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Flatten BST to sorted list | Increasing order

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  • Difficulty Level : Medium
  • Last Updated : 27 Jul, 2022
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Given a binary search tree, the task is to flatten it to a sorted list. Precisely, the value of each node must be lesser than the values of all the nodes at its right, and its left node must be NULL after flattening. We must do it in O(H) extra space where ‘H’ is the height of BST.

Examples: 

Input: 
          5 
        /   \ 
       3     7 
      / \   / \ 
     2   4 6   8
Output: 2 3 4 5 6 7 8
Input:
      1
       \
        2
         \
          3
           \
            4
             \
              5
Output: 1 2 3 4 5

Approach: A simple approach will be to recreate the BST from its in-order traversal. This will take O(N) extra space where N is the number of nodes in BST. 

To improve upon that, we will simulate in-order traversal of a binary tree as follows:  

  1. Create a dummy node.
  2. Create a variable called ‘prev’ and make it point to the dummy node.
  3. Perform in-order traversal and at each step. 
    • Set prev -> right = curr
    • Set prev -> left = NULL
    • Set prev = curr

This will improve the space complexity to O(H) in worst case as in-order traversal takes O(H) extra space.

Below is the implementation of the above approach: 

C++




// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// Node of the binary tree
struct node {
    int data;
    node* left;
    node* right;
    node(int data)
    {
        this->data = data;
        left = NULL;
        right = NULL;
    }
};
 
// Function to print flattened
// binary Tree
void print(node* parent)
{
    node* curr = parent;
    while (curr != NULL)
        cout << curr->data << " ", curr = curr->right;
}
 
// Function to perform in-order traversal
// recursively
void inorder(node* curr, node*& prev)
{
    // Base case
    if (curr == NULL)
        return;
    inorder(curr->left, prev);
    prev->left = NULL;
    prev->right = curr;
    prev = curr;
    inorder(curr->right, prev);
}
 
// Function to flatten binary tree using
// level order traversal
node* flatten(node* parent)
{
    // Dummy node
    node* dummy = new node(-1);
 
    // Pointer to previous element
    node* prev = dummy;
 
    // Calling in-order traversal
    inorder(parent, prev);
 
    prev->left = NULL;
    prev->right = NULL;
    node* ret = dummy->right;
 
    // Delete dummy node
    delete dummy;
    return ret;
}
 
// Driver code
int main()
{
    node* root = new node(5);
    root->left = new node(3);
    root->right = new node(7);
    root->left->left = new node(2);
    root->left->right = new node(4);
    root->right->left = new node(6);
    root->right->right = new node(8);
 
    // Calling required function
    print(flatten(root));
 
    return 0;
}

Java




// Java implementation of the
// above approach
import java.util.*;
class GFG{
  
// Node of the binary tree
static class node
{
  int data;
  node left;
  node right;
    
  node(int data)
  {
    this.data = data;
    left = null;
    right = null;
  }
};
  
// Function to print flattened
// binary tree
static void print(node parent)
{
  node curr = parent;
  while (curr != null)
  {
    System.out.print(curr.data + " ");
    curr = curr.right;
  }
}
  
static  node prev;
    
// Function to perform
// in-order traversal
static void Inorder(node curr)
{
  // Base case
  if (curr == null)
    return;
  Inorder(curr.left);
  prev.left = null;
  prev.right = curr;
  prev = curr;
  Inorder(curr.right);
}
  
// Function to flatten binary
// tree using level order
// traversal
static node flatten(node parent)
{
  // Dummy node
  node dummy = new node(-1);
  
  // Pointer to previous
  // element
  prev = dummy;
  
  // Calling in-order
  // traversal
  Inorder(parent);
  
  prev.left = null;
  prev.right = null;
  node ret = dummy.right;
  
  // Delete dummy node
  //delete dummy;
  return ret;
}
  
// Driver code
public static void main(String[] args)
{
  node root = new node(5);
  root.left = new node(3);
  root.right = new node(7);
  root.left.left = new node(2);
  root.left.right = new node(4);
  root.right.left = new node(6);
  root.right.right = new node(8);
  
  // Calling required function
  print(flatten(root));
}
}
  
// This code is contributed by Debojyoti Mandal

C#




// C# implementation of the
// above approach
using System;
public class Program{
  
