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Sum of nodes in bottom view of Binary Tree
  • Difficulty Level : Medium
  • Last Updated : 07 Dec, 2020

Given a binary tree, the task is to print the sum of nodes in the bottom view of the given Binary Tree. The bottom view of a binary tree is the set of nodes visible when the tree is viewed from the bottom. 

Examples: 

Input : 
     1
    /  \
   2    3
  / \    \
 4   5    6

Output : 20

Input :
        1         
       / \         
      2    3         
       \         
         4         
          \         
            5         
             \         
               6

Output : 17

Approach: The idea is to use a queue. 

  1. Put tree nodes in a queue for the level order traversal
  2. Start with the horizontal distance(hd) 0 of the root node, keep on adding left child to queue along with the horizontal distance as hd-1 and right child as hd+1.
  3. Use a map to store the hd value(as key) and the last node(as pair) having the corresponding hd value.
  4. Every time, we encounter a new horizontal distance or an existing horizontal distance put the node data for the horizontal distance as 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 in the map.
  5. Finally, traverse the map and calculate the sum of all the elements.

Below is the implementation of the above approach:

C++




// C++ implementation of the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Structure of binary tree
struct Node {
    Node* left;
    Node* right;
    int hd;
    int data;
};
 
// Function to create a new node
Node* newNode(int key)
{
    Node* node = new Node();
    node->left = node->right = NULL;
    node->data = key;
    return node;
}
 
// Function that returns the sum of
// nodes in bottom view of binary tree
int SumOfBottomView(Node* root)
{
    if (root == NULL)
        return 0;
    queue<Node*> q;
 
    map<int, int> m;
    int hd = 0;
    root->hd = hd;
 
    int sum = 0;
 
    // Push node and horizontal distance to queue
    q.push(root);
 
    while (q.size()) {
        Node* temp = q.front();
        q.pop();
 
        hd = temp->hd;
 
        // Put the dequeued tree node to Map
        // 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 (temp->left) {
            temp->left->hd = hd - 1;
            q.push(temp->left);
        }
        if (temp->right) {
            temp->right->hd = hd + 1;
            q.push(temp->right);
        }
    }
 
    map<int, int>::iterator itr;
 
    // Sum up all the nodes in bottom view of the tree
    for (itr = m.begin(); itr != m.end(); itr++)
        sum += itr->second;
 
    return sum;
}
 
// Driver Code
int main()
{
    Node* root = newNode(20);
    root->left = newNode(8);
    root->right = newNode(22);
    root->left->left = newNode(5);
    root->left->right = newNode(3);
    root->right->left = newNode(4);
    root->right->right = newNode(25);
    root->left->right->left = newNode(10);
    root->left->right->right = newNode(14);
 
    cout << SumOfBottomView(root);
 
    return 0;
}

Java




// Java implementation of
// the above approach
import java.util.*;
 
class GFG{
     
// Structure of binary tree
public static class Node
{
    public Node left;
    public Node right;
    public int hd;
    public int data;
};
   
// Function to create
// a new node
static Node newNode(int key)
{
    Node node = new Node();
    node.data = key;
    node.left = null;
    node.right = null;
    return node;
}
   
// Function that returns the sum of
// nodes in bottom view of binary tree
static int SumOfBottomView(Node root)
{
    if (root == null)
        return 0;
     
    Queue<Node> q = new LinkedList<>();
     
    HashMap<Integer,
            Integer> m = new HashMap<Integer,
                                     Integer>();
    int hd = 0;
    root.hd = hd;
    int sum = 0;
     
    // Push node and horizontal
    // distance to queue
    q.add(root);
     
    while (q.size() != 0)
    {
        Node temp = q.poll();
        hd = temp.hd;
         
        // Put the dequeued tree node
        // to Map 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.put(hd, temp.data);
         
        if (temp.left != null)
        {
            temp.left.hd = hd - 1;
            q.add(temp.left);
        }
        if (temp.right != null)
        {
            temp.right.hd = hd + 1;
            q.add(temp.right);
        }
    }   
     
    // Sum up all the nodes in
    // bottom view of the tree   
    for(int value : m.values())
    {
        sum += value;
    }
    return sum;
}
   
// Driver code
public static void main(String[] args)
{
    Node root = newNode(20);
    root.left = newNode(8);
    root.right = newNode(22);
    root.left.left = newNode(5);
    root.left.right = newNode(3);
    root.right.left = newNode(4);
    root.right.right = newNode(25);
    root.left.right.left = newNode(10);
    root.left.right.right = newNode(14);
     
    System.out.println(SumOfBottomView(root));
}
}
 
// This code is contributed by pratham76

Python3




# Python3 implementation of the above approach
 
class Node:
     
    def __init__(self, data):
        self.data = data
        self.left = None
        self.right = None
        self.hd = None
 
# Function that returns the Sum of
# nodes in bottom view of binary tree
def SumOfBottomView(root):
 
    if root == None:
        return 0
     
    q = []
    m = {}
    hd, Sum = 0, 0
    root.hd = hd
 
    # Push node and horizontal
    # distance to queue
    q.append(root)
 
    while len(q) > 0:
        temp = q.pop(0)
        hd = temp.hd
 
        # Put the dequeued tree node to Map
        # 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 temp.left != None:
            temp.left.hd = hd - 1
            q.append(temp.left)
         
        if temp.right != None:
            temp.right.hd = hd + 1
            q.append(temp.right)
 
    # Sum up all the nodes in bottom
    # view of the tree
    for itr in m:
        Sum += m[itr]
 
    return Sum
 
# 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(SumOfBottomView(root))
     
# This code is contributed by Rituraj Jain

C#




// C# implementation of
// the above approach
using System;
using System.Collections;
using System.Collections.Generic;
class GFG
{
// Structure of binary tree
public class Node
{
  public Node left;
  public Node right;
  public int hd;
  public int data;
};
  
// Function to create
// a new node
static Node newNode(int key)
{
  Node node = new Node();
  node.data = key;
  node.left = null;
  node.right = null;
  return node;
}
  
// Function that returns the sum of
// nodes in bottom view of binary tree
static int SumOfBottomView(Node root)
{
  if (root == null)
    return 0;
 
  Queue q = new Queue();
  Dictionary<int,
             int> m = new Dictionary<int,
                                     int>();
  int hd = 0;
  root.hd = hd;
  int sum = 0;
 
  // Push node and horizontal
  // distance to queue
  q.Enqueue(root);
 
  while (q.Count != 0)
  {
    Node temp = (Node)q.Peek();
    q.Dequeue();
    hd = temp.hd;
 
    // Put the dequeued tree node
    // to Map 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 (temp.left != null)
    {
      temp.left.hd = hd - 1;
      q.Enqueue(temp.left);
    }
    if (temp.right != null)
    {
      temp.right.hd = hd + 1;
      q.Enqueue(temp.right);
    }
  }   
   
  // Sum up all the nodes in
  // bottom view of the tree   
  foreach(KeyValuePair<int,
                       int> itr in m)
  {
    sum += itr.Value;
  }
  return sum;
}
  
// Driver code
public static void Main(string[] args)
{
  Node root = newNode(20);
  root.left = newNode(8);
  root.right = newNode(22);
  root.left.left = newNode(5);
  root.left.right = newNode(3);
  root.right.left = newNode(4);
  root.right.right = newNode(25);
  root.left.right.left = newNode(10);
  root.left.right.right = newNode(14);
  Console.Write(SumOfBottomView(root));
}
}
 
// This code is contributed by rutvik_56
Output: 
58

 

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