Skip to content
Related Articles

Related Articles

Improve Article

Bottom View of a Binary Tree using Recursion

  • Difficulty Level : Medium
  • Last Updated : 22 Jun, 2021
Geek Week

Given a binary tree, the task is to find the bottom view of a binary tree using recursion.

Examples:

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

Input:
        20
      /    \
    8       22
  /   \    /   \
5      10 21     25
      / \      
    9    14
 
Output: 5 9 21 14 25

Approach:
We can do so by using recursion and 2 arrays each with size 2n+1(for worst case), where n = number of elements in the given tree. Here, we take a Variable x which determines its Horizontal Distance. Let x is the horizontal distance of a Node. Now, the left child will have a horizontal distance of x-1(x minus 1)and the right child will have horizontal distance x+1(x plus 1). Take another Variable ‘p’ as a priority which will decide which level this element belongs to.

    1 (x=0, p=0)
      \
        2 (x=1, p=1)
          \
            4 (x=2, p=2)
          /  \
(x=1, p=3) 3     5 (x=3, p=3)

While Traversing the Tree In fashion Right-> Node-> Left, assign x and p to each Node and simultaneously insert the data of node in the first array if the array is empty at position (mid+x). If the array is not empty and a Node with higher Priority( p ) comes to update the array with the data of this Node as position(mid+x). The second array will be maintaining the priority( p ) of each inserted node in the first array check code for better understanding.

Below is the implementation of above approach:  



C++




#include <bits/stdc++.h>
using namespace std;
 
struct Node {
    int data;
    // left and right references
    Node *left, *right;
    // Constructor of tree Node
    Node(int key)
    {
        data = key;
        left = right = NULL;
    }
};
 
int l = 0, r = 0;
int N;
 
// Function to generate
// bottom view of
// binary tree
void Bottom(Node* root, int arr[], int arr2[], int x, int p, int mid)
{
    // Base case
    if (root == NULL) {
        return;
    }
 
    if (x < l) {
        // To store leftmost
        // value of x in l
        l = x;
    }
 
    // To store rightmost
    // value of x in r
    if (x > r) {
        r = x;
    }
 
    // To check if arr
    // is empty at mid+x
    if (arr[mid + x] == INT_MIN) {
        // Insert data of Node
        // at arr[mid+x]
        arr[mid + x] = root->data;
        // Insert priority of
        // that Node at arr2[mid+x]
        arr2[mid + x] = p;
    }
 
    // If not empty and priotiy
    // of previously inserted
    // Node is less than current*/
    else if (arr2[mid + x] < p) {
        // Insert current
        // Node data at arr[mid+x]
        arr[mid + x] = root->data;
 
        // Insert priotiy of
        // that Node at arr2[mid +x]
        arr2[mid + x] = p;
    }
 
    // Go right first
    // then left
    Bottom(root->right, arr, arr2, x + 1, p + 1, mid);
    Bottom(root->left, arr, arr2, x - 1, p + 1, mid);
}
 
// Utility function
// to generate bottom
// view of a biany tree
void bottomView(struct Node* root)
{
    int arr[2 * N + 1];
    int arr2[2 * N + 1];
 
    for (int i = 0; i < 2 * N + 1; i++) {
        arr[i] = INT_MIN;
        arr2[i] = INT_MIN;
    }
 
    int mid = N, x = 0, p = 0;
 
    Bottom(root, arr, arr2, x, p, mid);
 
    for (int i = mid + l; i <= mid + r; i++) {
        cout << arr[i] << " ";
    }
}
 
// Driver code
int main()
{
 
    N = 5;
    Node* root = new Node(1);
    root->right = new Node(2);
    root->right->right = new Node(4);
    root->right->right->left = new Node(3);
    root->right->right->right = new Node(5);
 
    bottomView(root);
 
    return 0;
}

Java




class GFG{
     
static class Node
{
    int data;
     
    // left and right references
    Node left, right;
     
    // Constructor of tree Node
    public Node(int key)
    {
        data = key;
        left = right = null;
    }
};
 
static int l = 0, r = 0, N;
 
// Function to generate
// bottom view of binary tree
static void Bottom(Node root, int arr[],
                  int arr2[], int x,
                       int p, int mid)
{
     
    // Base case
    if (root == null)
    {
        return;
    }
 
    if (x < l)
    {
         
        // To store leftmost
        // value of x in l
        l = x;
    }
 
    // To store rightmost
    // value of x in r
    if (x > r)
    {
        r = x;
    }
 
    // To check if arr
    // is empty at mid+x
    if (arr[mid + x] == Integer.MIN_VALUE)
    {
         
        // Insert data of Node
        // at arr[mid+x]
        arr[mid + x] = root.data;
         
        // Insert priority of
        // that Node at arr2[mid+x]
        arr2[mid + x] = p;
    }
 
    // If not empty and priotiy
    // of previously inserted
    // Node is less than current*/
    else if (arr2[mid + x] < p)
    {
         
        // Insert current
        // Node data at arr[mid+x]
        arr[mid + x] = root.data;
 
        // Insert priotiy of
        // that Node at arr2[mid +x]
        arr2[mid + x] = p;
    }
 
    // Go right first
    // then left
    Bottom(root.right, arr, arr2,
           x + 1, p + 1, mid);
    Bottom(root.left, arr, arr2,
           x - 1, p + 1, mid);
}
 
// Utility function to generate
// bottom view of a biany tree
static void bottomView(Node root)
{
    int[] arr = new int[2 * N + 1];
    int[] arr2 = new int[2 * N + 1];
 
    for(int i = 0; i < 2 * N + 1; i++)
    {
        arr[i] = Integer.MIN_VALUE;
        arr2[i] = Integer.MIN_VALUE;
    }
 
    int mid = N, x = 0, p = 0;
 
    Bottom(root, arr, arr2, x, p, mid);
 
    for(int i = mid + l; i <= mid + r; i++)
    {
        System.out.print(arr[i] + " ");
    }
}
 
// Driver code
public static void main(String[] args)
{
    N = 5;
     
    Node root = new Node(1);
    root.right = new Node(2);
    root.right.right = new Node(4);
    root.right.right.left = new Node(3);
    root.right.right.right = new Node(5);
 
    bottomView(root);
}
}
 
// This code is contributed by sanjeev2552

Python3




class Node:
    def __init__(self, data):
        self.data = data
        self.left = None
        self.right = None
 
l = 0
r = 0
INT_MIN = -(2**32)
 
# Function to generate
# bottom view of
# binary tree
def Bottom(root, arr, arr2, x, p, mid):
    global INT_MIN, l, r
     
    # Base case
    if (root == None):
        return
     
    if (x < l):
         
        # To store leftmost
        # value of x in l
        l = x
     
    # To store rightmost
    # value of x in r
    if (x > r):
        r = x
         
    # To check if arr
    # is empty at mid+x
    if (arr[mid + x] == INT_MIN):
 
        # Insert data of Node
        # at arr[mid+x]
        arr[mid + x] = root.data
 
        # Insert priority of
        # that Node at arr2[mid+x]
        arr2[mid + x] = p
         
    # If not empty and priotiy
    # of previously inserted
    # Node is less than current*/
    elif (arr2[mid + x] < p):
 
        # Insert current
        # Node data at arr[mid+x]
        arr[mid + x] = root.data
         
        # Insert priotiy of
        # that Node at arr2[mid +x]
        arr2[mid + x] = p
     
    # Go right first
    # then left
    Bottom(root.right, arr, arr2, x + 1, p + 1, mid)
    Bottom(root.left, arr, arr2, x - 1, p + 1, mid)
 
# Utility function
# to generate bottom
# view of a biany tree
def bottomView(root):
    global INT_MIN
    arr = [0]*(2 * N + 1)
    arr2 = [0]*(2 * N + 1)
     
    for i in range(2 * N + 1):
        arr[i] = INT_MIN
        arr2[i] = INT_MIN
    mid = N
    x = 0
    p = 0
    Bottom(root, arr, arr2, x, p, mid)
     
    for i in range(mid + l,mid + r + 1):
        print(arr[i], end = " ")
         
# Driver code
N = 5
root = Node(1)
root.right = Node(2)
root.right.right = Node(4)
root.right.right.left = Node(3)
root.right.right.right = Node(5)
 
bottomView(root)
     
# This code is contributed by SHUBHAMSINGH10

C#




using System;
 
class GFG{
     
class Node{
     
public int data;
 
// left and right references
public Node left, right;
 
// Constructor of tree Node
public Node(int key)
{
    data = key;
    left = right = null;
}
};
 
static int l = 0, r = 0, N;
 
// Function to generate
// bottom view of binary tree
static void Bottom(Node root, int []arr,
                  int []arr2, int x,
                       int p, int mid)
{
     
    // Base case
    if (root == null)
    {
        return;
    }
 
    if (x < l)
    {
         
        // To store leftmost
        // value of x in l
        l = x;
    }
 
    // To store rightmost
    // value of x in r
    if (x > r)
    {
        r = x;
    }
 
    // To check if arr
    // is empty at mid+x
    if (arr[mid + x] == Int32.MinValue)
    {
         
        // Insert data of Node
        // at arr[mid+x]
        arr[mid + x] = root.data;
         
        // Insert priority of
        // that Node at arr2[mid+x]
        arr2[mid + x] = p;
    }
 
    // If not empty and priotiy
    // of previously inserted
    // Node is less than current*/
    else if (arr2[mid + x] < p)
    {
         
        // Insert current
        // Node data at arr[mid+x]
        arr[mid + x] = root.data;
 
        // Insert priotiy of
        // that Node at arr2[mid +x]
        arr2[mid + x] = p;
    }
 
    // Go right first
    // then left
    Bottom(root.right, arr, arr2,
           x + 1, p + 1, mid);
    Bottom(root.left, arr, arr2,
           x - 1, p + 1, mid);
}
 
// Utility function to generate
// bottom view of a biany tree
static void bottomView(Node root)
{
    int[] arr = new int[2 * N + 1];
    int[] arr2 = new int[2 * N + 1];
 
    for(int i = 0; i < 2 * N + 1; i++)
    {
        arr[i] = Int32.MinValue;
        arr2[i] = Int32.MinValue;
    }
 
    int mid = N, x = 0, p = 0;
 
    Bottom(root, arr, arr2, x, p, mid);
 
    for(int i = mid + l; i <= mid + r; i++)
    {
        Console.Write(arr[i] + " ");
    }
}
 
// Driver code
public static void Main(string[] args)
{
    N = 5;
     
    Node root = new Node(1);
    root.right = new Node(2);
    root.right.right = new Node(4);
    root.right.right.left = new Node(3);
    root.right.right.right = new Node(5);
 
    bottomView(root);
}
}
 
// This code is contributed by rutvik_56

Javascript




<script>
 
class Node{
 
    // Constructor of tree Node
    constructor(key)
    {
        this.data = key;
        this.left = null;
        this.right = null;
    }
 
};
 
var l = 0, r = 0, N;
 
// Function to generate
// bottom view of binary tree
function Bottom(root, arr, arr2, x, p, mid)
{
     
    // Base case
    if (root == null)
    {
        return;
    }
 
    if (x < l)
    {
         
        // To store leftmost
        // value of x in l
        l = x;
    }
 
    // To store rightmost
    // value of x in r
    if (x > r)
    {
        r = x;
    }
 
    // To check if arr
    // is empty at mid+x
    if (arr[mid + x] == -1000000000)
    {
         
        // Insert data of Node
        // at arr[mid+x]
        arr[mid + x] = root.data;
         
        // Insert priority of
        // that Node at arr2[mid+x]
        arr2[mid + x] = p;
    }
 
    // If not empty and priotiy
    // of previously inserted
    // Node is less than current*/
    else if (arr2[mid + x] < p)
    {
         
        // Insert current
        // Node data at arr[mid+x]
        arr[mid + x] = root.data;
 
        // Insert priotiy of
        // that Node at arr2[mid +x]
        arr2[mid + x] = p;
    }
 
    // Go right first
    // then left
    Bottom(root.right, arr, arr2,
           x + 1, p + 1, mid);
    Bottom(root.left, arr, arr2,
           x - 1, p + 1, mid);
}
 
// Utility function to generate
// bottom view of a biany tree
function bottomView(root)
{
    var arr = Array(2*N +1).fill(-1000000000);
    var arr2 = Array(2*N +1).fill(-1000000000);
   
    var mid = N, x = 0, p = 0;
 
    Bottom(root, arr, arr2, x, p, mid);
 
    for(var i = mid + l; i <= mid + r; i++)
    {
        document.write(arr[i] + " ");
    }
}
 
// Driver code
N = 5;
 
var root = new Node(1);
root.right = new Node(2);
root.right.right = new Node(4);
root.right.right.left = new Node(3);
root.right.right.right = new Node(5);
bottomView(root);
 
</script>
Output: 
1 3 4 5

 

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.




My Personal Notes arrow_drop_up
Recommended Articles
Page :