Aplanar BST a lista ordenada | orden creciente

Dado un árbol de búsqueda binario, la tarea es aplanarlo en una lista ordenada. Precisamente, el valor de cada Node debe ser menor que los valores de todos los Nodes a su derecha, y su Node izquierdo debe ser NULL después del aplanamiento. Debemos hacerlo en O(H) espacio extra donde ‘H’ es la altura de BST.

Ejemplos: 

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

Enfoque: un enfoque simple será recrear el BST a partir de su recorrido en orden . Esto tomará O(N) espacio extra donde N es el número de Nodes en BST. 

Para mejorar eso, simularemos el recorrido en orden de un árbol binario de la siguiente manera:  

1. Cree un Node ficticio.
2. Cree una variable llamada ‘prev’ y haga que apunte al Node ficticio.
3. Realice un recorrido en orden y en cada paso. 
   • Establecer anterior -> derecha = actual
   • Establecer anterior -> izquierda = NULL
   • Establecer anterior = actual

Esto mejorará la complejidad del espacio a O(H) en el peor de los casos, ya que el recorrido en orden requiere espacio adicional de O(H).

A continuación se muestra la implementación del enfoque anterior: 

// 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 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# 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.

<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 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))

2 3 4 5 6 7 8

Complejidad de tiempo: O(N)

Espacio Auxiliar: O(H)