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 classclass 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 treeclass 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#
// C# code to find the vertical width // of a binary treeusing 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
6
Time Complexity: O(n)
Auxiliary Space: O(n)
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