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Bottom View of a Binary Tree

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  • Difficulty Level : Medium
  • Last Updated : 24 Jun, 2022

Given a Binary Tree, we need to print the bottom view from left to right. A node x is there in output if x is the bottommost node at its horizontal distance. The horizontal distance of the left child of a node x is equal to a horizontal distance of x minus 1, and that of a right child is the horizontal distance of x plus 1. 

Examples:

                      20
                    /    \
                  8       22
                /   \      \
              5      3      25
                    / \      
                  10    14

For the above tree, the output should be 5, 10, 3, 14, 25.

If there are multiple bottom-most nodes for a horizontal distance from the root, then print the later one in the level traversal. For example, in the below diagram, 3 and 4 are both the bottom-most nodes at a horizontal distance of 0, we need to print 4. 

                      20
                    /    \
                  8       22
                /   \    /   \
              5      3 4     25
                    / \      
                  10    14

For the above tree, the output should be 5 10 4 14 25. 

Method 1 (Using Queue): The following are steps to print the Bottom View of the Binary Tree. 

  1. We put tree nodes in a queue for the level order traversal. 
  2. Start with the horizontal distance(hd) 0 of the root node, and keep on adding a left child to the queue along with the horizontal distance as hd-1 and the right child as hd+1. 
  3. Also, use a TreeMap which stores key-value pairs sorted on key. 
  4. Every time, we encounter a new horizontal distance or an existing horizontal distance put the node data for the horizontal distance as the key. For the first time it will add to the map, next time it will replace the value. This will make sure that the bottom-most element for that horizontal distance is present on the map and if you see the tree from beneath that you will see that element.

Below is the implementation of the above:

C++




// C++ Program to print Bottom View of Binary Tree
#include<bits/stdc++.h>
using namespace std;
  
// Tree node class
struct Node
{
    int data; //data of the node
    int hd; //horizontal distance of the node
    Node *left, *right; //left and right references
  
    // Constructor of tree node
    Node(int key)
    {
        data = key;
        hd = INT_MAX;
        left = right = NULL;
    }
};
  
// Method that prints the bottom view.
void bottomView(Node *root)
{
    if (root == NULL)
        return;
  
    // Initialize a variable 'hd' with 0
    // for the root element.
    int hd = 0;
  
    // TreeMap which stores key value pair
    // sorted on key value
    map<int, int> m;
  
    // Queue to store tree nodes in level
    // order traversal
    queue<Node *> q;
  
    // Assign initialized horizontal distance
    // value to root node and add it to the queue.
    root->hd = hd;
    q.push(root);  // In STL, push() is used enqueue an item
  
    // Loop until the queue is empty (standard
    // level order loop)
    while (!q.empty())
    {
        Node *temp = q.front();
        q.pop();   // In STL, pop() is used dequeue an item
  
        // Extract the horizontal distance value
        // from the dequeued tree node.
        hd = temp->hd;
  
        // Put the dequeued tree node to TreeMap
        // having key as horizontal distance. Every
        // time we find a node having same horizontal
        // distance we need to replace the data in
        // the map.
        m[hd] = temp->data;
  
        // If the dequeued node has a left child, add
        // it to the queue with a horizontal distance hd-1.
        if (temp->left != NULL)
        {
            temp->left->hd = hd-1;
            q.push(temp->left);
        }
  
        // If the dequeued node has a right child, add
        // it to the queue with a horizontal distance
        // hd+1.
        if (temp->right != NULL)
        {
            temp->right->hd = hd+1;
            q.push(temp->right);
        }
    }
  
    // Traverse the map elements using the iterator.
    for (auto i = m.begin(); i != m.end(); ++i)
        cout << i->second << " ";
}
  
// Driver Code
int main()
{
    Node *root = new Node(20);
    root->left = new Node(8);
    root->right = new Node(22);
    root->left->left = new Node(5);
    root->left->right = new Node(3);
    root->right->left = new Node(4);
    root->right->right = new Node(25);
    root->left->right->left = new Node(10);
    root->left->right->right = new Node(14);
    cout << "Bottom view of the given binary tree :\n";
    bottomView(root);
    return 0;
}


