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Print Bottom-Right View of a Binary Tree

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Given a Binary Tree, print Bottom-Right view of it. The Bottom Right view of a Binary Tree is a set of nodes visible when the tree is visited from Bottom Right side, return the values of the nodes ordered from right to left. 
In the bottom-right view, on viewing the tree at an angle of 45 degrees from the bottom-right side and only a few nodes would be visible and rest would be hidden behind them.
Examples: 
 

Input :
   1           
 /   \
2     3        
 \     \
  5     4    
Output : [4, 5]
Visible nodes from the bottom right direction are 4 and 5

Input :
     1           
   /   \
  2     3        
 /     /
4     5
       \
        6
Output: [3, 6, 4]


 


Approach : 
 

  • The problem can be solved using simple recursive traversal.
  • Keep track of the level of a node by passing a parameter to all recursive calls. Consider the level of a tree at an angle of 45% (as explained in an example), so whenever we move towards the left, its level would increase by one.
  • The idea is to keep track of the maximum level and traverse the tree in a manner that right subtree is visited before left subtree.
  • A node whose level is more than maximum level so far, Print the node because this is the last node in its level (Traverse the right subtree before left subtree).


Below is the implementation of the above approach:
 

C++

// C++ program to print bottom
// right view of binary tree
#include<bits/stdc++.h>
using namespace std;
 
// A binary tree node
struct Node
{
    int data;
    Node *left, *right;
 
    Node(int item)
    {
        data = item;
        left = right = NULL;
    }
};
 
// class to access maximum level
// by reference
struct _Max_level
{
    int _max_level;
};
 
Node *root;
_Max_level *_max = new _Max_level();
 
// Recursive function to print bottom
// right view of a binary tree
void bottomRightViewUtil(Node* node, int level,
                        _Max_level *_max_level)
{
 
    // Base Case
    if (node == NULL)
        return;
 
    // Recur for right subtree first
    bottomRightViewUtil(node->right,
                        level, _max_level);
 
    // If this is the last Node of its level
    if (_max_level->_max_level < level)
    {
        cout << node->data << " ";
        _max_level->_max_level = level;
    }
 
    // Recur for left subtree
    // with increased level
    bottomRightViewUtil(node->left,
                        level + 1, _max_level);
}
 
// A wrapper over bottomRightViewUtil()
void bottomRightView(Node *node)
{
    bottomRightViewUtil(node, 1, _max);
}
 
void bottomRightView()
{
    bottomRightView(root);
}
 
// Driver Code
int main()
{
    root = new Node(1);
    root->left = new Node(2);
    root->right = new Node(3);
    root->left->left = new Node(4);
    root->right->left = new Node(5);
    root->right->left->right = new Node(6);
 
    bottomRightView();
}
 
// This code is contributed by Arnab Kundu

                    

Java

// Java program to print bottom
// right view of binary tree
 
// A binary tree node
class Node {
 
    int data;
    Node left, right;
 
    Node(int item)
    {
        data = item;
        left = right = null;
    }
}
 
// class to access maximum level by reference
class Max_level {
 
    int max_level;
}
 
class BinaryTree {
 
    Node root;
    Max_level max = new Max_level();
 
    // Recursive function to print bottom
    // right view of a binary tree.
    void bottomRightViewUtil(Node node, int level,
                             Max_level max_level)
    {
 
        // Base Case
        if (node == null)
            return;
 
        // Recur for right subtree first
        bottomRightViewUtil(node.right,
                            level, max_level);
 
        // If this is the last Node of its level
        if (max_level.max_level < level) {
            System.out.print(node.data + " ");
            max_level.max_level = level;
        }
 
        // Recur for left subtree with increased level
        bottomRightViewUtil(node.left,
                            level + 1, max_level);
    }
 
    void bottomRightView()
    {
        bottomRightView(root);
    }
 
    // A wrapper over bottomRightViewUtil()
    void bottomRightView(Node node)
    {
 
        bottomRightViewUtil(node, 1, max);
    }
 
    // Driver program to test the above functions
    public static void main(String args[])
    {
        BinaryTree tree = new BinaryTree();
        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.right.left = new Node(5);
        tree.root.right.left.right = new Node(6);
 
        tree.bottomRightView();
    }
}

                    

Python3

# Python3 program to print bottom
# right view of binary tree
 
# A binary tree node
class Node:
     
    # Construct to create a newNode
    def __init__(self, item):
        self.data = item
        self.left = None
        self.right = None
 
maxlevel = [0]
 
# Recursive function to print bottom
# right view of a binary tree.
def bottomRightViewUtil(node, level, maxlevel):
     
    # Base Case
    if (node == None):
        return
     
    # Recur for right subtree first
    bottomRightViewUtil(node.right, level,
                                 maxlevel)
     
    # If this is the last Node of its level
    if (maxlevel[0] < level):
        print(node.data, end = " ")
        maxlevel[0] = level
         
    # Recur for left subtree with increased level
    bottomRightViewUtil(node.left, level + 1
                                maxlevel)
 
