Sucesor posterior al orden de un Node en el árbol binario

Dado un árbol binario y un Node en el árbol binario, encuentre el sucesor Postorder del Node dado.
 

Examples: Consider the following binary tree
              20            
           /      \         
          10       26       
         /  \     /   \     
       4     18  24    27   
            /  \
           14   19
          /  \
         13  15

Postorder traversal of given tree is 4, 13, 15, 14,
19, 18, 10, 24, 27, 26, 20.

Input :  24
Output : 27

Input : 4
Output : 13

Una solución simple es almacenar primero el recorrido posterior al orden del árbol dado en una array, luego buscar linealmente el Node dado e imprimir el Node al lado. 
Complejidad de tiempo: O(n) 
Espacio auxiliar: O(n)
Una solución eficiente se basa en las siguientes observaciones. 
 

1. Si el Node dado es la raíz, entonces el sucesor del orden posterior es NULL, ya que la raíz es la última impresión del Node en un recorrido del orden posterior
2. Si el Node dado es el hijo derecho del padre o el hijo derecho del padre es NULL, entonces el padre es el sucesor del orden posterior.
3. Si el Node dado es el hijo izquierdo del padre y el hijo derecho del padre no es NULL, entonces el sucesor del orden posterior es el Node más a la izquierda del subárbol derecho del padre.

// CPP program to find postorder successor of
// given node.
#include <iostream>
using namespace std;
  
struct Node {
    struct Node *left, *right, *parent;
    int value;
};
  
// Utility function to create a new node with
// given value.
struct Node* newNode(int value)
{
    Node* temp = new Node;
    temp->left = temp->right = temp->parent = NULL;
    temp->value = value;
    return temp;
}
  
Node* postorderSuccessor(Node* root, Node* n)
{
    // Root has no successor in postorder
    // traversal
    if (n == root)
        return NULL;
  
    // If given node is right child of its
    // parent or parent's right is empty, then
    // parent is postorder successor.
    Node* parent = n->parent;
    if (parent->right == NULL || parent->right == n)
        return parent;
  
    // In all other cases, find the leftmost
    // child in right subtree of parent.
    Node* curr = parent->right;
    while (curr->left != NULL)
        curr = curr->left;
  
    return curr;
}
  
// Driver code
int main()
{
    struct Node* root = newNode(20);
    root->parent = NULL;
    root->left = newNode(10);
    root->left->parent = root;
    root->left->left = newNode(4);
    root->left->left->parent = root->left;
    root->left->right = newNode(18);
    root->left->right->parent = root->left;
    root->right = newNode(26);
    root->right->parent = root;
    root->right->left = newNode(24);
    root->right->left->parent = root->right;
    root->right->right = newNode(27);
    root->right->right->parent = root->right;
    root->left->right->left = newNode(14);
    root->left->right->left->parent = root->left->right;
    root->left->right->left->left = newNode(13);
    root->left->right->left->left->parent = root->left->right->left;
    root->left->right->left->right = newNode(15);
    root->left->right->left->right->parent = root->left->right->left;
    root->left->right->right = newNode(19);
    root->left->right->right->parent = root->left->right;
  
    struct Node* res = postorderSuccessor(root, root->left->right->right);
    if (res)
        printf("Postorder successor of %d is %d\n",
               root->left->right->right->value, res->value);   
    else
        printf("Postorder successor of %d is NULL\n",
               root->left->right->right->value);   
  
    return 0;
}

// Java program to find postorder successor of
// given node.
import java.util.*;
class GfG {
 
static class Node {
    Node left, right, parent;
    int value;
}
 
// Utility function to create a new node with
// given value.
static Node newNode(int value)
{
    Node temp = new Node();
    temp.left = null;
    temp.right = null;
    temp.parent = null;
    temp.value = value;
    return temp;
}
 
static Node postorderSuccessor(Node root, Node n)
{
    // Root has no successor in postorder
    // traversal
    if (n == root)
        return null;
 
