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Vertical width of Binary tree | Set 1
• Difficulty Level : Medium
• Last Updated : 06 Sep, 2019

Given a binary tree, find the vertical width of the binary tree. The width of a binary tree is the number of vertical paths.

In this image, the tree contains 6 vertical lines which are the required width of the tree.

Examples :

```Input :
7
/  \
6    5
/ \  / \
4   3 2  1
Output :
5

Input :
1
/    \
2       3
/ \     / \
4   5   6   7
\   \
8   9
Output :
6
```

Approach : Take inorder traversal and then take a temporary variable if we go left then temp value decreases and if go to right then temp value increases. Assert a condition in this, if the minimum is greater than temp, then minimum = temp and if maximum less then temp then maximum = temp. In the end, print minimum + maximum which is the vertical width of the tree.

## C++

 `// CPP program to print vertical width``// of a tree``#include ``using` `namespace` `std;`` ` `// A Binary Tree Node``struct` `Node``{``    ``int` `data;``    ``struct` `Node *left, *right;``};`` ` `// get vertical width``void` `lengthUtil(Node* root, ``int` `&maximum,``                ``int` `&minimum, ``int` `curr=0)``{``    ``if` `(root == NULL)``        ``return``;`` ` `    ``// traverse left``    ``lengthUtil(root->left, maximum,``               ``minimum, curr - 1);`` ` `    ``// if curr is decrease then get``    ``// value in minimum``    ``if` `(minimum > curr)``        ``minimum = curr;`` ` `    ``// if curr is increase then get``    ``// value in maximum``    ``if` `(maximum < curr)``        ``maximum = curr;`` ` ` ` `    ``// traverse right``    ``lengthUtil(root->right, maximum,``               ``minimum,  curr + 1);`` ` `}`` ` `int` `getLength(Node* root)``{``    ``int` `maximum = 0, minimum = 0;``    ``lengthUtil(root, maximum, minimum, 0);`` ` `    ``// 1 is added to include root in the width``    ``return` `(``abs``(minimum) + maximum) + 1;``}`` ` `// Utility function to create a new tree node``Node* newNode(``int` `data)``{``    ``Node* curr = ``new` `Node;``    ``curr->data = data;``    ``curr->left = curr->right = NULL;``    ``return` `curr;``}`` ` `// Driver program to test above functions``int` `main()``{`` ` `    ``Node* root = newNode(7);``    ``root->left = newNode(6);``    ``root->right = newNode(5);``    ``root->left->left = newNode(4);``    ``root->left->right = newNode(3);``    ``root->right->left = newNode(2);``    ``root->right->right = newNode(1);`` ` `    ``cout << getLength(root) << ``"\n"``;`` ` `    ``return` `0;``}`

## Java

 `// Java program to print vertical width``// of a tree``import` `java.util.*;`` ` `class` `GFG``{`` ` `// A Binary Tree Node``static` `class` `Node``{``    ``int` `data;``    ``Node left, right;``};``static` `int` `maximum = ``0``, minimum = ``0``;`` ` `// get vertical width``static` `void` `lengthUtil(Node root, ``int` `curr)``{``    ``if` `(root == ``null``)``        ``return``;`` ` `    ``// traverse left``    ``lengthUtil(root.left, curr - ``1``);`` ` `    ``// if curr is decrease then get``    ``// value in minimum``    ``if` `(minimum > curr)``        ``minimum = curr;`` ` `    ``// if curr is increase then get``    ``// value in maximum``    ``if` `(maximum < curr)``        ``maximum = curr;`` ` `    ``// traverse right``    ``lengthUtil(root.right, curr + ``1``);``}`` ` `static` `int` `getLength(Node root)``{``    ``maximum = ``0``; minimum = ``0``;``    ``lengthUtil(root, ``0``);`` ` `    ``// 1 is added to include root in the width``    ``return` `(Math.abs(minimum) + maximum) + ``1``;``}`` ` `// Utility function to create a new tree node``static` `Node newNode(``int` `data)``{``    ``Node curr = ``new` `Node();``    ``curr.data = data;``    ``curr.left = curr.right = ``null``;``    ``return` `curr;``}`` ` `// Driver Code``public` `static` `void` `main(String[] args) ``{``    ``Node root = newNode(``7``);``    ``root.left = newNode(``6``);``    ``root.right = newNode(``5``);``    ``root.left.left = newNode(``4``);``    ``root.left.right = newNode(``3``);``    ``root.right.left = newNode(``2``);``    ``root.right.right = newNode(``1``);`` ` `    ``System.out.println(getLength(root));``}``}`` ` `// This code is contributed by Rajput-Ji`