# A wrapper over bottomRightViewUtil()
def bottomRightView(node):
     
    bottomRightViewUtil(node, 1, maxlevel)
         
# Driver Code
root = Node(1)
root.left = Node(2)
root.right = Node(3)
root.left.left = Node(4)
root.right.left = Node(5)
root.right.left.right = Node(6)
 
bottomRightView(root)
 
# This code is contributed by SHUBHAMSINGH10

                    

C#

// C# program to print bottom
// right view of binary tree
using System;
 
// A binary tree node
class Node
{
    public int data;
    public Node left, right;
 
    public Node(int item)
    {
        data = item;
        left = right = null;
    }
}
 
// class to access maximum level by reference
class Max_level
{
    public int max_level;
}
 
class GFG
{
    Node root;
    Max_level max = new Max_level();
 
    // Recursive function to print bottom
    // right view of a binary tree.
    void bottomRightViewUtil(Node node, int level,
                             Max_level max_level)
    {
 
        // Base Case
        if (node == null)
            return;
 
        // Recur for right subtree first
        bottomRightViewUtil(node.right,
                            level, max_level);
 
        // If this is the last Node of its level
        if (max_level.max_level < level)
        {
            Console.Write(node.data + " ");
            max_level.max_level = level;
        }
 
        // Recur for left subtree with increased level
        bottomRightViewUtil(node.left,
                            level + 1, max_level);
    }
 
    void bottomRightView()
    {
        bottomRightView(root);
    }
 
    // A wrapper over bottomRightViewUtil()
    void bottomRightView(Node node)
    {
 
        bottomRightViewUtil(node, 1, max);
    }
 
    // Driver Code
    public static void Main(String []args)
    {
        GFG tree = new GFG();
        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.right.left = new Node(5);
        tree.root.right.left.right = new Node(6);
 
        tree.bottomRightView();
    }
}
 
// This code is contributed by Princi Singh

                    

Javascript

<script>
 
// Javascript program to print bottom
// right view of binary tree
 
// A binary tree node
class Node
{
    constructor(item)
    {
        this.data = item;
        this.left = null;
        this.right = null;
    }
}
 
// class to access maximum level by reference
class Max_level
{
    constructor()
    {
        this.max_level = 0;
    }
}
 
var max = new Max_level();
// Recursive function to print bottom
// right view of a binary tree.
function bottomRightViewUtil(node, level,max_level)
{
    // Base Case
    if (node == null)
        return;
    // Recur for right subtree first
    bottomRightViewUtil(node.right,
                        level, max_level);
    // If this is the last Node of its level
    if (max_level.max_level < level)
    {
        document.write(node.data + " ");
        max_level.max_level = level;
    }
    // Recur for left subtree with increased level
    bottomRightViewUtil(node.left,
                        level + 1, max_level);
}
 
// A wrapper over bottomRightViewUtil()
function bottomRightView(node)
{
    bottomRightViewUtil(node, 1, max);
}
 
// Driver Code
var root = new Node(1);
root.left = new Node(2);
root.right = new Node(3);
root.left.left = new Node(4);
root.right.left = new Node(5);
root.right.left.right = new Node(6);
bottomRightView(root);
 
// This code is contributed by rrrtnx.
</script>

                    

Output
3 6 4 

Time Complexity : O(N), where N is the number of nodes of the binary tree.
Auxiliary space: O(n) for implicit call stack as using recursion.

Iterative Approach:

C++

// C++ program to print
// bottom right view of BT
#include <bits/stdc++.h>
using namespace std;
 
// A binary Tree node
struct Node {
    int data;
    Node *left, *right;
};
 
// create and returns a new node
Node* newNode(int val)
{
    Node* temp = new Node();
    temp->data = val;
    temp->left = temp->right = NULL;
    return temp;
}
 
// fun to print bottom right view of a BT
void bottomRightView(Node* root)
{
    // Base case
    if (!root)
        return;
 
    queue<Node*> q;
    q.push(root);
 
    while (!q.empty()) {
        int size = q.size();
        while (size--) {
            root = q.front();
            q.pop();
            // traverse all right nodes and push leftnodes
            // (if any) into the queue for the next level
            // traverse
            while (root->right) {
                if (root->left)
                    q.push(root->left);
                root = root->right;
            }
            // if last node has any left node
            if (root->left)
                q.push(root->left);
        }
        // print the data
        cout << root->data << " ";
    }
}
 
int main()
{
    Node* root = newNode(1);
    root->left = newNode(2);
    root->right = newNode(3);
    root->left->left = newNode(4);
    root->right->left = newNode(5);
    root->right->left->right = newNode(6);
 
    bottomRightView(root);
 
    return 0;
}
// This code is contributed by Modem Upendra.

