Construct a Binary Search Tree from given postorder
Last Updated :
23 Jul, 2025
Given postorder traversal of a binary search tree, construct the BST.
For example, if the given traversal is {1, 7, 5, 50, 40, 10}, then following tree should be constructed and root of the tree should be returned.
10
/ \
5 40
/ \ \
1 7 50
Method 1 ( O(n^2) time complexity ):
The last element of postorder traversal is always root. We first construct the root. Then we find the index of last element which is smaller than root. Let the index be 'i'. The values between 0 and 'i' are part of left subtree, and the values between 'i+1' and 'n-2' are part of right subtree. Divide given post[] at index "i" and recur for left and right sub-trees.
For example in {1, 7, 5, 50, 40, 10}, 10 is the last element, so we make it root. Now we look for the last element smaller than 10, we find 5. So we know the structure of BST is as following.
10
/ \
/ \
{1, 7, 5} {50, 40}
We recursively follow above steps for subarrays {1, 7, 5} and {40, 50}, and get the complete tree.
Method 2 ( O(n) time complexity ):
The trick is to set a range {min .. max} for every node. Initialize the range as {INT_MIN .. INT_MAX}. The last node will definitely be in range, so create root node. To construct the left subtree, set the range as {INT_MIN …root->data}. If a values is in the range {INT_MIN .. root->data}, the values is part of left subtree. To construct the right subtree, set the range as {root->data .. INT_MAX}.
Following code is used to generate the exact Binary Search Tree of a given post order traversal.
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
/* 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;
}
/* 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
# 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
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
<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>
OutputInorder traversal of the constructed tree:
1 5 7 10 40 50
Time Complexity: O(n)
Space Complexity: O(h), where h is the height of the BST
Note that the output to the program will always be a sorted sequence as we are printing the inorder traversal of a Binary Search Tree.
Similar Reads
Basics & Prerequisites
Data Structures
Array Data StructureIn this article, we introduce array, implementation in different popular languages, its basic operations and commonly seen problems / interview questions. An array stores items (in case of C/C++ and Java Primitive Arrays) or their references (in case of Python, JS, Java Non-Primitive) at contiguous
3 min read
String in Data StructureA string is a sequence of characters. The following facts make string an interesting data structure.Small set of elements. Unlike normal array, strings typically have smaller set of items. For example, lowercase English alphabet has only 26 characters. ASCII has only 256 characters.Strings are immut
2 min read
Hashing in Data StructureHashing is a technique used in data structures that efficiently stores and retrieves data in a way that allows for quick access. Hashing involves mapping data to a specific index in a hash table (an array of items) using a hash function. It enables fast retrieval of information based on its key. The
2 min read
Linked List Data StructureA linked list is a fundamental data structure in computer science. It mainly allows efficient insertion and deletion operations compared to arrays. Like arrays, it is also used to implement other data structures like stack, queue and deque. Here’s the comparison of Linked List vs Arrays Linked List:
2 min read
Stack Data StructureA Stack is a linear data structure that follows a particular order in which the operations are performed. The order may be LIFO(Last In First Out) or FILO(First In Last Out). LIFO implies that the element that is inserted last, comes out first and FILO implies that the element that is inserted first
2 min read
Queue Data StructureA Queue Data Structure is a fundamental concept in computer science used for storing and managing data in a specific order. It follows the principle of "First in, First out" (FIFO), where the first element added to the queue is the first one to be removed. It is used as a buffer in computer systems
2 min read
Tree Data StructureTree Data Structure is a non-linear data structure in which a collection of elements known as nodes are connected to each other via edges such that there exists exactly one path between any two nodes. Types of TreeBinary Tree : Every node has at most two childrenTernary Tree : Every node has at most
4 min read
Graph Data StructureGraph Data Structure is a collection of nodes connected by edges. It's used to represent relationships between different entities. If you are looking for topic-wise list of problems on different topics like DFS, BFS, Topological Sort, Shortest Path, etc., please refer to Graph Algorithms. Basics of
3 min read
Trie Data StructureThe Trie data structure is a tree-like structure used for storing a dynamic set of strings. It allows for efficient retrieval and storage of keys, making it highly effective in handling large datasets. Trie supports operations such as insertion, search, deletion of keys, and prefix searches. In this
15+ min read
Algorithms
Searching AlgorithmsSearching algorithms are essential tools in computer science used to locate specific items within a collection of data. In this tutorial, we are mainly going to focus upon searching in an array. When we search an item in an array, there are two most common algorithms used based on the type of input
2 min read
Sorting AlgorithmsA Sorting Algorithm is used to rearrange a given array or list of elements in an order. For example, a given array [10, 20, 5, 2] becomes [2, 5, 10, 20] after sorting in increasing order and becomes [20, 10, 5, 2] after sorting in decreasing order. There exist different sorting algorithms for differ
3 min read
Introduction to RecursionThe process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. A recursive algorithm takes one step toward solution and then recursively call itself to further move. The algorithm stops once we reach the solution
14 min read
Greedy AlgorithmsGreedy algorithms are a class of algorithms that make locally optimal choices at each step with the hope of finding a global optimum solution. At every step of the algorithm, we make a choice that looks the best at the moment. To make the choice, we sometimes sort the array so that we can always get
3 min read
Graph AlgorithmsGraph is a non-linear data structure like tree data structure. The limitation of tree is, it can only represent hierarchical data. For situations where nodes or vertices are randomly connected with each other other, we use Graph. Example situations where we use graph data structure are, a social net
3 min read
Dynamic Programming or DPDynamic Programming is an algorithmic technique with the following properties.It is mainly an optimization over plain recursion. Wherever we see a recursive solution that has repeated calls for the same inputs, we can optimize it using Dynamic Programming. The idea is to simply store the results of
3 min read
Bitwise AlgorithmsBitwise algorithms in Data Structures and Algorithms (DSA) involve manipulating individual bits of binary representations of numbers to perform operations efficiently. These algorithms utilize bitwise operators like AND, OR, XOR, NOT, Left Shift, and Right Shift.BasicsIntroduction to Bitwise Algorit
4 min read
Advanced
Segment TreeSegment Tree is a data structure that allows efficient querying and updating of intervals or segments of an array. It is particularly useful for problems involving range queries, such as finding the sum, minimum, maximum, or any other operation over a specific range of elements in an array. The tree
3 min read
Pattern SearchingPattern searching algorithms are essential tools in computer science and data processing. These algorithms are designed to efficiently find a particular pattern within a larger set of data. Patten SearchingImportant Pattern Searching Algorithms:Naive String Matching : A Simple Algorithm that works i
2 min read
GeometryGeometry is a branch of mathematics that studies the properties, measurements, and relationships of points, lines, angles, surfaces, and solids. From basic lines and angles to complex structures, it helps us understand the world around us.Geometry for Students and BeginnersThis section covers key br
2 min read
Interview Preparation
Practice Problem