## Python3

 `# Python3 program to prvertical width ``# of a tree `` ` `# class to create a new tree node ``class` `newNode:``    ``def` `__init__(``self``, data): ``        ``self``.data ``=` `data ``        ``self``.left ``=` `self``.right ``=` `None`` ` `# get vertical width ``def` `lengthUtil(root, maximum, minimum, curr ``=` `0``):``    ``if` `(root ``=``=` `None``):``        ``return`` ` `    ``# traverse left ``    ``lengthUtil(root.left, maximum, ``                ``minimum, curr ``-` `1``) `` ` `    ``# if curr is decrease then get ``    ``# value in minimum ``    ``if` `(minimum[``0``] > curr):``        ``minimum[``0``] ``=` `curr `` ` `    ``# if curr is increase then get ``    ``# value in maximum ``    ``if` `(maximum[``0``] < curr):``        ``maximum[``0``] ``=` `curr `` ` `    ``# traverse right ``    ``lengthUtil(root.right, maximum, ``                 ``minimum, curr ``+` `1``)`` ` `def` `getLength(root):``    ``maximum ``=` `[``0``]``    ``minimum ``=` `[``0``] ``    ``lengthUtil(root, maximum, minimum, ``0``) `` ` `    ``# 1 is added to include root in the width ``    ``return` `(``abs``(minimum[``0``]) ``+` `maximum[``0``]) ``+` `1`` ` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:`` ` `    ``root ``=` `newNode(``7``) ``    ``root.left ``=` `newNode(``6``) ``    ``root.right ``=` `newNode(``5``) ``    ``root.left.left ``=` `newNode(``4``) ``    ``root.left.right ``=` `newNode(``3``) ``    ``root.right.left ``=` `newNode(``2``) ``    ``root.right.right ``=` `newNode(``1``) `` ` `    ``print``(getLength(root))`` ` `# This code is contributed by PranchalK`

## C#

 `// C# program to print vertical width``// of a tree``using` `System;``     ` `class` `GFG``{`` ` `// A Binary Tree Node``public` `class` `Node``{``    ``public` `int` `data;``    ``public` `Node left, right;``};``static` `int` `maximum = 0, minimum = 0;`` ` `// get vertical width``static` `void` `lengthUtil(Node root,``                        ``int` `curr)``{``    ``if` `(root == ``null``)``        ``return``;`` ` `    ``// traverse left``    ``lengthUtil(root.left, curr - 1);`` ` `    ``// if curr is decrease then get``    ``// value in minimum``    ``if` `(minimum > curr)``        ``minimum = curr;`` ` `    ``// if curr is increase then get``    ``// value in maximum``    ``if` `(maximum < curr)``        ``maximum = curr;`` ` `    ``// traverse right``    ``lengthUtil(root.right, curr + 1);``}`` ` `static` `int` `getLength(Node root)``{``    ``maximum = 0; minimum = 0;``    ``lengthUtil(root, 0);`` ` `    ``// 1 is added to include root in the width``    ``return` `(Math.Abs(minimum) + maximum) + 1;``}`` ` `// Utility function to create a new tree node``static` `Node newNode(``int` `data)``{``    ``Node curr = ``new` `Node();``    ``curr.data = data;``    ``curr.left = curr.right = ``null``;``    ``return` `curr;``}`` ` `// Driver Code``public` `static` `void` `Main(String[] args) ``{``    ``Node root = newNode(7);``    ``root.left = newNode(6);``    ``root.right = newNode(5);``    ``root.left.left = newNode(4);``    ``root.left.right = newNode(3);``    ``root.right.left = newNode(2);``    ``root.right.right = newNode(1);`` ` `    ``Console.WriteLine(getLength(root));``}``}`` ` `// This code is contributed by PrinciRaj1992`
Output:
```5
```

Time Complexity: O(n)
Auxiliary Space: O(h) where h is the height of the binary tree. This much space is needed for recursive calls.

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