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Check if a Binary Tree consists of a pair of leaf nodes with sum K
• Last Updated : 03 Nov, 2020

Given a Binary Tree and an integer K, the task is to check if the Tree consists of a pair of leaf nodes with sum exactly K. In case of multiple pairs, print any one of them. Otherwise print -1.

Note: Assume that the given binary tree will always have more than 1 leaf node.

Examples:

Input: X = 13

```             1
/   \
2     3
/ \   / \
4   5 6   7
\
8
```

Output: [5, 8]
Explanation:
The given binary tree consists of 4 leaf nodes [4, 5, 6, 8].
The pair of nodes valued 5 and 8 have sum 13.

Input: X = 6

```           -1
/  \
2    3
/ \
4   5
```

Output: [-1]
Explanation:
The given binary tree consists of 3 leaf nodes [4, 5, 3].
No valid pair of nodes exists whose sum of their values equal to 6.
Therefore, print -1.

Naive Approach: The simplest approach to solve the problem is to traverse the tree and store all the leaf nodes in an array. Then sort the array and use two pointer technique to find if a required pair exists or not.

Time Complexity: O(NlogN)
Auxiliary Space: O(N)

Efficient Approach: The above approach can be optimized using HashSet. Follow the steps below to solve the problem:

• Create a Set to store values of leaf nodes.
• Traverse the tree and for every leaf node, check if (K – value of leaf node) exists in the unordered set or not.
• If found to be true, print the oair of node values.
• Otherwise store the value of the current node into the unordered set.

Below is the implementation of the above approach:

## C++

 `// C++ Program to implement``// the above approach` `#include ``using` `namespace` `std;` `// Stores if a pair exists or not``bool` `pairFound = ``false``;` `// Struct binary tree node``struct` `Node {``    ``int` `data;``    ``Node *left, *right;``};` `// Creates a new node``Node* newNode(``int` `data)``{``    ``Node* temp = ``new` `Node();``    ``temp->data = data;``    ``temp->left = temp->right = NULL;``    ``return` `temp;``}` `// Function to check if a pair of leaf``// nodes exists with sum K``void` `pairSum(Node* root, ``int` `target,``             ``unordered_set<``int``>& S)``{``    ``// checks if root is NULL``    ``if` `(!root)``        ``return``;` `    ``// Checks if the current node is a leaf node``    ``if` `(!root->left and !root->right) {` `        ``// Checks for a valid pair of leaf nodes``        ``if` `(S.count(target - root->data)) {` `            ``cout << target - root->data << ``" "``                 ``<< root->data;` `            ``pairFound = ``true``;``            ``return``;``        ``}` `        ``// Insert value of current node``        ``// into the set``        ``else``            ``S.insert(root->data);``    ``}` `    ``// Traverse left and right subtree``    ``pairSum(root->left, target, S);``    ``pairSum(root->right, target, S);``}` `// Driver Code``int` `main()``{``    ``// Construct binary tree``    ``Node* root = newNode(1);``    ``root->left = newNode(2);``    ``root->left->left = newNode(4);``    ``root->left->right = newNode(5);``    ``root->right = newNode(3);``    ``root->right->left = newNode(6);``    ``root->right->right = newNode(7);` `    ``root->right->right->right = newNode(8);` `    ``// Stores the leaf nodes``    ``unordered_set<``int``> S;` `    ``int` `K = 13;` `    ``pairSum(root, K, S);` `    ``if` `(pairFound == ``false``)``        ``cout << ``"-1"``;` `    ``return` `0;``}`

## Java

 `// Java program to implement``// the above approach``import` `java.util.*;` `class` `GFG{` `// Stores if a pair exists or not``static` `boolean` `pairFound = ``false``;` `// Struct binary tree node``static` `class` `Node``{``    ``int` `data;``    ``Node left, right;``};` `// Creates a new node``static` `Node newNode(``int` `data)``{``    ``Node temp = ``new` `Node();``    ``temp.data = data;``    ``temp.left = temp.right = ``null``;``    ``return` `temp;``}` `// Function to check if a pair of leaf``// nodes exists with sum K``static` `void` `pairSum(Node root, ``int` `target,``                    ``HashSet S)``{``    ` `    ``// Checks if root is null``    ``if` `(root == ``null``)``        ``return``;` `    ``// Checks if the current node is a leaf node``    ``if` `(root.left == ``null` `&& root.right == ``null``)``    ``{``        ` `        ``// Checks for a valid pair of leaf nodes``        ``if` `(S.contains(target - root.data))``        ``{``            ``System.out.print(target - root.data +``                                ``" "` `+ root.data);``            ``pairFound = ``true``;``            ``return``;``        ``}` `        ``// Insert value of current node``        ``// into the set``        ``else``            ``S.add(root.data);``    ``}` `    ``// Traverse left and right subtree``    ``pairSum(root.left, target, S);``    ``pairSum(root.right, target, S);``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ` `    ``// Construct binary tree``    ``Node root = newNode(``1``);``    ``root.left = newNode(``2``);``    ``root.left.left = newNode(``4``);``    ``root.left.right = newNode(``5``);``    ``root.right = newNode(``3``);``    ``root.right.left = newNode(``6``);``    ``root.right.right = newNode(``7``);``    ``root.right.right.right = newNode(``8``);` `    ``// Stores the leaf nodes``    ``HashSet S = ``new` `HashSet();` `    ``int` `K = ``13``;` `    ``pairSum(root, K, S);` `    ``if` `(pairFound == ``false``)``        ``System.out.print(``"-1"``);``}``}` `// This code is contributed by 29AjayKumar`