Java




// Java Program to print Bottom View of Binary Tree
import java.util.*;
import java.util.Map.Entry;
  
// Tree node class
class Node
{
    int data; //data of the node
    int hd; //horizontal distance of the node
    Node left, right; //left and right references
  
    // Constructor of tree node
    public Node(int key)
    {
        data = key;
        hd = Integer.MAX_VALUE;
        left = right = null;
    }
}
  
//Tree class
class Tree
{
    Node root; //root node of tree
  
    // Default constructor
    public Tree() {}
  
    // Parameterized tree constructor
    public Tree(Node node)
    {
        root = node;
    }
  
    // Method that prints the bottom view.
    public void bottomView()
    {
        if (root == null)
            return;
  
        // Initialize a variable 'hd' with 0 for the root element.
        int hd = 0;
  
        // TreeMap which stores key value pair sorted on key value
        Map<Integer, Integer> map = new TreeMap<>();
  
         // Queue to store tree nodes in level order traversal
        Queue<Node> queue = new LinkedList<Node>();
  
        // Assign initialized horizontal distance value to root
        // node and add it to the queue.
        root.hd = hd;
        queue.add(root);
  
        // Loop until the queue is empty (standard level order loop)
        while (!queue.isEmpty())
        {
            Node temp = queue.remove();
  
            // Extract the horizontal distance value from the
            // dequeued tree node.
            hd = temp.hd;
  
            // Put the dequeued tree node to TreeMap having key
            // as horizontal distance. Every time we find a node
            // having same horizontal distance we need to replace
            // the data in the map.
            map.put(hd, temp.data);
  
            // If the dequeued node has a left child add it to the
            // queue with a horizontal distance hd-1.
            if (temp.left != null)
            {
                temp.left.hd = hd-1;
                queue.add(temp.left);
            }
            // If the dequeued node has a right child add it to the
            // queue with a horizontal distance hd+1.
            if (temp.right != null)
            {
                temp.right.hd = hd+1;
                queue.add(temp.right);
            }
        }
  
        // Extract the entries of map into a set to traverse
        // an iterator over that.
        Set<Entry<Integer, Integer>> set = map.entrySet();
  
        // Make an iterator
        Iterator<Entry<Integer, Integer>> iterator = set.iterator();
  
        // Traverse the map elements using the iterator.
        while (iterator.hasNext())
        {
            Map.Entry<Integer, Integer> me = iterator.next();
            System.out.print(me.getValue()+" ");
        }
    }
}
  
// Main driver class
public class BottomView
{
    public static void main(String[] args)
    {
        Node root = new Node(20);
        root.left = new Node(8);
        root.right = new Node(22);
        root.left.left = new Node(5);
        root.left.right = new Node(3);
        root.right.left = new Node(4);
        root.right.right = new Node(25);
        root.left.right.left = new Node(10);
        root.left.right.right = new Node(14);
        Tree tree = new Tree(root);
        System.out.println("Bottom view of the given binary tree:");
        tree.bottomView();
    }
}


Python3




# Python3 program to print Bottom
# View of Binary Tree
  
# deque supports efficient pish and pop on both ends
from collections import deque
   
# Tree node class
class Node:
      
    def __init__(self, key):
          
        self.data = key
        self.hd = float('inf')
        self.left = None
        self.right = None
   
# Method that prints the bottom view.
def bottomView(root):
  
    if (root == None):
        return
      
    # Initialize a variable 'hd' with 0
    # for the root element.
    hd = 0
      
    # Store minimum and maximum horizontal distance
    # so that we do not have to sort keys at the end
    min_hd, max_hd = 0, 0
      
    hd_dict = dict()
   
    # Queue to store tree nodes in level
    # order traversal
    q = deque()
   
    # Assign initialized horizontal distance
    # value to root node and add it to the queue.
    root.hd = hd
    q.append(root)  
   
