Dado el recorrido posterior al orden de un árbol de búsqueda binario, construya el BST.
Por ejemplo, si el recorrido dado es {1, 7, 5, 50, 40, 10}, entonces se debe construir el siguiente árbol y se debe devolver la raíz del árbol.
10 / \ 5 40 / \ \ 1 7 50
Método 1 ( O (n ^ 2) complejidad de tiempo):
El último elemento del recorrido posterior al orden siempre es raíz. Primero construimos la raíz. Luego encontramos el índice del último elemento que es más pequeño que la raíz. Sea el índice ‘i’. Los valores entre 0 y ‘i’ son parte del subárbol izquierdo, y los valores entre ‘i+1’ y ‘n-2’ son parte del subárbol derecho. Divida la publicación dada [] en el índice «i» y recurra a los subárboles izquierdo y derecho.
Por ejemplo, en {1, 7, 5, 50, 40, 10}, 10 es el último elemento, por lo que lo hacemos raíz. Ahora buscamos el último elemento menor que 10, encontramos 5. Entonces sabemos que la estructura de BST es la siguiente.
10
/ \
/ \
{1, 7, 5} {50, 40}
Seguimos recursivamente los pasos anteriores para los subarreglos {1, 7, 5} y {40, 50} y obtenemos el árbol completo.
Método 2 (complejidad de tiempo O(n)):
El truco es establecer un rango {min .. max} para cada Node. Inicialice el rango como {INT_MIN .. INT_MAX}. El último Node definitivamente estará dentro del rango, así que cree un Node raíz. Para construir el subárbol izquierdo, establezca el rango como {INT_MIN…raíz->datos}. Si un valor está en el rango {INT_MIN .. root->data}, el valor es parte del subárbol izquierdo. Para construir el subárbol derecho, establezca el rango como {raíz->datos .. INT_MAX}.
El siguiente código se utiliza para generar el árbol de búsqueda binario exacto de un recorrido de orden posterior dado.
C++
/* A O(n) program for construction of
BST from postorder traversal */
#include <bits/stdc++.h>
using namespace std;
/* A binary tree node has data,
pointer to left child and a
pointer to right child */
struct node
{
int data;
struct node *left, *right;
};
// A utility function to create a node
struct node* newNode (int data)
{
struct node* temp =
(struct node *) malloc(sizeof(struct node));
temp->data = data;
temp->left = temp->right = NULL;
return temp;
}
// A recursive function to construct
// BST from post[]. postIndex is used
// to keep track of index in post[].
struct node* constructTreeUtil(int post[], int* postIndex,
int key, int min, int max,
int size)
{
// Base case
if (*postIndex < 0)
return NULL;
struct node* root = NULL;
// If current element of post[] is
// in range, then only it is part
// of current subtree
if (key > min && key < max)
{
// Allocate memory for root of this
// subtree and decrement *postIndex
root = newNode(key);
*postIndex = *postIndex - 1;
if (*postIndex >= 0)
{
// All nodes which are in range {key..max}
// will go in right subtree, and first such
// node will be root of right subtree.
root->right = constructTreeUtil(post, postIndex,
post[*postIndex],
key, max, size );
// Construct the subtree under root
// All nodes which are in range {min .. key}
// will go in left subtree, and first such
// node will be root of left subtree.
root->left = constructTreeUtil(post, postIndex,
post[*postIndex],
min, key, size );
}
}
return root;
}
// The main function to construct BST
// from given postorder traversal.