## Python3

 `# Python3 program to implement``# the above approach` `# Stores if a pair exists or not``pairFound ``=` `False``S ``=` `set``()` `# Struct binary tree node``class` `newNode:``    ` `    ``def` `__init__(``self``, data):``        ` `        ``self``.data ``=` `data``        ``self``.left ``=` `None``        ``self``.right ``=` `None` `# Function to check if a pair of``# leaf nodes exists with sum K``def` `pairSum(root, target):``    ` `    ``global` `pairFound``    ``global` `S``    ` `    ``# Checks if root is NULL``    ``if` `(root ``=``=` `None``):``        ``return` `    ``# Checks if the current node``    ``# is a leaf node``    ``if` `(root.left ``=``=` `None` `and``       ``root.right ``=``=` `None``):``        ``temp ``=` `list``(S)``        ` `        ``# Checks for a valid pair of leaf nodes``        ``if` `(temp.count(target ``-` `root.data)):``            ``print``(target ``-` `root.data, root.data)` `            ``pairFound ``=` `True``            ``return``        ` `        ``# Insert value of current node``        ``# into the set``        ``else``:``            ``S.add(root.data)` `    ``# Traverse left and right subtree``    ``pairSum(root.left, target)``    ``pairSum(root.right, target)` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``    ` `    ``# Construct binary tree``    ``root ``=` `newNode(``1``)``    ``root.left ``=` `newNode(``2``)``    ``root.left.left ``=` `newNode(``4``)``    ``root.left.right ``=` `newNode(``5``)``    ``root.right ``=` `newNode(``3``)``    ``root.right.left ``=` `newNode(``6``)``    ``root.right.right ``=` `newNode(``7``)``    ``root.right.right.right ``=` `newNode(``8``)``    ` `    ``K ``=` `13` `    ``pairSum(root, K)` `    ``if` `(pairFound ``=``=` `False``):``        ``print``(``-``1``)``        ` `# This code is contributed by bgangwar59`

## C#

 `// C# program to implement``// the above approach``using` `System;``using` `System.Collections.Generic;` `class` `GFG{` `// Stores if a pair exists or not``static` `bool` `pairFound = ``false``;` `// Struct binary tree node``class` `Node``{``    ``public` `int` `data;``    ``public` `Node left, right;``};` `// Creates a new node``static` `Node newNode(``int` `data)``{``    ``Node temp = ``new` `Node();``    ``temp.data = data;``    ``temp.left = temp.right = ``null``;``    ``return` `temp;``}` `// Function to check if a pair of leaf``// nodes exists with sum K``static` `void` `pairSum(Node root, ``int` `target,``                    ``HashSet<``int``> S)``{``    ` `    ``// Checks if root is null``    ``if` `(root == ``null``)``        ``return``;` `    ``// Checks if the current node is a leaf node``    ``if` `(root.left == ``null` `&& root.right == ``null``)``    ``{``        ` `        ``// Checks for a valid pair of leaf nodes``        ``if` `(S.Contains(target - root.data))``        ``{``            ``Console.Write(target - root.data +``                             ``" "` `+ root.data);``            ``pairFound = ``true``;``            ``return``;``        ``}` `        ``// Insert value of current node``        ``// into the set``        ``else``            ``S.Add(root.data);``    ``}` `    ``// Traverse left and right subtree``    ``pairSum(root.left, target, S);``    ``pairSum(root.right, target, S);``}` `// Driver Code``public` `static` `void` `Main(String[] args)``{``    ` `    ``// Construct binary tree``    ``Node root = newNode(1);``    ``root.left = newNode(2);``    ``root.left.left = newNode(4);``    ``root.left.right = newNode(5);``    ``root.right = newNode(3);``    ``root.right.left = newNode(6);``    ``root.right.right = newNode(7);``    ``root.right.right.right = newNode(8);` `    ``// Stores the leaf nodes``    ``HashSet<``int``> S = ``new` `HashSet<``int``>();` `    ``int` `K = 13;` `    ``pairSum(root, K, S);` `    ``if` `(pairFound == ``false``)``        ``Console.Write(``"-1"``);``}``}` `// This code is contributed by 29AjayKumar`
Output:
```5 8

```

Time Complexity: O(N)
Auxiliary Space: O(N)

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