    # Loop until the queue is empty (standard
    # level order loop)
    while q:
        curr_node = q.popleft()
           
        # Extract the horizontal distance value
        # from the dequeued tree node.
        hd = curr_node.hd
          
        # Update the minimum and maximum hd
        min_hd = min(min_hd, hd)
        max_hd = max(max_hd, hd)
   
        # Put the dequeued tree node to dictionary
        # having key as horizontal distance. Every
        # time we find a node having same horizontal
        # distance we need to update the value in
        # the map.
        hd_dict[hd] = curr_node.data
   
        # If the dequeued node has a left child, add
        # it to the queue with a horizontal distance hd-1.
        if curr_node.left:
            curr_node.left.hd = hd - 1
            q.append(curr_node.left)
   
        # If the dequeued node has a right child, add
        # it to the queue with a horizontal distance
        # hd+1.
        if curr_node.right:
            curr_node.right.hd = hd + 1
            q.append(curr_node.right)
   
    # Traverse the map from least horizontal distance to
    # most horizontal distance.
    for i in range(min_hd, max_hd+1):
        print(hd_dict[i], end = ' ')
          
# Driver Code
if __name__=='__main__':
      
    root = Node(20)
    root.left = Node(8)
    root.right = Node(22)
    root.left.left = Node(5)
    root.left.right = Node(3)
    root.right.left = Node(4)
    root.right.right = Node(25)
    root.left.right.left = Node(10)
    root.left.right.right = Node(14)
      
    print("Bottom view of the given binary tree :")
      
    bottomView(root)
      
# This code is contributed by rutvik_56


C#




// C# program to print Bottom View of Binary Tree
using System;
using System.Collections;
using System.Collections.Generic;
   
// Tree node class
class Node
{
      
    // Data of the node
    public int data; 
      
    // Horizontal distance of the node
    public int hd; 
      
    // left and right references
    public Node left, right;
      
    // Constructor of tree node
    public Node(int key)
    {
        data = key;
        hd = 1000000;
        left = right = null;
    }
}
  
// Tree class
class Tree
{
      
    // Root node of tree
    Node root;
      
    // Default constructor
    public Tree(){}
      
    // Parameterized tree constructor
    public Tree(Node node)
    {
        root = node;
    }
   
    // Method that prints the bottom view.
    public void bottomView()
    {
        if (root == null)
            return;
              
        // Initialize a variable 'hd' with
        // 0 for the root element.
        int hd = 0;
   
        // TreeMap which stores key value
        // pair sorted on key value
        SortedDictionary<int,
                         int> map = new SortedDictionary<int,
                                                         int>();
   
        // Queue to store tree nodes in level order
        // traversal
        Queue queue = new Queue();
          
        // Assign initialized horizontal distance 
        // value to root node and add it to the queue.
        root.hd = hd;
        queue.Enqueue(root);
   
        // Loop until the queue is empty 
        // (standard level order loop)
        while (queue.Count != 0)
        {
            Node temp = (Node) queue.Dequeue();
   
            // Extract the horizontal distance value 
            // from the dequeued tree node.
            hd = temp.hd;
   
            // Put the dequeued tree node to TreeMap 
            // having key as horizontal distance.
            // Every time we find a node having same
            // horizontal distance we need to replace
            // the data in the map.
            map[hd] = temp.data;
   
            // If the dequeued node has a left child 
            // add it to the queue with a horizontal
            // distance hd-1.
            if (temp.left != null)
            {
                temp.left.hd = hd - 1;
                queue.Enqueue(temp.left);
            }
              
            // If the dequeued node has a right 
            // child add it to the queue with a
            // horizontal distance hd+1.
            if (temp.right != null)
            {
                temp.right.hd = hd + 1;
                queue.Enqueue(temp.right);
            }
        }
          
        foreach(int i in map.Values)
        {
            Console.Write(i + " ");
        }
    }
}
   
public class BottomView{
    
// Driver code
public static void Main(string[] args)
{
    Node root = new Node(20);
    root.left = new Node(8);
    root.right = new Node(22);
    root.left.left = new Node(5);
    root.left.right = new Node(3);
    root.right.left = new Node(4);
    root.right.right = new Node(25);
    root.left.right.left = new Node(10);
    root.left.right.right = new Node(14);
    Tree tree = new Tree(root);
      
