Vertical width of Binary tree | Set 2

Given a binary tree, find the vertical width of the binary tree. 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.

C++

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// 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;
}

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Java














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/* 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 bunary 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 */



















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Python3














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# 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 



















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C#














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// 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 bunary 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  



















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Output:


6












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