `    ``root.left.right.right ``=` `newnode(``12``)  ` `    ``root.left.right.right.right ``=` `newnode(``2``)  ` `    ``root.right.right ``=` `newnode(``11``)  ` `    ``root.right.right.left ``=` `newnode(``3``)  ` `    ``print``(``"Yes"``) ``if` `(isPathSum(root)) ``else` `print``(``"No"``) ` ` `  `# This code is contributed  ` `# by SHUBHAMSINGH10 `

Output:

```Yes
```

Time Complexity: O(n) under the assumption that hash search, insert and erase take O(1) time.

Exercise : Extend the above solution to print all root to leaf paths that have a pair with sum equals to root’s data.

## tags:

Hash Tree Hash Tree