# Find the kth node in vertical order traversal of a Binary Tree

Given a binary tree and an integer k, the task is to print the kth node in the vertical order traversal of binary tree.If no such node exists then print -1.

The vertical order traversal of a binary tree means to print it vertically.

Examples:

```Input:
1
/   \
2       3
/  \     /  \
4     5   6    7
\    \
8    9
k = 3
Output: 1
The vertical order traversal of above tree is:
4
2
1 5 6
3 8
7
9

Input:
1
/   \
2       3
/  \     /  \
4     5   6    7
\    \
8    9
k = 13
Output: -1
```

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

Approach: The idea is to perform vertical order traversal and check if the current node is the kth node then print its value, if number of nodes in the tree is less than K then print -1.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Structure for a binary tree node ` `struct` `Node { ` `    ``int` `key; ` `    ``Node *left, *right; ` `}; ` ` `  `// A utility function to create a new node ` `Node* newNode(``int` `key) ` `{ ` `    ``Node* node = ``new` `Node; ` `    ``node->key = key; ` `    ``node->left = node->right = NULL; ` `    ``return` `node; ` `} ` ` `  `// Function to find kth node ` `// in vertcial order traversal ` `int` `KNodeVerticalOrder(Node* root, ``int` `k) ` `{ ` `    ``// Base case ` `    ``if` `(!root || k == 0) ` `        ``return` `-1; ` ` `  `    ``int` `n = 0; ` ` `  `    ``// Variable to store kth node ` `    ``int` `k_node = -1; ` ` `  `    ``// Create a map and store vertical order in ` `    ``// map ` `    ``map<``int``, vector<``int``> > m; ` `    ``int` `hd = 0; ` ` `  `    ``// Create queue to do level order traversal ` `    ``// Every item of queue contains node and ` `    ``// horizontal distance ` `    ``queue > que; ` `    ``que.push(make_pair(root, hd)); ` ` `  `    ``while` `(!que.empty()) { ` `        ``// Pop from queue front ` `        ``pair temp = que.front(); ` `        ``que.pop(); ` `        ``hd = temp.second; ` `        ``Node* node = temp.first; ` ` `  `        ``// Insert this node's data in vector of hash ` `        ``m[hd].push_back(node->key); ` ` `  `        ``if` `(node->left != NULL) ` `            ``que.push(make_pair(node->left, hd - 1)); ` `        ``if` `(node->right != NULL) ` `            ``que.push(make_pair(node->right, hd + 1)); ` `    ``} ` ` `  `    ``// Traverse the map and find kth ` `    ``// node ` `    ``map<``int``, vector<``int``> >::iterator it; ` `    ``for` `(it = m.begin(); it != m.end(); it++) { ` `        ``for` `(``int` `i = 0; i < it->second.size(); ++i) { ` `            ``n++; ` `            ``if` `(n == k) ` `                ``return` `(it->second[i]); ` `        ``} ` `    ``} ` ` `  `    ``if` `(k_node == -1) ` `        ``return` `-1; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``Node* root = newNode(1); ` `    ``root->left = newNode(2); ` `    ``root->right = newNode(3); ` `    ``root->left->left = newNode(4); ` `    ``root->left->right = newNode(5); ` `    ``root->right->left = newNode(6); ` `    ``root->right->right = newNode(7); ` `    ``root->right->left->right = newNode(8); ` `    ``root->right->right->right = newNode(9); ` `    ``root->right->right->left = newNode(10); ` `    ``root->right->right->left->right = newNode(11); ` `    ``root->right->right->left->right->right = newNode(12); ` ` `  `    ``int` `k = 5; ` `    ``cout << KNodeVerticalOrder(root, k); ` ` `  `    ``return` `0; ` `} `

## Python3

 `# Python3 implementation of the approach  ` ` `  `# Tree node structure  ` `class` `Node: ` `     `  `    ``def` `__init__(``self``, key): ` `        ``self``.key ``=` `key ` `        ``self``.left ``=` `None` `        ``self``.right ``=` `None` ` `  `# Function to find kth node  ` `# in vertcial order traversal  ` `def` `KNodeVerticalOrder(root, k):  ` ` `  `    ``# Base case  ` `    ``if` `not` `root ``or` `k ``=``=` `0``: ` `        ``return` `-``1` ` `  `    ``n ``=` `0` `     `  `    ``# Variable to store kth node  ` `    ``k_node ``=` `-``1` ` `  `    ``# Create a map and store  ` `    ``# vertical order in map  ` `    ``m ``=` `{} ` `    ``hd ``=` `0` ` `  `    ``# Create queue to do level order  ` `    ``# traversal Every item of queue contains  ` `    ``# node and horizontal distance  ` `    ``que ``=` `[]  ` `    ``que.append((root, hd))  ` ` `  `    ``while` `len``(que) > ``0``:  ` `         `  `        ``# Pop from queue front  ` `        ``temp ``=` `que.pop(``0``)  ` `        ``hd ``=` `temp[``1``] ` `        ``node ``=` `temp[``0``]  ` ` `  `        ``# Insert this node's data in vector of hash  ` `        ``if` `hd ``not` `in` `m: m[hd] ``=` `[] ` `        ``m[hd].append(node.key)  ` ` `  `        ``if` `node.left !``=` `None``:  ` `            ``que.append((node.left, hd ``-` `1``))  ` `        ``if` `node.right !``=` `None``:  ` `            ``que.append((node.right, hd ``+` `1``))  ` ` `  `    ``# Traverse the map and find kth node  ` `    ``for` `it ``in` `sorted``(m):  ` `        ``for` `i ``in` `range``(``0``, ``len``(m[it])):  ` `            ``n ``+``=` `1` `            ``if` `n ``=``=` `k:  ` `                ``return` `m[it][i]  ` ` `  `    ``if` `k_node ``=``=` `-``1``: ` `        ``return` `-``1` ` `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"``:  ` ` `  `    ``root ``=` `Node(``1``)  ` `    ``root.left ``=` `Node(``2``)  ` `    ``root.right ``=` `Node(``3``)  ` `    ``root.left.left ``=` `Node(``4``)  ` `    ``root.left.right ``=` `Node(``5``)  ` `    ``root.right.left ``=` `Node(``6``)  ` `    ``root.right.right ``=` `Node(``7``)  ` `    ``root.right.left.right ``=` `Node(``8``)  ` `    ``root.right.right.right ``=` `Node(``9``)  ` `    ``root.right.right.left ``=` `Node(``10``)  ` `    ``root.right.right.left.right ``=` `Node(``11``)  ` `    ``root.right.right.left.right.right ``=` `Node(``12``)  ` ` `  `    ``k ``=` `5` `    ``print``(KNodeVerticalOrder(root, k))  ` ` `  `# This code is contributed by Rituraj Jain `

Output:

```6
```

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