Vertical width of Binary tree | Set 1
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 <bits/stdc++.h> 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; } |
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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 |
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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 |
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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 |
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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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- Print a Binary Tree in Vertical Order | Set 2 (Map based Method)
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- Print a Binary Tree in Vertical Order | Set 3 (Using Level Order Traversal)
- Vertical Zig-Zag traversal of a Tree
- Complexity of different operations in Binary tree, Binary Search Tree and AVL tree
- Minimum swap required to convert binary tree to binary search tree
- Check whether a binary tree is a full binary tree or not | Iterative Approach
- Convert a Binary Tree to Threaded binary tree | Set 1 (Using Queue)
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