    // If given node is right child of its
    // parent or parent's right is empty, then
    // parent is postorder successor.
    Node parent = n.parent;
    if (parent.right == null || parent.right == n)
        return parent;
 
    // In all other cases, find the leftmost
    // child in right subtree of parent.
    Node curr = parent.right;
    while (curr.left != null)
        curr = curr.left;
 
    return curr;
}
 
// Driver code
public static void main(String[] args)
{
    Node root = newNode(20);
    root.parent = null;
    root.left = newNode(10);
    root.left.parent = root;
    root.left.left = newNode(4);
    root.left.left.parent = root.left;
    root.left.right = newNode(18);
    root.left.right.parent = root.left;
    root.right = newNode(26);
    root.right.parent = root;
    root.right.left = newNode(24);
    root.right.left.parent = root.right;
    root.right.right = newNode(27);
    root.right.right.parent = root.right;
    root.left.right.left = newNode(14);
    root.left.right.left.parent = root.left.right;
    root.left.right.left.left = newNode(13);
    root.left.right.left.left.parent = root.left.right.left;
    root.left.right.left.right = newNode(15);
    root.left.right.left.right.parent = root.left.right.left;
    root.left.right.right = newNode(19);
    root.left.right.right.parent = root.left.right;
 
    Node res = postorderSuccessor(root, root.left.right.right);
    if (res != null)
        System.out.println("Postorder successor of "+
        root.left.right.right.value + " is "+ res.value);
    else
        System.out.println("Postorder successor of " +
        root.left.right.right.value + " is NULL");
}
}

""" Python3 program to find postorder
successor of a node in Binary Tree."""
 
# A Binary Tree Node
# Utility function to create a new tree node
class newNode:
 
    # Constructor to create a new node
    def __init__(self, data):
        self.value = data
        self.left = None
        self.right = None
        self.parent=None
 
def postorderSuccessor(root, n) :
 
    # Root has no successor in postorder
    # traversal
    if (n == root):
        return None
     
    # If given node is right child of its
    # parent or parent's right is empty,
    # then parent is postorder successor.
    parent = n.parent
    if (parent.right == None or parent.right == n):
        return parent
     
    # In all other cases, find the leftmost
    # child in right subtree of parent.
    curr = parent.right
    while (curr.left != None):
        curr = curr.left
     
    return curr
     
# Driver Code
if __name__ == '__main__':
    root = newNode(20)
    root.parent = None
    root.left = newNode(10)
    root.left.parent = root
    root.left.left = newNode(4)
    root.left.left.parent = root.left
    root.left.right = newNode(18)
    root.left.right.parent = root.left
    root.right = newNode(26)
    root.right.parent = root
    root.right.left = newNode(24)
    root.right.left.parent = root.right
    root.right.right = newNode(27)
    root.right.right.parent = root.right
    root.left.right.left = newNode(14)
    root.left.right.left.parent = root.left.right
    root.left.right.left.left = newNode(13)
    root.left.right.left.left.parent = root.left.right.left
    root.left.right.left.right = newNode(15)
    root.left.right.left.right.parent = root.left.right.left
    root.left.right.right = newNode(19)
    root.left.right.right.parent = root.left.right
    res = postorderSuccessor(root, root.left.right.right)
 
    if (res) :
        print("postorder successor of",
               root.left.right.right.value,
               "is", res.value)
     
    else:
        print("postorder successor of",
               root.left.right.right.value,
                                 "is None")
 
# This code is contributed by SHUBHAMSINGH10

// C# program to find postorder successor of
// given node.
using System;
 
class GfG
{
 
class Node
{
    public Node left, right, parent;
    public int value;
}
 
// Utility function to create 
// a new node with given value.
static Node newNode(int value)
{
    Node temp = new Node();
    temp.left = null;
    temp.right = null;
    temp.parent = null;
    temp.value = value;
    return temp;
}
 
static Node postorderSuccessor(Node root, Node n)
{
    // Root has no successor in 
    // postorder traversal
    if (n == root)
        return null;
 
