# Construct BST from given preorder traversal | Set 1

Given preorder traversal of a binary search tree, construct the BST.

For example, if the given traversal is {10, 5, 1, 7, 40, 50}, then the output should be the root of the following tree.

```     10
/   \
5     40
/  \      \
1    7      50
```

Method 1 ( O(n2) time complexity )
The first element of preorder traversal is always root. We first construct the root. Then we find the index of first element which is greater than root. Let the index be ‘i’. The values between root and ‘i’ will be part of left subtree, and the values between ‘i+1’ and ‘n-1’ will be part of right subtree. Divide given pre[] at index “i” and recur for left and right sub-trees.

For example in {10, 5, 1, 7, 40, 50}, 10 is the first element, so we make it root. Now we look for the first element greater than 10, we find 40. So we know the structure of BST is as following.

```             10
/    \
/      \
{5, 1, 7}       {40, 50}
```

We recursively follow above steps for subarrays {5, 1, 7} and {40, 50}, and get the complete tree.

 `/* A O(n^2) program for construction of BST from preorder` ` ``* traversal */` `#include ` `using` `namespace` `std;`   `/* A binary tree node has data, pointer to left child` `and a pointer to right child */` `class` `node ` `{` `public``:` `    ``int` `data;` `    ``node* left;` `    ``node* right;` `};`   `// A utility function to create a node` `node* newNode(``int` `data)` `{` `    ``node* temp = ``new` `node();`   `    ``temp->data = data;` `    ``temp->left = temp->right = NULL;`   `    ``return` `temp;` `}`   `// A recursive function to construct Full from pre[].` `// preIndex is used to keep track of index in pre[].` `node* constructTreeUtil(``int` `pre[], ``int``* preIndex, ``int` `low,` `                        ``int` `high, ``int` `size)` `{` `    ``// Base case` `    ``if` `(*preIndex >= size || low > high)` `        ``return` `NULL;`   `    ``// The first node in preorder traversal is root. So take` `    ``// the node at preIndex from pre[] and make it root, and` `    ``// increment preIndex` `    ``node* root = newNode(pre[*preIndex]);` `    ``*preIndex = *preIndex + 1;`   `    ``// If the current subarry has only one element, no need` `    ``// to recur` `    ``if` `(low == high)` `        ``return` `root;`   `    ``// Search for the first element greater than root` `    ``int` `i;` `    ``for` `(i = low; i <= high; ++i)` `        ``if` `(pre[i] > root->data)` `            ``break``;`   `    ``// Use the index of element found in preorder to divide` `    ``// preorder array in two parts. Left subtree and right` `    ``// subtree` `    ``root->left = constructTreeUtil(pre, ` `                                   ``preIndex, ` `                                   ``*preIndex,` `                                   ``i - 1, ` `                                   ``size);` `    ``root->right` `        ``= constructTreeUtil(pre, preIndex, i, high, size);`   `    ``return` `root;` `}`   `// The main function to construct BST from given preorder` `// traversal. This function mainly uses constructTreeUtil()` `node* constructTree(``int` `pre[], ``int` `size)` `{` `    ``int` `preIndex = 0;` `    ``return` `constructTreeUtil(pre, ` `                             ``&preIndex, ` `                             ``0, ` `                             ``size - 1,` `                             ``size);` `}`   `// A utility function to print inorder traversal of a Binary` `// Tree` `void` `printInorder(node* node)` `{` `    ``if` `(node == NULL)` `        ``return``;` `    ``printInorder(node->left);` `    ``cout << node->data << ``" "``;` `    ``printInorder(node->right);` `}`   `// Driver code` `int` `main()` `{` `    ``int` `pre[] = { 10, 5, 1, 7, 40, 50 };` `    ``int` `size = ``sizeof``(pre) / ``sizeof``(pre[0]);`   `    ``node* root = constructTree(pre, size);`   `    ``cout << ``"Inorder traversal of the constructed tree: \n"``;` `    ``printInorder(root);`   `    ``return` `0;` `}`   `// This code is contributed by rathbhupendra`