// This function mainly uses constructTreeUtil()
struct node *constructTree (int post[],
int size)
{
int postIndex = size-1;
return constructTreeUtil(post, &postIndex,
post[postIndex],
INT_MIN, INT_MAX, size);
}
// A utility function to print
// inorder traversal of a Binary Tree
void printInorder (struct node* node)
{
if (node == NULL)
return;
printInorder(node->left);
cout << node->data << " ";
printInorder(node->right);
}
// Driver Code
int main ()
{
int post[] = {1, 7, 5, 50, 40, 10};
int size = sizeof(post) / sizeof(post[0]);
struct node *root = constructTree(post, size);
cout << "Inorder traversal of "
<< "the constructed tree: \n";
printInorder(root);
return 0;
}
// This code is contributed
// by Akanksha Rai
C
/* A O(n) program for construction of BST from
postorder traversal */
#include <stdio.h>
#include <stdlib.h>
#include <limits.h>
/* A binary tree node has data, pointer to left child
and a pointer to right child */
struct node
{
int data;
struct node *left, *right;
};
// A utility function to create a node
struct node* newNode (int data)
{
struct node* temp =
(struct node *) malloc( sizeof(struct node));
temp->data = data;
temp->left = temp->right = NULL;
return temp;
}
// A recursive function to construct BST from post[].
// postIndex is used to keep track of index in post[].
struct node* constructTreeUtil(int post[], int* postIndex,
int key, int min, int max, int size)
{
// Base case
if (*postIndex < 0)
return NULL;
struct node* root = NULL;
// If current element of post[] is in range, then
// only it is part of current subtree
if (key > min && key < max)
{
// Allocate memory for root of this subtree and decrement
// *postIndex
root = newNode(key);
*postIndex = *postIndex - 1;
if (*postIndex >= 0)
{
// All nodes which are in range {key..max} will go in right
// subtree, and first such node will be root of right subtree.
root->right = constructTreeUtil(post, postIndex, post[*postIndex],
key, max, size );
// Construct the subtree under root
// All nodes which are in range {min .. key} will go in left
// subtree, and first such node will be root of left subtree.
root->left = constructTreeUtil(post, postIndex, post[*postIndex],
min, key, size );
}
}
return root;
}
// The main function to construct BST from given postorder
// traversal. This function mainly uses constructTreeUtil()
struct node *constructTree (int post[], int size)
{
int postIndex = size-1;
return constructTreeUtil(post, &postIndex, post[postIndex],
INT_MIN, INT_MAX, size);
}
// A utility function to print inorder traversal of a Binary Tree
void printInorder (struct node* node)
{
if (node == NULL)
return;
printInorder(node->left);
printf("%d ", node->data);
printInorder(node->right);
}
// Driver program to test above functions
int main ()
{
int post[] = {1, 7, 5, 50, 40, 10};
int size = sizeof(post) / sizeof(post[0]);
struct node *root = constructTree(post, size);
printf("Inorder traversal of the constructed tree: \n");
printInorder(root);
return 0;
}
Java
/* A O(n) program for construction of BST from
postorder traversal */
/* A binary tree node has data, pointer to left child
and a pointer to right child */
class Node
{
int data;
Node left, right;
Node(int data)
{
this.data = data;
left = right = null;
}
}
// Class containing variable that keeps a track of overall
// calculated postindex
class Index
{
int postindex = 0;
}
class BinaryTree
{
// A recursive function to construct BST from post[].
// postIndex is used to keep track of index in post[].
Node constructTreeUtil(int post[], Index postIndex,
int key, int min, int max, int size)
{
// Base case
if (postIndex.postindex < 0)
return null;
Node root = null;
// If current element of post[] is in range, then
// only it is part of current subtree
if (key > min && key < max)
{
// Allocate memory for root of this subtree and decrement
// *postIndex
root = new Node(key);
postIndex.postindex = postIndex.postindex - 1;
if (postIndex.postindex >= 0)
{
// All nodes which are in range {key..max} will go in
// right subtree, and first such node will be root of right
// subtree
root.right = constructTreeUtil(post, postIndex,
post[postIndex.postindex],key, max, size);
// Construct the subtree under root
// All nodes which are in range {min .. key} will go in left
// subtree, and first such node will be root of left subtree.