    Console.WriteLine("Bottom view of the "
                      "given binary tree:");
      
    tree.bottomView();
}
}
  
// This code is contributed by pratham76


Javascript




<script>
  
      // JavaScript program to print Bottom View of Binary Tree
      // Tree node class
      class Node {
        // Constructor of tree node
        constructor(key) {
          this.data = key; // Data of the node
          this.hd = 1000000; // Horizontal distance of the node
          this.left = null; // left and right references
          this.right = null;
        }
      }
  
      // Tree class
      class Tree {
        // Parameterized tree constructor
        constructor(node) {
          // Root node of tree
          this.root = node;
        }
  
        // Method that prints the bottom view.
        bottomView() {
          if (this.root == null) return;
  
          // Initialize a variable 'hd' with
          // 0 for the root element.
          var hd = 0;
  
          // TreeMap which stores key value
          // pair sorted on key value
          var map = {};
  
          // Queue to store tree nodes in level order
          // traversal
          var queue = [];
  
          // Assign initialized horizontal distance
          // value to root node and add it to the queue.
          this.root.hd = hd;
          queue.push(this.root);
  
          // Loop until the queue is empty
          // (standard level order loop)
          while (queue.length != 0) {
            var temp = queue.shift();
  
            // Extract the horizontal distance value
            // from the dequeued tree node.
            hd = temp.hd;
  
            // Put the dequeued tree node to TreeMap
            // having key as horizontal distance.
            // Every time we find a node having same
            // horizontal distance we need to replace
            // the data in the map.
            map[hd] = temp.data;
  
            // If the dequeued node has a left child
            // add it to the queue with a horizontal
            // distance hd-1.
            if (temp.left != null) {
              temp.left.hd = hd - 1;
              queue.push(temp.left);
            }
  
            // If the dequeued node has a right
            // child add it to the queue with a
            // horizontal distance hd+1.
            if (temp.right != null) {
              temp.right.hd = hd + 1;
              queue.push(temp.right);
            }
          }
  
          for (const [key, value] of Object.entries(map).sort(
            (a, b) => a[0] - b[0]
          )) {
            document.write(value + " ");
          }
        }
      }
  
      // Driver code
      var root = new Node(20);
      root.left = new Node(8);
      root.right = new Node(22);
      root.left.left = new Node(5);
      root.left.right = new Node(3);
      root.right.left = new Node(4);
      root.right.right = new Node(25);
      root.left.right.left = new Node(10);
      root.left.right.right = new Node(14);
      var tree = new Tree(root);
  
      document.write("Bottom view of the " + "given binary tree:<br>");
  
      tree.bottomView();
        
</script>


Output

Bottom view of the given binary tree :
5 10 4 14 25 

Method 2 (Using HashMap()): Create a map where the key is the horizontal distance and the value is a pair(a, b) where a is the value of the node and b is the height of the node. Perform a pre-order traversal of the tree. If the current node at a horizontal distance of h is the first we’ve seen, insert it into the map. Otherwise, compare the node with the existing one in map and if the height of the new node is greater, update the Map.

Below is the implementation of the above:

C++




// C++ Program to print Bottom View of Binary Tree
#include <bits/stdc++.h> 
#include <map>
using namespace std;
  
// Tree node class
struct Node 
{
    // data of the node
    int data;
      
    // horizontal distance of the node
    int hd; 
      
    //left and right references
    Node * left, * right; 
      
    // Constructor of tree node
    Node(int key) 
    {
        data = key;
        hd = INT_MAX;
        left = right = NULL;
    }
};
  
void printBottomViewUtil(Node * root, int curr, int hd, map <int, pair <int, int>> & m)
{
    // Base case
    if (root == NULL)
        return;
      
    // If node for a particular 
    // horizontal distance is not
    // present, add to the map.
    if (m.find(hd) == m.end()) 
    {
        m[hd] = make_pair(root -> data, curr);
    
    // Compare height for already 
    // present node at similar horizontal
    // distance
    else 
    {
        pair < int, int > p = m[hd];
        if (p.second <= curr)
        {
            m[hd].second = curr;
            m[hd].first = root -> data;
        }
    }
      
    // Recur for left subtree
    printBottomViewUtil(root -> left, curr + 1, hd - 1, m);
      
    // Recur for right subtree
    printBottomViewUtil(root -> right, curr + 1, hd + 1, m);
}
  
void printBottomView(Node * root) 
{
      
    // Map to store Horizontal Distance,
    // Height and Data.
    map < int, pair < int, int > > m;
      
    printBottomViewUtil(root, 0, 0, m);
      
     // Prints the values stored by printBottomViewUtil()
    map < int, pair < int, int > > ::iterator it;
    for (it = m.begin(); it != m.end(); ++it)
    {
        pair < int, int > p = it -> second;
        cout << p.first << " ";
    }
}
  
int main() 
{
    Node * root = new Node(20);
    root -> left = new Node(8);
    root -> right = new Node(22);
    root -> left -> left = new Node(5);
    root -> left -> right = new Node(3);
    root -> right -> left = new Node(4);
    root -> right -> right = new Node(25);
    root -> left -> right -> left = new Node(10);
    root -> left -> right -> right = new Node(14);
    cout << "Bottom view of the given binary tree :\n";
    printBottomView(root);
    return 0;
}


Java




// Java program to print Bottom View of Binary Tree 
import java.io.*;
import java.lang.*;
import java.util.*;
  
class GFG{
  
// Tree node class
static class Node
{
      
    // Data of the node
    int data;
  
    // Horizontal distance of the node
    int hd;
  
    // Left and right references
    Node left, right;
  
    // Constructor of tree node
    public Node(int key)
    {
        data = key;
        hd = Integer.MAX_VALUE;
        left = right = null;
    }
}
  
static void printBottomViewUtil(Node root, int curr, int hd,
                                TreeMap<Integer, int[]> m)
{
      
    // Base case
    if (root == null)
        return;
  
    // If node for a particular
    // horizontal distance is not
    // present, add to the map.
    if (!m.containsKey(hd))
    {
        m.put(hd, new int[]{ root.data, curr });
    }
      
    // Compare height for already
    // present node at similar horizontal
    // distance
    else 
    {
        int[] p = m.get(hd);
        if (p[1] <= curr)
        {
            p[1] = curr;
            p[0] = root.data;
        }
        m.put(hd, p);
    }
  
    // Recur for left subtree
    printBottomViewUtil(root.left, curr + 1,
                        hd - 1, m);
  
    // Recur for right subtree
    printBottomViewUtil(root.right, curr + 1
                        hd + 1, m);
}
  
static void printBottomView(Node root)
{
  
    // Map to store Horizontal Distance,
    // Height and Data.
    TreeMap<Integer, int[]> m = new TreeMap<>();
  
    printBottomViewUtil(root, 0, 0, m);
  
    // Prints the values stored by printBottomViewUtil()
    for(int val[] : m.values()) 
    {
        System.out.print(val[0] + " ");
    }
}
  
// Driver Code
public static void main(String[] args)
{
    Node root = new Node(20);
    root.left = new Node(8);
    root.right = new Node(22);
    root.left.left = new Node(5);
    root.left.right = new Node(3);
    root.right.left = new Node(4);
    root.right.right = new Node(25);
    root.left.right.left = new Node(10);
    root.left.right.right = new Node(14);
  
    System.out.println(
        "Bottom view of the given binary tree:");
  
    printBottomView(root);
}
}
  
// This code is contributed by Kingash


Python3




# Python3 program to print Bottom
# View of Binary Tree 
class Node:
      
    def __init__(self, key = None
                      left = None
                     right = None):
                           
        self.data = key
        self.left = left
        self.right = right
          
def printBottomView(root):
      
      # Create a dictionary where
    # key -> relative horizontal distance
    # of the node from root node and
    # value -> pair containing node's 
    # value and its level
    d = dict()
      
    printBottomViewUtil(root, d, 0, 0)
      
    # Traverse the dictionary in sorted 
    # order of their keys and print
    # the bottom view
    for i in sorted(d.keys()):
        print(d[i][0], end = " ")
  
def printBottomViewUtil(root, d, hd, level):
      
