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: 
            
            / \ 
        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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Output:

6


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Improved By : PranchalKatiyar, coded9