Vertical width of Binary tree | Set 2

Last Updated : 18 Nov, 2022

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

Examples:

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

Prerequisite: Print Binary Tree in Vertical order

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

Approach:

In this approach, we use the approach for printing vertical View of binary tree. Store the horizontal distances in a set and return 1 + highest horizontal distance - lowest horizontal distance. 1 is added to consider horizontal distance 0 as well. While going left, do hd - 1 and for right do hd + 1. We insert all possible distances in a hash table and finally return size of the hash table.

Implementation:

C++

// CPP code to find vertical // width of a binary tree #include <bits/stdc++.h> using namespace std;  // Tree class class Node { public :     int data;     Node *left, *right;      // Constructor     Node(int data_new)     {         data = data_new;         left = right = NULL;     } };  // Function to fill hd in set. void fillSet(Node* root, unordered_set<int>& s,                                        int hd) {     if (!root)         return;      fillSet(root->left, s, hd - 1);     s.insert(hd);     fillSet(root->right, s, hd + 1); }  int verticalWidth(Node* root) {     unordered_set<int> s;      // Third parameter is horizontal     // distance     fillSet(root, s, 0);      return s.size(); }  int main() {     Node* root = NULL;      // Creating the above tree     root = new Node(1);     root->left = new Node(2);     root->right = new Node(3);     root->left->left = new Node(4);     root->left->right = new Node(5);     root->right->left = new Node(6);     root->right->right = new Node(7);     root->right->left->right = new Node(8);     root->right->right->right = new Node(9);      cout << verticalWidth(root) << "\n";      return 0; }

Java

/* Java code to find the vertical width of a binary tree */ import java.io.*; import java.util.*;  /* A binary tree node has data, pointer to left child  and a pointer to right child */ class Node  {      int data;      Node left, right;           Node(int item)      {          data = item;          left = right = null;      }  }   class BinaryTree  {      Node root;       /* UTILITY FUNCTIONS */     // Function to fill hd in set.      void fillSet(Node root,Set<Integer> set,int hd)     {         if(root == null) return;         fillSet(root.left,set,hd - 1);         set.add(hd);         fillSet(root.right,set,hd + 1);     }       int verticalWidth(Node root)     {         Set<Integer> set = new HashSet<Integer>();                   // Third parameter is horizontal distance          fillSet(root,set,0);         return set.size();     }          /* Driver program to test above functions */     public static void main(String args[])      {          BinaryTree tree = new BinaryTree();                   /*          Constructed binary tree is:              1              / \          2 3          / \ \          4 5     8                  / \                  6 7          */         tree.root = new Node(1);          tree.root.left = new Node(2);          tree.root.right = new Node(3);          tree.root.left.left = new Node(4);          tree.root.left.right = new Node(5);          tree.root.right.right = new Node(8);          tree.root.right.right.left = new Node(6);          tree.root.right.right.right = new Node(7);          System.out.println(tree.verticalWidth(tree.root));              }  }   /* This code is contributed by Ashok Borra */

Python3

# Python code to find vertical  # width of a binary tree  class Node:     def __init__(self, data):         self.data = data         self.left = self.right = None  # Function to fill hd in set.  def fillSet(root, s, hd):     if (not root):         return      fillSet(root.left, s, hd - 1)      s.add(hd)     fillSet(root.right, s, hd + 1)  def verticalWidth(root):     s = set()      # Third parameter is horizontal      # distance      fillSet(root, s, 0)       return len(s)  if __name__ == '__main__':      # Creating the above tree      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)       print(verticalWidth(root))  # This code is contributed by PranchalK

// C# code to find the vertical width  // of a binary tree using System; using System.Collections.Generic;  /* A binary tree node has data,  pointer to left child and a  pointer to right child */ public class Node  {      public int data;      public Node left, right;           public Node(int item)      {          data = item;          left = right = null;      }  }   public class BinaryTree  {      Node root;       /* UTILITY FUNCTIONS */     // Function to fill hd in set.      void fillSet(Node root, HashSet<int> set, int hd)     {         if(root == null) return;         fillSet(root.left, set, hd - 1);         set.Add(hd);         fillSet(root.right, set, hd + 1);     }      int verticalWidth(Node root)     {         HashSet<int> set = new HashSet<int>();                   // Third parameter is horizontal distance          fillSet(root,set, 0);         return set.Count;     }          // Driver Code     public static void Main(String []args)      {          BinaryTree tree = new BinaryTree();                   /*          Constructed binary tree is:              1              / \          2 3          / \ \          4 5     8                  / \                  6 7          */         tree.root = new Node(1);          tree.root.left = new Node(2);          tree.root.right = new Node(3);          tree.root.left.left = new Node(4);          tree.root.left.right = new Node(5);          tree.root.right.right = new Node(8);          tree.root.right.right.left = new Node(6);          tree.root.right.right.right = new Node(7);          Console.WriteLine(tree.verticalWidth(tree.root));              }  }  // This code is contributed by PrinciRaj1992

JavaScript

<script>  // Javascript code to find the vertical  // width of a binary tree  /* A binary tree node has data,  pointer to left child and a  pointer to right child */ class Node  {      constructor(item)     {         this.data = item;         this.left = null;         this.right = null;     } }   var root;   /* UTILITY FUNCTIONS */ // Function to fill hd in set.  function fillSet(root,set, hd) {     if (root == null)          return;              fillSet(root.left, set, hd - 1);     set.add(hd);     fillSet(root.right, set, hd + 1); }  function verticalWidth(root) {     var set = new Set();           // Third parameter is horizontal      // distance      fillSet(root,set, 0);     return set.size; }  // Driver Code /*  Constructed binary tree is:       1      / \     2   3    / \   \   4   5   8          / \          6 7  */ root = new Node(1);  root.left = new Node(2);  root.right = new Node(3);  root.left.left = new Node(4);  root.left.right = new Node(5);  root.right.right = new Node(8);  root.right.right.left = new Node(6);  root.right.right.right = new Node(7);   document.write(verticalWidth(root));  // This code is contributed by rrrtnx  </script>

Output

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

Vertical width of Binary tree | Set 1

Aashish Chauhan

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Vertical width of Binary tree | Set 2

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