                    

Java

// Java code for the above approach
import java.util.*;
 
public class GFG {
  // A binary Tree node
  static class Node {
    int data;
    Node left, right;
 
    Node(int data)
    {
      this.data = data;
      this.left = this.right = null;
    }
  }
   
  // create and returns a new node
  static Node newNode(int val)
  {
    Node temp = new Node(val);
    return temp;
  }
   
  // fun to print bottom right view of a BT
  static void bottomRightView(Node root)
  {
     
    // Base case
    if (root == null) {
      return;
    }
 
    Queue<Node> q = new LinkedList<>();
    q.add(root);
 
    while (!q.isEmpty()) {
      int size = q.size();
      while (size-- > 0) {
        root = q.poll();
         
        // traverse all right nodes and push
        // leftnodes
        // (if any) into the queue for the next
        // level traverse
        while (root.right != null) {
          if (root.left != null) {
            q.add(root.left);
          }
          root = root.right;
        }
         
        // if last node has any left node
        if (root.left != null) {
          q.add(root.left);
        }
      }
       
      // print the data
      System.out.print(root.data + " ");
    }
  }
   
  // Driver Code
  public static void main(String[] args)
  {
    Node root = newNode(1);
    root.left = newNode(2);
    root.right = newNode(3);
    root.left.left = newNode(4);
    root.right.left = newNode(5);
    root.right.left.right = newNode(6);
 
    bottomRightView(root);
  }
}
 
// This code is contributed by Potta Lokesh

                    

Python3

# Python3 program to print bottom right
# view of a BT
 
# A binary Tree node
class Node:
    def __init__(self, val):
        self.data = val
        self.left = None
        self.right = None
 
# fun to print bottom right view of a BT
def bottomRightView(root):
    # Base case
    if not root:
        return
 
    q = []
    q.append(root)
 
    while q:
        size = len(q)
        while size > 0:
            root = q.pop(0)
            # traverse all right nodes and push leftnodes
            # (if any) into the queue for the next level
            # traverse
            while root.right:
                if root.left:
                    q.append(root.left)
                root = root.right
            # if last node has any left node
            if root.left:
                q.append(root.left)
            size -= 1
        # print the data
        print(root.data, end=" ")
 
# create and returns a new node
def newNode(val):
    temp = Node(val)
    return temp
 
#Driver code
root = newNode(1)
root.left = newNode(2)
root.right = newNode(3)
root.left.left = newNode(4)
root.right.left = newNode(5)
root.right.left.right = newNode(6)
 
bottomRightView(root)
 
#This code is contributed by Potta Lokesh

                    

C#

using System;
using System.Collections;
using System.Collections.Generic;
 
public class Gfg{
  public class Node {
    public int data;
    public Node left, right;
 
    public Node(int item)
    {
      data = item;
      left = right = null;
    }
  }
 
  // create and returns a new node
  /*Node* newNode(int val)
    {
        Node* temp = new Node();
        temp.data = val;
        temp.left = temp.right = NULL;
        return temp;
    }*/
 
  // fun to print bottom right view of a BT
  static void bottomRightView(Node root)
  {
    // Base case
    if (root==null)
      return;
 
    Queue<Node> q=new Queue<Node>();
    q.Enqueue(root);
 
    while (q.Count != 0) {
      int size = q.Count;
      while (size-->0) {
        root = q.Peek();
        q.Dequeue();
         
        // traverse all right nodes and push leftnodes
        // (if any) into the queue for the next level
        // traverse
        while (root.right != null) {
          if (root.left != null)
            q.Enqueue(root.left);
          root = root.right;
        }
         
        // if last node has any left node
        if (root.left != null)
          q.Enqueue(root.left);
      }
       
      // print the data
      Console.Write(root.data+" ");
    }
  }
 
  public static void Main(string[] args)
  {
    Node root = new Node(1);
    root.left = new Node(2);
    root.right = new Node(3);
    root.left.left = new Node(4);
    root.right.left = new Node(5);
    root.right.left.right = new Node(6);
 
    bottomRightView(root);
  }
}
 
// This code is contributed by poojaagarwal2.

                    

Javascript

<script>
// Javascript program to print bottom
// right view of BT
 
// A binary tree node
class Node
{
    constructor(item)
    {
        this.data = item;
        this.left = null;
        this.right = null;
    }
}
 
// Iterative function to print bottom
// right view of a binary tree.
function bottomRightView(root){
    // Base Case
    if (root == null)
        return;
    var queue = [];
    queue.push(root);
    while (queue.length) {
        var size = queue.length;
        while(size--){
            root = queue.shift();
            while(root.right != null){
                if(root.left != null)
                    queue.push(root.left);
                root = root.right;
            }
            if(root.left != null)
                queue.push(root.left);
        }
        document.write(root.data + " ");
    }
}
 
// Driver Code
var root = new Node(1);
root.left = new Node(2);
root.right = new Node(3);
root.left.left = new Node(4);
root.right.left = new Node(5);
root.right.left.right = new Node(6);
bottomRightView(root);
 
// This code is contributed by Susobhan Akhuli
</script>

                    

Output
3 6 4 

Time Complexity: O(N), where N is the total nodes in a BT.
Auxiliary Space: O(n), where n is the maximum nodes possible in a diagonal.
 



Last Updated : 29 Jan, 2023
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