 `/* A O(n^2) program for construction of BST from preorder` ` ``* traversal */` `#include ` `#include `   `/* A binary tree node has data, pointer to left child` `   ``and a pointer to right child */` `struct` `node ` `{` `    ``int` `data;` `    ``struct` `node* left;` `    ``struct` `node* 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 Full from pre[].` `// preIndex is used to keep track of index in pre[].` `struct` `node* constructTreeUtil(``int` `pre[], ``int``* preIndex,` `                               ``int` `low, ``int` `high, ``int` `size)` `{` `    ``// Base case` `    ``if` `(*preIndex >= size || low > high)` `        ``return` `NULL;`   `    ``// The first node in preorder traversal is root. So take` `    ``// the node at preIndex from pre[] and make it root, and` `    ``// increment preIndex` `    ``struct` `node* root = newNode(pre[*preIndex]);` `    ``*preIndex = *preIndex + 1;`   `    ``// If the current subarry has only one element, no need` `    ``// to recur` `    ``if` `(low == high)` `        ``return` `root;`   `    ``// Search for the first element greater than root` `    ``int` `i;` `    ``for` `(i = low; i <= high; ++i)` `        ``if` `(pre[i] > root->data)` `            ``break``;`   `    ``// Use the index of element found in preorder to divide` `    ``// preorder array in two parts. Left subtree and right` `    ``// subtree` `    ``root->left = constructTreeUtil(pre, ` `                                   ``preIndex, ` `                                   ``*preIndex,` `                                   ``i - 1, ` `                                   ``size);` `    ``root->right` `        ``= constructTreeUtil(pre, preIndex, i, high, size);`   `    ``return` `root;` `}`   `// The main function to construct BST from given preorder` `// traversal. This function mainly uses constructTreeUtil()` `struct` `node* constructTree(``int` `pre[], ``int` `size)` `{` `    ``int` `preIndex = 0;` `    ``return` `constructTreeUtil(pre, &preIndex, 0, size - 1,` `                             ``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 code` `int` `main()` `{` `    ``int` `pre[] = { 10, 5, 1, 7, 40, 50 };` `    ``int` `size = ``sizeof``(pre) / ``sizeof``(pre[0]);`   `    ``struct` `node* root = constructTree(pre, size);`   `    ``printf``(``"Inorder traversal of the constructed tree: \n"``);` `    ``printInorder(root);`   `    ``return` `0;` `}`

 `// Java program to construct BST from given preorder` `// traversal`   `// A binary tree node` `class` `Node ` `{`   `    ``int` `data;` `    ``Node left, right;`   `    ``Node(``int` `d)` `    ``{` `        ``data = d;` `        ``left = right = ``null``;` `    ``}` `}`   `class` `Index ` `{`   `    ``int` `index = ``0``;` `}`   `class` `BinaryTree ` `{`   `    ``Index index = ``new` `Index();`   `    ``// A recursive function to construct Full from pre[].` `    ``// preIndex is used to keep track of index in pre[].` `    ``Node constructTreeUtil(``int` `pre[], Index preIndex,` `                           ``int` `low, ``int` `high, ``int` `size)` `    ``{`   `        ``// Base case` `        ``if` `(preIndex.index >= size || low > high) ` `        ``{` `            ``return` `null``;` `        ``}`   `        ``// The first node in preorder traversal is root. So` `        ``// take the node at preIndex from pre[] and make it` `        ``// root, and increment preIndex` `        ``Node root = ``new` `Node(pre[preIndex.index]);` `        ``preIndex.index = preIndex.index + ``1``;`   `        ``// If the current subarry has only one element, no` `        ``// need to recur` `        ``if` `(low == high) ` `        ``{` `            ``return` `root;` `        ``}`   `        ``// Search for the first element greater than root` `        ``int` `i;` `        ``for` `(i = low; i <= high; ++i) ` `        ``{` `            ``if` `(pre[i] > root.data) ` `            ``{` `                ``break``;` `            ``}` `        ``}`   `        ``// Use the index of element found in preorder to` `        ``// divide preorder array in two parts. Left subtree` `        ``// and right subtree` `        ``root.left = constructTreeUtil(` `            ``pre, preIndex, preIndex.index, i - ``1``, size);` `        ``root.right = constructTreeUtil(pre, preIndex, i,` `                                       ``high, size);`   `        ``return` `root;` `    ``}`   `    ``// The main function to construct BST from given` `    ``// preorder traversal. This function mainly uses` `    ``// constructTreeUtil()` `    ``Node constructTree(``int` `pre[], ``int` `size)` `    ``{` `        ``return` `constructTreeUtil(pre, index, ``0``, size - ``1``,` `                                 ``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 code` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``BinaryTree tree = ``new` `BinaryTree();` `        ``int` `pre[] = ``new` `int``[] { ``10``, ``5``, ``1``, ``7``, ``40``, ``50` `};` `        ``int` `size = pre.length;` `        ``Node root = tree.constructTree(pre, size);` `        ``System.out.println(` `            ``"Inorder traversal of the constructed tree is "``);` `        ``tree.printInorder(root);` `    ``}` `}`   `// This code has been contributed by Mayank Jaiswal`

 `# A O(n^2) Python3 program for construction of BST from preorder traversal`   `# A binary tree node`     `class` `Node():`   `    ``# A constructor to create a new node` `    ``def` `__init__(``self``, data):` `        ``self``.data ``=` `data` `        ``self``.left ``=` `None` `        ``self``.right ``=` `None`     `# constructTreeUtil.preIndex is a static variable of` `# function constructTreeUtil`   `# Function to get the value of static variable` `# constructTreeUtil.preIndex` `def` `getPreIndex():` `    ``return` `constructTreeUtil.preIndex`   `# Function to increment the value of static variable` `# constructTreeUtil.preIndex`     `def` `incrementPreIndex():` `    ``constructTreeUtil.preIndex ``+``=` `1`   `# A recurseive function to construct Full from pre[].` `# preIndex is used to keep track of index in pre[[].`     `def` `constructTreeUtil(pre, low, high, size):`   `    ``# Base Case` `    ``if``(getPreIndex() >``=` `size ``or` `low > high):` `        ``return` `None`   `    ``# The first node in preorder traversal is root. So take` `    ``# the node at preIndex from pre[] and make it root,` `    ``# and increment preIndex` `    ``root ``=` `Node(pre[getPreIndex()])` `    ``incrementPreIndex()`   `    ``# If the current subarray has onlye one element,` `    ``# no need to recur` `    ``if` `low ``=``=` `high:` `        ``return` `root`   `    ``# Search for the first element greater than root` `    ``for` `i ``in` `range``(low, high``+``1``):` `        ``if` `(pre[i] > root.data):` `            ``break`   `    ``# Use the index of element found in preorder to divide` `    ``# preorder array in two parts. Left subtree and right` `    ``# subtree` `    ``root.left ``=` `constructTreeUtil(pre, getPreIndex(),  i``-``1``, size)`   `    ``root.right ``=` `constructTreeUtil(pre, i, high, size)`   `    ``return` `root`   `# The main function to construct BST from given preorder` `# traversal. This function mailny uses constructTreeUtil()`     `def` `constructTree(pre):` `    ``size ``=` `len``(pre)` `    ``constructTreeUtil.preIndex ``=` `0` `    ``return` `constructTreeUtil(pre, ``0``, size``-``1``, size)`     `def` `printInorder(root):` `    ``if` `root ``is` `None``:` `        ``return` `    ``printInorder(root.left)` `    ``print` `root.data,` `    ``printInorder(root.right)`     `# Driver code` `pre ``=` `[``10``, ``5``, ``1``, ``7``, ``40``, ``50``]`   `root ``=` `constructTree(pre)` `print` `"Inorder traversal of the constructed tree:"` `printInorder(root)`   `# This code is contributed by Nikhil Kumar Singh(nickzuck_007)`

 `using` `System;`   `// C# program to construct BST from given preorder traversal`   `// A binary tree node` `public` `class` `Node ` `{`   `    ``public` `int` `data;` `    ``public` `Node left, right;`   `    ``public` `Node(``int` `d)` `    ``{` `        ``data = d;` `        ``left = right = ``null``;` `    ``}` `}`   `public` `class` `Index ` `{`   `    ``public` `int` `index = 0;` `}`   `public` `class` `BinaryTree ` `{`   `    ``public` `Index index = ``new` `Index();`   `    ``// A recursive function to construct Full from pre[].` `    ``// preIndex is used to keep track of index in pre[].` `    ``public` `virtual` `Node constructTreeUtil(``int``[] pre,` `                                          ``Index preIndex,` `                                          ``int` `low, ``int` `high,` `                                          ``int` `size)` `    ``{`   `        ``// Base case` `        ``if` `(preIndex.index >= size || low > high) ` `        ``{` `            ``return` `null``;` `        ``}`   `        ``// The first node in preorder traversal is root. So` `        ``// take the node at preIndex from pre[] and make it` `        ``// root, and increment preIndex` `        ``Node root = ``new` `Node(pre[preIndex.index]);` `        ``preIndex.index = preIndex.index + 1;`   `        ``// If the current subarry has only one element, no` `        ``// need to recur` `        ``if` `(low == high) ` `        ``{` `            ``return` `root;` `        ``}`   `        ``// Search for the first element greater than root` `        ``int` `i;` `        ``for` `(i = low; i <= high; ++i) ` `        ``{` `            ``if` `(pre[i] > root.data) ` `            ``{` `                ``break``;` `            ``}` `        ``}`   `        ``// Use the index of element found in preorder to` `        ``// divide preorder array in two parts. Left subtree` `        ``// and right subtree` `        ``root.left = constructTreeUtil(` `            ``pre, preIndex, preIndex.index, i - 1, size);` `        ``root.right = constructTreeUtil(pre, preIndex, i,` `                                       ``high, size);`   `        ``return` `root;` `    ``}`   `    ``// The main function to construct BST from given` `    ``// preorder traversal. This function mainly uses` `    ``// constructTreeUtil()` `    ``public` `virtual` `Node constructTree(``int``[] pre, ``int` `size)` `    ``{` `        ``return` `constructTreeUtil(pre, index, 0, size - 1,` `                                 ``size);` `    ``}`   `    ``// A utility function to print inorder traversal of a` `    ``// Binary Tree` `    ``public` `virtual` `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``[] pre = ``new` `int``[] { 10, 5, 1, 7, 40, 50 };` `        ``int` `size = pre.Length;` `        ``Node root = tree.constructTree(pre, size);` `        ``Console.WriteLine(` `            ``"Inorder traversal of the constructed tree is "``);` `        ``tree.printInorder(root);` `    ``}` `}`   `// This code is contributed by Shrikant13`

Output
```Inorder traversal of the constructed tree:
1 5 7 10 40 50 ```

Time Complexity: O(n2)

Method 2 ( O(n) time complexity )
The idea used here is inspired from method 3 of this post. The trick is to set a range {min .. max} for every node. Initialize the range as {INT_MIN .. INT_MAX}. The first 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 part of left subtree. To construct the right subtree, set the range as {root->data..max .. INT_MAX}.

Below is the implementation of the above idea:

 `/* A O(n) program for construction` `of BST from preorder traversal */` `#include ` `using` `namespace` `std;`   `/* A binary tree node has data, pointer to left child` `and a pointer to right child */` `class` `node ` `{` `public``:` `    ``int` `data;` `    ``node* left;` `    ``node* right;` `};`   `// A utility function to create a node` `node* newNode(``int` `data)` `{` `    ``node* temp = ``new` `node();`   `    ``temp->data = data;` `    ``temp->left = temp->right = NULL;`   `    ``return` `temp;` `}`   `// A recursive function to construct` `// BST from pre[]. preIndex is used` `// to keep track of index in pre[].` `node* constructTreeUtil(``int` `pre[], ``int``* preIndex, ``int` `key,` `                        ``int` `min, ``int` `max, ``int` `size)` `{` `    ``// Base case` `    ``if` `(*preIndex >= size)` `        ``return` `NULL;`   `    ``node* root = NULL;`   `    ``// If current element of pre[] is in range, then` `    ``// only it is part of current subtree` `    ``if` `(key > min && key < max) ` `    ``{` `        ``// Allocate memory for root of this` `        ``// subtree and increment *preIndex` `        ``root = newNode(key);` `        ``*preIndex = *preIndex + 1;`   `        ``if` `(*preIndex < 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(pre, preIndex,` `                                           ``pre[*preIndex],` `                                           ``min, key, size);` `        ``}` `        ``if` `(*preIndex < size) ` `        ``{` `            ``// 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(pre, preIndex,` `                                            ``pre[*preIndex],` `                                            ``key, max, size);` `        ``}` `    ``}`   `    ``return` `root;` `}`   `// The main function to construct BST` `// from given preorder traversal.` `// This function mainly uses constructTreeUtil()` `node* constructTree(``int` `pre[], ``int` `size)` `{` `    ``int` `preIndex = 0;` `    ``return` `constructTreeUtil(pre, &preIndex, pre[0],` `                             ``INT_MIN, INT_MAX, size);` `}`   `// A utility function to print inorder` `// traversal of a Binary Tree` `void` `printInorder(node* node)` `{` `    ``if` `(node == NULL)` `        ``return``;` `    ``printInorder(node->left);` `    ``cout << node->data << ``" "``;` `    ``printInorder(node->right);` `}`   `// Driver code` `int` `main()` `{` `    ``int` `pre[] = { 10, 5, 1, 7, 40, 50 };` `    ``int` `size = ``sizeof``(pre) / ``sizeof``(pre[0]);`   `    ``// Function call` `    ``node* root = constructTree(pre, size);`   `    ``cout << ``"Inorder traversal of the constructed tree: \n"``;` `    ``printInorder(root);`   `    ``return` `0;` `}`   `// This is code is contributed by rathbhupendra`

 `/* A O(n) program for construction of BST from preorder` ` ``* traversal */` `#include ` `#include ` `#include `   `/* A binary tree node has data, pointer to left child` `   ``and a pointer to right child */` `struct` `node ` `{` `    ``int` `data;` `    ``struct` `node* left;` `    ``struct` `node* 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 pre[].` `// preIndex is used to keep track of index in pre[].` `struct` `node* constructTreeUtil(``int` `pre[], ``int``* preIndex,` `                               ``int` `key, ``int` `min, ``int` `max,` `                               ``int` `size)` `{` `    ``// Base case` `    ``if` `(*preIndex >= size)` `        ``return` `NULL;`   `    ``struct` `node* root = NULL;`   `    ``// If current element of pre[] is in range, then` `    ``// only it is part of current subtree` `    ``if` `(key > min && key < max) ` `    ``{` `        ``// Allocate memory for root of this subtree and` `        ``// increment *preIndex` `        ``root = newNode(key);` `        ``*preIndex = *preIndex + 1;`   `        ``if` `(*preIndex < 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(pre, preIndex,` `                                           ``pre[*preIndex],` `                                           ``min, key, size);` `        ``}` `        ``if` `(*preIndex < size) ` `        ``{` `            ``// 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(pre, preIndex,` `                                            ``pre[*preIndex],` `                                            ``key, max, size);` `        ``}` `    ``}`   `    ``return` `root;` `}`   `// The main function to construct BST from given preorder` `// traversal. This function mainly uses constructTreeUtil()` `struct` `node* constructTree(``int` `pre[], ``int` `size)` `{` `    ``int` `preIndex = 0;` `    ``return` `constructTreeUtil(pre, &preIndex, pre[0],` `                             ``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 code` `int` `main()` `{` `    ``int` `pre[] = { 10, 5, 1, 7, 40, 50 };` `    ``int` `size = ``sizeof``(pre) / ``sizeof``(pre[0]);`   `    ``// function call` `    ``struct` `node* root = constructTree(pre, size);`   `    ``printf``(``"Inorder traversal of the constructed tree: \n"``);` `    ``printInorder(root);`   `    ``return` `0;` `}`

 `// Java program to construct BST from given preorder` `// traversal`   `// A binary tree node` `class` `Node ` `{`   `    ``int` `data;` `    ``Node left, right;`   `    ``Node(``int` `d)` `    ``{` `        ``data = d;` `        ``left = right = ``null``;` `    ``}` `}`   `class` `Index ` `{`   `    ``int` `index = ``0``;` `}`   `class` `BinaryTree ` `{`   `    ``Index index = ``new` `Index();`   `    ``// A recursive function to construct BST from pre[].` `    ``// preIndex is used to keep track of index in pre[].` `    ``Node constructTreeUtil(``int` `pre[], Index preIndex,` `                           ``int` `key, ``int` `min, ``int` `max,` `                           ``int` `size)` `    ``{`   `        ``// Base case` `        ``if` `(preIndex.index >= size) ` `        ``{` `            ``return` `null``;` `        ``}`   `        ``Node root = ``null``;`   `        ``// If current element of pre[] is in range, then` `        ``// only it is part of current subtree` `        ``if` `(key > min && key < max) ` `        ``{`   `            ``// Allocate memory for root of this` `            ``// subtree and increment *preIndex` `            ``root = ``new` `Node(key);` `            ``preIndex.index = preIndex.index + ``1``;`   `            ``if` `(preIndex.index < 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(` `                    ``pre, preIndex, pre[preIndex.index], min,` `                    ``key, size);` `            ``}` `            ``if` `(preIndex.index < size) ` `            ``{` `                ``// 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(` `                    ``pre, preIndex, pre[preIndex.index], key,` `                    ``max, size);` `            ``}` `        ``}`   `        ``return` `root;` `    ``}`   `    ``// The main function to construct BST from given` `    ``// preorder traversal. This function mainly uses` `    ``// constructTreeUtil()` `    ``Node constructTree(``int` `pre[], ``int` `size)` `    ``{` `        ``int` `preIndex = ``0``;` `        ``return` `constructTreeUtil(pre, index, pre[``0``],` `                                 ``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 code` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``BinaryTree tree = ``new` `BinaryTree();` `        ``int` `pre[] = ``new` `int``[] { ``10``, ``5``, ``1``, ``7``, ``40``, ``50` `};` `        ``int` `size = pre.length;` `      `  `        ``// Function call` `        ``Node root = tree.constructTree(pre, size);` `        ``System.out.println(` `            ``"Inorder traversal of the constructed tree is "``);` `        ``tree.printInorder(root);` `    ``}` `}`   `// This code has been contributed by Mayank Jaiswal`

 `# A O(n) program for construction of BST from preorder traversal`   `INT_MIN ``=` `float``(``"-infinity"``)` `INT_MAX ``=` `float``(``"infinity"``)`   `# A Binary tree node`     `class` `Node:`   `    ``# Constructor to created a new node` `    ``def` `__init__(``self``, data):` `        ``self``.data ``=` `data` `        ``self``.left ``=` `None` `        ``self``.right ``=` `None`   `# Methods to get and set the value of static variable` `# constructTreeUtil.preIndex for function construcTreeUtil()`     `def` `getPreIndex():` `    ``return` `constructTreeUtil.preIndex`     `def` `incrementPreIndex():` `    ``constructTreeUtil.preIndex ``+``=` `1`   `# A recursive function to construct BST from pre[].` `# preIndex is used to keep track of index in pre[]`     `def` `constructTreeUtil(pre, key, mini, maxi, size):`   `    ``# Base Case` `    ``if``(getPreIndex() >``=` `size):` `        ``return` `None`   `    ``root ``=` `None`   `    ``# If current element of pre[] is in range, then` `    ``# only it is part of current subtree` `    ``if``(key > mini ``and` `key < maxi):`   `        ``# Allocate memory for root of this subtree` `        ``# and increment constructTreeUtil.preIndex` `        ``root ``=` `Node(key)` `        ``incrementPreIndex()`   `        ``if``(getPreIndex() < 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(pre,` `                                          ``pre[getPreIndex()], ` `                                          ``mini, key, size)` `        ``if``(getPreindex() < size):`   `            ``# All nodes which are in range{key..max} will` `            ``# go to right subtree, and first such node will` `            ``# be root of right subtree` `            ``root.right ``=` `constructTreeUtil(pre,` `                                           ``pre[getPreIndex()], ` `                                           ``key, maxi, size)`   `    ``return` `root`   `# This is the main function to construct BST from given` `# preorder traversal. This function mainly uses` `# constructTreeUtil()`     `def` `constructTree(pre):` `    ``constructTreeUtil.preIndex ``=` `0` `    ``size ``=` `len``(pre)` `    ``return` `constructTreeUtil(pre, pre[``0``], INT_MIN, INT_MAX, size)`     `# A utility function to print inorder traversal of Binary Tree` `def` `printInorder(node):`   `    ``if` `node ``is` `None``:` `        ``return` `    ``printInorder(node.left)` `    ``print` `node.data,` `    ``printInorder(node.right)`     `# Driver code` `pre ``=` `[``10``, ``5``, ``1``, ``7``, ``40``, ``50``]`   `# Function call` `root ``=` `constructTree(pre)`   `print` `"Inorder traversal of the constructed tree: "` `printInorder(root)`   `# This code is contributed by Nikhil Kumar Singh(nickzuck_007)`

 `// C# program to construct BST from given preorder traversal` `using` `System;`   `// A binary tree node` `public` `class` `Node ` `{`   `    ``public` `int` `data;` `    ``public` `Node left, right;`   `    ``public` `Node(``int` `d)` `    ``{` `        ``data = d;` `        ``left = right = ``null``;` `    ``}` `}`   `public` `class` `Index ` `{` `    ``public` `int` `index = 0;` `}`   `public` `class` `BinaryTree ` `{`   `    ``public` `Index index = ``new` `Index();`   `    ``// A recursive function to construct BST from pre[].` `    ``// preIndex is used to keep track of index in pre[].` `    ``public` `virtual` `Node constructTreeUtil(``int``[] pre,` `                                          ``Index preIndex,` `                                          ``int` `key, ``int` `min,` `                                          ``int` `max, ``int` `size)` `    ``{`   `        ``// Base case` `        ``if` `(preIndex.index >= size) ` `        ``{` `            ``return` `null``;` `        ``}`   `        ``Node root = ``null``;`   `        ``// If current element of pre[] is in range, then` `        ``// only it is part of current subtree` `        ``if` `(key > min && key < max) ` `        ``{`   `            ``// Allocate memory for root of this subtree` `            ``// and increment *preIndex` `            ``root = ``new` `Node(key);` `            ``preIndex.index = preIndex.index + 1;`   `            ``if` `(preIndex.index < 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(` `                    ``pre, preIndex, pre[preIndex.index], min,` `                    ``key, size);` `            ``}` `            ``if` `(preIndex.index < size)` `            ``{` `                ``// 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(` `                    ``pre, preIndex, pre[preIndex.index], key,` `                    ``max, size);` `            ``}` `        ``}`   `        ``return` `root;` `    ``}`   `    ``// The main function to construct BST from given` `    ``// preorder traversal. This function mainly uses` `    ``// constructTreeUtil()` `    ``public` `virtual` `Node constructTree(``int``[] pre, ``int` `size)` `    ``{`   `        ``return` `constructTreeUtil(pre, index, pre[0],` `                                 ``int``.MinValue, ``int``.MaxValue,` `                                 ``size);` `    ``}`   `    ``// A utility function to print inorder traversal of a` `    ``// Binary Tree` `    ``public` `virtual` `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``[] pre = ``new` `int``[] { 10, 5, 1, 7, 40, 50 };` `        ``int` `size = pre.Length;` `      `  `        ``// Function call` `        ``Node root = tree.constructTree(pre, size);` `        ``Console.WriteLine(` `            ``"Inorder traversal of the constructed tree is "``);` `        ``tree.printInorder(root);` `    ``}` `}`   `// This code is contributed by Shrikant13`

Output
```Inorder traversal of the constructed tree:
1 5 7 10 40 50 ```

Time Complexity: O(n)

We will soon publish a O(n) iterative solution as a separate post.