      # Base case
    if root is None:
        return
      
    # If current level is more than or equal 
    # to maximum level seen so far for the 
    # same horizontal distance or horizontal
    # distance is seen for the first time, 
    # update the dictionary
    if hd in d:
        if level >= d[hd][1]:
            d[hd] = [root.data, level]
    else:
        d[hd] = [root.data, level]
          
    # recur for left subtree by decreasing
    # horizontal distance and increasing
    # level by 1
    printBottomViewUtil(root.left, d, hd - 1
                                   level + 1)
      
    # recur for right subtree by increasing
    # horizontal distance and increasing 
    # level by 1
    printBottomViewUtil(root.right, d, hd + 1
                                    level + 1)
  
# Driver Code    
if __name__ == '__main__':
      
    root = Node(20)
    root.left = Node(8)
    root.right = Node(22
    root.left.left = Node(5
    root.left.right = Node(3
    root.right.left = Node(4
    root.right.right = Node(25
    root.left.right.left = Node(10
    root.left.right.right = Node(14
      
    print("Bottom view of the given binary tree :")
      
    printBottomView(root)
  
# This code is contributed by tusharroy


Output

Bottom view of the given binary tree :
5 10 4 14 25 

Method 3 (Calling the function recursively):

  • Step 1: First create the Node class and declare the int data, left and right nodes.
  • Step 2: Create the constructor of the class node.
  • Step 3: Create the main class and declare the root node. In the main method, declare and initialize the tree node values.
  • Step 4: Now, call the static function print_bottom_view() with root node as argument.
  • Step 5: Check whether the current node is null.
  • Step 6: Now, check whether the left node and right side of the current node are null. If both the nodes are null then it will be at the bottom of the tree. The, simply print the data in that node. 
  • Step 7: To check for the next node, call the function in the same method by specifying print_bottom_view(n.left) and print_bottom_view(n.right). It will call the functions until the current node value becomes null.

Java




/*package whatever //do not write package name here */
  
import java.io.*;
class Node // tree node class
{
  int data;
  Node right,left;
 public Node(int d) //constructor of the Node
  {
    data=d;
    left=null;
    right=null;
  }
}
  
class GFG {
   Node root;
   public static void print_bottom_view(Node n)
   {
     if(n==null) //check whether the node is null
       return;
     if(n.left==null && n.right==null) // check whether the right and left side of the current nodes are null
     {
       System.out.print(n.data+" ");
     }
     print_bottom_view(n.left); 
     print_bottom_view(n.right);                 
   }
    public static void main (String[] args) {
      GFG tree=new GFG(); 
      tree.root=new Node(20);  
      tree.root.left=new Node(8);  
      tree.root.right=new Node(22);  
      tree.root.left.left=new Node(5);  
      tree.root.left.right=new Node(3);  
      tree.root.right.left=new Node(4);  
      tree.root.right.right=new Node(25);  
      tree.root.left.right.left=new Node(10);
      tree.root.left.right.right=new Node(14);
      System.out.println("Bottom View of the Tree :");
      print_bottom_view(tree.root); //calling the function
        
    }
}
//contributed by keerthikarathan123


Output

Bottom View of the Tree :
5 10 14 4 25 

Python3




# code
class Node:
       
    def __init__(self, key = None,
                      left = None,
                     right = None):
                            
        self.data = key
        self.left = left
        self.right = right
           
def print_bottom_view(root):
  if root is None:
        return
  if root.left is None and root.right is None :
    print(root.data,end=" ")
  print_bottom_view(root.left)
  print_bottom_view(root.right)
  
if __name__ == '__main__':
       
    root = Node(20)
    root.left = Node(8)
    root.right = Node(22)
    root.left.left = Node(5)
    root.left.right = Node(3)
    root.right.left = Node(4)
    root.right.right = Node(25)
    root.left.right.left = Node(10)
    root.left.right.right = Node(14)
       
    print("Bottom view of the tree :")
       
    print_bottom_view(root)
#contributed by keerthikarathan123


Output

Bottom view of the tree :
5 10 14 4 25 


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