root.left = constructTreeUtil(post, postIndex,
post[postIndex.postindex],min, key, size);
}
}
return root;
}
// The main function to construct BST from given postorder
// traversal. This function mainly uses constructTreeUtil()
Node constructTree(int post[], int size)
{
Index index = new Index();
index.postindex = size - 1;
return constructTreeUtil(post, index, post[index.postindex],
Integer.MIN_VALUE, Integer.MAX_VALUE, size);
}
// A utility function to print inorder traversal of a Binary Tree
void printInorder(Node node)
{
if (node == null)
return;
printInorder(node.left);
System.out.print(node.data + " ");
printInorder(node.right);
}
// Driver program to test above functions
public static void main(String[] args)
{
BinaryTree tree = new BinaryTree();
int post[] = new int[]{1, 7, 5, 50, 40, 10};
int size = post.length;
Node root = tree.constructTree(post, size);
System.out.println("Inorder traversal of the constructed tree:");
tree.printInorder(root);
}
}
// This code has been contributed by Mayank Jaiswal
Python3
# A O(n) program for construction of BST
# from postorder traversal
INT_MIN = -2**31
INT_MAX = 2**31
# A binary tree node has data, pointer to
# left child and a pointer to right child
# A utility function to create a node
class newNode:
def __init__(self, data):
self.data = data
self.left = self.right = None
# A recursive function to construct
# BST from post[]. postIndex is used
# to keep track of index in post[].
def constructTreeUtil(post, postIndex,
key, min, max, size):
# Base case
if (postIndex[0] < 0):
return None
root = None
# If current element of post[] is
# in range, then only it is part
# of current subtree
if (key > min and key < max) :
# Allocate memory for root of this
# subtree and decrement *postIndex
root = newNode(key)
postIndex[0] = postIndex[0] - 1
if (postIndex[0] >= 0) :
# All nodes which are in range key..
# max will go in right subtree, and
# first such node will be root of
# right subtree.
root.right = constructTreeUtil(post, postIndex,
post[postIndex[0]],
key, max, size )
# Construct the subtree under root
# All nodes which are in range min ..
# key will go in left subtree, and
# first such node will be root of
# left subtree.
root.left = constructTreeUtil(post, postIndex,
post[postIndex[0]],
min, key, size )
return root
# The main function to construct BST
# from given postorder traversal. This
# function mainly uses constructTreeUtil()
def constructTree (post, size) :
postIndex = [size-1]
return constructTreeUtil(post, postIndex,
post[postIndex[0]],
INT_MIN, INT_MAX, size)
# A utility function to printInorder
# traversal of a Binary Tree
def printInorder (node) :
if (node == None) :
return
printInorder(node.left)
print(node.data, end = " ")
printInorder(node.right)
# Driver Code
if __name__ == '__main__':
post = [1, 7, 5, 50, 40, 10]
size = len(post)
root = constructTree(post, size)
print("Inorder traversal of the",
"constructed tree: ")
printInorder(root)
# This code is contributed
# by SHUBHAMSINGH10
C#
using System;
/* A O(n) program for
construction of BST from
postorder traversal */
/* A binary tree node has data,
pointer to left child and a
pointer to right child */
class Node
{
public int data;
public Node left, right;
public Node(int data)
{
this.data = data;
left = right = null;
}
}
// Class containing variable
// that keeps a track of overall
// calculated postindex
class Index
{
public int postindex = 0;
}
public class BinaryTree
{
// A recursive function to
// construct BST from post[].
// postIndex is used to
// keep track of index in post[].
Node constructTreeUtil(int []post, Index postIndex,
int key, int min, int max, int size)
{
// Base case
if (postIndex.postindex < 0)
return null;
Node root = null;
// If current element of post[] is in range, then
// only it is part of current subtree
if (key > min && key < max)
{
// Allocate memory for root of
// this subtree and decrement *postIndex
root = new Node(key);
postIndex.postindex = postIndex.postindex - 1;
if (postIndex.postindex >= 0)
{
// All nodes which are in range
// {key..max} will go in right subtree,
// and first such node will be root of
// right subtree
root.right = constructTreeUtil(post, postIndex,
post[postIndex.postindex], key, max, size);
// Construct the subtree under root
// All nodes which are in range
// {min .. key} will go in left
// subtree, and first such node
// will be root of left subtree.
root.left = constructTreeUtil(post, postIndex,
post[postIndex.postindex],min, key, size);
}
}
return root;
}
// The main function to construct
// BST from given postorder traversal.