// Node of the binary tree
public class node
{
  public int data;
  public node left;
  public node right;
    
  public node(int data)
  {
    this.data = data;
    left = null;
    right = null;
  }
};
  
// Function to print flattened
// binary tree
static void print(node parent)
{
  node curr = parent;
  while (curr != null)
  {
    Console.Write(curr.data + " ");
    curr = curr.right;
  }
}
  
static  node prev;
    
// Function to perform
// in-order traversal
static void Inorder(node curr)
{
  // Base case
  if (curr == null)
    return;
  Inorder(curr.left);
  prev.left = null;
  prev.right = curr;
  prev = curr;
  Inorder(curr.right);
}
  
// Function to flatten binary
// tree using level order
// traversal
static node flatten(node parent)
{
  // Dummy node
  node dummy = new node(-1);
  
  // Pointer to previous
  // element
  prev = dummy;
  
  // Calling in-order
  // traversal
  Inorder(parent);
  
  prev.left = null;
  prev.right = null;
  node ret = dummy.right;
  
  // Delete dummy node
  //delete dummy;
  return ret;
}
  
// Driver code
public static void Main(string[] args)
{
  node root = new node(5);
  root.left = new node(3);
  root.right = new node(7);
  root.left.left = new node(2);
  root.left.right = new node(4);
  root.right.left = new node(6);
  root.right.right = new node(8);
  
  // Calling required function
  print(flatten(root));
}
}
 
// This code is contributed by rrrtnx.

Javascript




<script>
 
// Javascript implementation of the approach
 
// Node of the binary tree
class node
{
    constructor(data)
    {
        this.left = null;
        this.right = null;
        this.data = data;
    }
}
 
let prev;
 
// Function to print flattened
// binary Tree
function print(parent)
{
    let curr = parent;
    while (curr != null)
    {
        document.write(curr.data + " ");
        curr = curr.right;
    }
}
 
// Function to perform in-order traversal
// recursively
function inorder(curr)
{
     
    // Base case
    if (curr == null)
        return;
         
    inorder(curr.left);
    prev.left = null;
    prev.right = curr;
    prev = curr;
    inorder(curr.right);
}
 
// Function to flatten binary tree using
// level order traversal
function flatten(parent)
{
     
    // Dummy node
    let dummy = new node(-1);
 
    // Pointer to previous element
    prev = dummy;
 
    // Calling in-order traversal
    inorder(parent);
 
    prev.left = null;
    prev.right = null;
    let ret = dummy.right;
 
    // Delete dummy node
    return ret;
}
 
// Driver code
let root = new node(5);
root.left = new node(3);
root.right = new node(7);
root.left.left = new node(2);
root.left.right = new node(4);
root.right.left = new node(6);
root.right.right = new node(8);
 
// Calling required function
print(flatten(root));
 
// This code is contributed by divyeshrabadiya07
 
</script>

Python3




# Python3 implementation of the approach
 
global prev
# Node of the binary tree
class node :
    def __init__(self, data):
        self.data = data
        self.left = None
        self.right = None
     
 
 
# Function to print flattened
# binary Tree
def printTree(parent):
    curr = parent
    while (curr != None):
        print(curr.data,end=' ')
        curr = curr.right
 
 
# Function to perform in-order traversal
# recursively
def inorder(curr):
    global prev
    # Base case
    if (curr == None):
        return
    inorder(curr.left)
    prev.left = None
    prev.right = curr
    prev = curr
    inorder(curr.right)
 
 
# Function to flatten binary tree using
# level order traversal
def flatten(parent):
    global prev
    # Dummy node
    dummy = node(-1)
 
    # Pointer to previous element
    prev = dummy
 
    # Calling in-order traversal
    inorder(parent)
 
    prev.left = None
    prev.right = None
    ret = dummy.right
 
    # Delete dummy node
    return ret
 
 
# Driver code
if __name__ == '__main__':
    root = node(5)
    root.left = node(3)
    root.right = node(7)
    root.left.left = node(2)
    root.left.right = node(4)
    root.right.left = node(6)
    root.right.right = node(8)
 
    # Calling required function
    printTree(flatten(root))

Output: 

2 3 4 5 6 7 8

 

Time Complexity: O(N)

Auxiliary Space: O(H)


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