    // If given node is right child of its
    // parent or parent's right is empty, then
    // parent is postorder successor.
    Node parent = n.parent;
    if (parent.right == null || parent.right == n)
        return parent;
 
    // In all other cases, find the leftmost
    // child in right subtree of parent.
    Node curr = parent.right;
    while (curr.left != null)
        curr = curr.left;
 
    return curr;
}
 
// Driver code
public static void Main(String[] args)
{
    Node root = newNode(20);
    root.parent = null;
    root.left = newNode(10);
    root.left.parent = root;
    root.left.left = newNode(4);
    root.left.left.parent = root.left;
    root.left.right = newNode(18);
    root.left.right.parent = root.left;
    root.right = newNode(26);
    root.right.parent = root;
    root.right.left = newNode(24);
    root.right.left.parent = root.right;
    root.right.right = newNode(27);
    root.right.right.parent = root.right;
    root.left.right.left = newNode(14);
    root.left.right.left.parent = root.left.right;
    root.left.right.left.left = newNode(13);
    root.left.right.left.left.parent = root.left.right.left;
    root.left.right.left.right = newNode(15);
    root.left.right.left.right.parent = root.left.right.left;
    root.left.right.right = newNode(19);
    root.left.right.right.parent = root.left.right;
 
    Node res = postorderSuccessor(root, root.left.right.right);
    if (res != null)
        Console.WriteLine("Postorder successor of "+
        root.left.right.right.value + " is "+ res.value);
    else
        Console.WriteLine("Postorder successor of " +
        root.left.right.right.value + " is NULL");
}
}
 
// This code is contributed by 29AjayKumar

<script>
 
// javascript program to find postorder successor of
// given node.
 
class Node
{
    constructor()
    {
        this.value = 0;
        this.left = null;
        this.right = null;
        this.parent = null;
    }
}
 
// Utility function to create 
// a new node with given value.
function newNode(value)
{
    var temp = new Node();
    temp.left = null;
    temp.right = null;
    temp.parent = null;
    temp.value = value;
    return temp;
}
 
function postorderSuccessor(root, n)
{
    // Root has no successor in 
    // postorder traversal
    if (n == root)
        return null;
 
    // If given node is right child of its
    // parent or parent's right is empty, then
    // parent is postorder successor.
    var parent = n.parent;
    if (parent.right == null || parent.right == n)
        return parent;
 
    // In all other cases, find the leftmost
    // child in right subtree of parent.
    var curr = parent.right;
    while (curr.left != null)
        curr = curr.left;
 
    return curr;
}
 
// Driver code
var root = newNode(20);
root.parent = null;
root.left = newNode(10);
root.left.parent = root;
root.left.left = newNode(4);
root.left.left.parent = root.left;
root.left.right = newNode(18);
root.left.right.parent = root.left;
root.right = newNode(26);
root.right.parent = root;
root.right.left = newNode(24);
root.right.left.parent = root.right;
root.right.right = newNode(27);
root.right.right.parent = root.right;
root.left.right.left = newNode(14);
root.left.right.left.parent = root.left.right;
root.left.right.left.left = newNode(13);
root.left.right.left.left.parent = root.left.right.left;
root.left.right.left.right = newNode(15);
root.left.right.left.right.parent = root.left.right.left;
root.left.right.right = newNode(19);
root.left.right.right.parent = root.left.right;
var res = postorderSuccessor(root, root.left.right.right);
if (res != null)
    document.write("Postorder successor of "+
    root.left.right.right.value + " is "+ res.value);
else
    document.write("Postorder successor of " +
    root.left.right.right.value + " is NULL");
 
// This code is contributed by famously.
 
</script>

Postorder successor of 19 is 18

Complejidad de tiempo: O (h) donde h es la altura del 
espacio auxiliar del árbol binario dado: O (1) ya que no se usan arrays, pilas, colas.