// This function mainly uses constructTreeUtil()
Node constructTree(int []post, int size)
{
Index index = new Index();
index.postindex = size - 1;
return constructTreeUtil(post, index,
post[index.postindex],
int.MinValue, int.MaxValue, size);
}
// A utility function to print
// inorder traversal of a Binary Tree
void printInorder(Node node)
{
if (node == null)
return;
printInorder(node.left);
Console.Write(node.data + " ");
printInorder(node.right);
}
// Driver code
public static void Main(String[] args)
{
BinaryTree tree = new BinaryTree();
int []post = new int[]{1, 7, 5, 50, 40, 10};
int size = post.Length;
Node root = tree.constructTree(post, size);
Console.WriteLine("Inorder traversal of" +
"the constructed tree:");
tree.printInorder(root);
}
}
// This code has been contributed by PrinciRaj1992
Javascript
<script>
/* A O(n) program for
construction of BST from
postorder traversal */
/* A binary tree node has data,
pointer to left child and a
pointer to right child */
class Node {
constructor(data) {
this.data = data;
this.left = null;
this.right = null;
}
}
// Class containing variable
// that keeps a track of overall
// calculated postindex
class Index {
constructor() {
this.postindex = 0;
}
}
class BinaryTree {
// A recursive function to
// construct BST from post[].
// postIndex is used to
// keep track of index in post[].
constructTreeUtil(post, postIndex, key, min, max, size) {
// Base case
if (postIndex.postindex < 0) return null;
var root = null;
// If current element of post[] is in range, then
// only it is part of current subtree
if (key > min && key < max) {
// Allocate memory for root of
// this subtree and decrement *postIndex
root = new Node(key);
postIndex.postindex = postIndex.postindex - 1;
if (postIndex.postindex >= 0) {
// All nodes which are in range
// {key..max} will go in right subtree,
// and first such node will be root of
// right subtree
root.right = this.constructTreeUtil(
post,
postIndex,
post[postIndex.postindex],
key,
max,
size
);
// Construct the subtree under root
// All nodes which are in range
// {min .. key} will go in left
// subtree, and first such node
// will be root of left subtree.
root.left = this.constructTreeUtil(
post,
postIndex,
post[postIndex.postindex],
min,
key,
size
);
}
}
return root;
}
// The main function to construct
// BST from given postorder traversal.
// This function mainly uses constructTreeUtil()
constructTree(post, size) {
var index = new Index();
index.postindex = size - 1;
return this.constructTreeUtil(
post,
index,
post[index.postindex],
-2147483648,
2147483647,
size
);
}
// A utility function to print
// inorder traversal of a Binary Tree
printInorder(node) {
if (node == null) return;
this.printInorder(node.left);
document.write(node.data + " ");
this.printInorder(node.right);
}
}
// Driver code
var tree = new BinaryTree();
var post = [1, 7, 5, 50, 40, 10];
var size = post.length;
var root = tree.constructTree(post, size);
document.write("Inorder traversal of " +
"the constructed tree: <br>");
tree.printInorder(root);
</script>
Producción
Inorder traversal of the constructed tree: 1 5 7 10 40 50
Tenga en cuenta que la salida del programa siempre será una secuencia ordenada, ya que estamos imprimiendo el recorrido en orden de un árbol de búsqueda binaria.
Este artículo es una contribución de Aditya Goel . Si le gusta GeeksforGeeks y le gustaría contribuir, también puede escribir un artículo y enviarlo por correo a review-team@geeksforgeeks.org. Vea su artículo que aparece en la página principal de GeeksforGeeks y ayude a otros Geeks.
Publicación traducida automáticamente
Artículo escrito por GeeksforGeeks-1 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA