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# Construct BST from given preorder traversal | Set 1

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

Examples:

Input: {10, 5, 1, 7, 40, 50}
Output:   10
/   \
5     40
/  \       \
1    7       50

Naive approach: To solve the problem follow the below idea:

The first element of preorder traversal is always the root. We first construct the root. Then we find the index of the first element which is greater than the root. Let the index be ‘i’. The values between root and ‘i’ will be part of the left subtree, and the values between ‘i'(inclusive) and ‘n-1’ will be part of the right subtree. Divide the 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 follows.:

10
/    \
{5, 1, 7}     {40, 50}

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

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach` `#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 subarray 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]);`   `      ``// Function call` `    ``node* root = constructTree(pre, size);`   `    ``printInorder(root);`   `    ``return` `0;` `}`   `// This code is contributed by rathbhupendra`

## C

 `// C program for the above approach` `#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 subarray 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]);`   `      ``// Function call` `    ``struct` `node* root = constructTree(pre, size);`   `    `  `    ``printInorder(root);`   `    ``return` `0;` `}`

## Java

 `// 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 subarray 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);` `        `  `        ``tree.printInorder(root);` `    ``}` `}`   `// This code has been contributed by Mayank Jaiswal`

## Python3

 `# 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 recursive function to construct Full from pre[].` `# preIndex is used to keep track of index in pre[[].`     `def` `constructTreeUtil(pre, low, high):`   `        ``# Base Case` `    ``if``(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 only one element,` `    ``# no need to recur` `    ``if` `low ``=``=` `high:` `        ``return` `root`   `    ``r_root ``=` `-``1`   `    ``# Search for the first element greater than root` `    ``for` `i ``in` `range``(low, high``+``1``):` `        ``if` `(pre[i] > root.data):` `            ``r_root ``=` `i` `            ``break`   `    ``# If no elements are greater than the current root,` `    ``# all elements are left children` `    ``# so assign root appropriately` `    ``if` `r_root ``=``=` `-``1``:` `        ``r_root ``=` `getPreIndex() ``+` `(high ``-` `low)`   `    ``# 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(), r_root``-``1``)`   `    ``root.right ``=` `constructTreeUtil(pre, r_root, high)`   `    ``return` `root`   `# The main function to construct BST from given preorder` `# traversal. This function mainly uses constructTreeUtil()`     `def` `constructTree(pre):` `    ``size ``=` `len``(pre)` `    ``constructTreeUtil.preIndex ``=` `0` `    ``return` `constructTreeUtil(pre, ``0``, size``-``1``)`     `def` `printInorder(root):` `    ``if` `root ``is` `None``:` `        ``return` `    ``printInorder(root.left)` `    ``print``(root.data, end``=``' '``)` `    ``printInorder(root.right)`     `# Driver code` `if` `__name__ ``=``=` `'__main__'``:` `  ``pre ``=` `[``10``, ``5``, ``1``, ``7``, ``40``, ``50``]`   `  ``root ``=` `constructTree(pre)` `  `  `  ``printInorder(root)`   `# This code is contributed by Nikhil Kumar Singh(nickzuck_007) and Rhys Compton`

## C#

 `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 subarray 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);` `        `  `        ``tree.printInorder(root);` `    ``}` `}`   `// This code is contributed by Shrikant13`

## Javascript

 ``

Output

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

Time Complexity: O(N2)
Auxiliary Space: O(N)

Approach: To solve the problem follow the below idea:

Using the recursion concept and iterating through the array of the given elements we can generate the BST

Follow the below steps to solve the problem:

• Create a new Node for every value in the array
• Create a BST using these new Nodes and insert them according to the rules of the BST
• Print the inorder of the BST

Below is the implementation of the above approach:

## C++

 `// C++ Program for the same approach` `#include ` `using` `namespace` `std;`   `/*Construct a BST from given pre-order traversal` `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 */`   `class` `Node {` `public``:` `    ``int` `data;` `    ``Node* left;` `    ``Node* right;` `    ``Node(``int` `data)` `    ``{` `        ``this``->data = data;` `        ``this``->left = ``this``->right = NULL;` `    ``}` `};`   `static` `Node* node;`   `// This will create the BST` `Node* createNode(Node* node, ``int` `data)` `{` `    ``if` `(node == NULL)` `        ``node = ``new` `Node(data);`   `    ``if` `(node->data > data)` `        ``node->left = createNode(node->left, data);` `    ``if` `(node->data < data)` `        ``node->right = createNode(node->right, data);`   `    ``return` `node;` `}`   `// A wrapper function of createNode` `void` `create(``int` `data) { node = createNode(node, data); }` `// A function to print BST in inorder` `void` `inorderRec(Node* root)` `{` `    ``if` `(root != NULL) {` `        ``inorderRec(root->left);` `        ``cout << root->data << ``" "``;` `        ``inorderRec(root->right);` `    ``}` `}`   `// Driver code` `int` `main()` `{` `    ``vector<``int``> nodeData = { 10, 5, 1, 7, 40, 50 };`   `    ``for` `(``int` `i = 0; i < nodeData.size(); i++) {` `        ``create(nodeData[i]);` `    ``}` `    ``inorderRec(node);` `}`   `// This code is contributed by shinjanpatra`

## Java

 `/*Construct a BST from given pre-order traversal` `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 */`   `class` `Node {` `    ``int` `data;` `    ``Node left, right;` `    ``Node(``int` `data)` `    ``{` `        ``this``.data = data;` `        ``this``.left = ``this``.right = ``null``;` `    ``}` `}`   `class` `CreateBSTFromPreorder {` `    ``private` `static` `Node node;`   `    ``// This will create the BST` `    ``public` `static` `Node createNode(Node node, ``int` `data)` `    ``{` `        ``if` `(node == ``null``)` `            ``node = ``new` `Node(data);`   `        ``if` `(node.data > data)` `            ``node.left = createNode(node.left, data);` `        ``if` `(node.data < data)` `            ``node.right = createNode(node.right, data);`   `        ``return` `node;` `    ``}`   `    ``// A wrapper function of createNode` `    ``public` `static` `void` `create(``int` `data)` `    ``{` `        ``node = createNode(node, data);` `    ``}` `    ``// A function to print BST in inorder` `    ``public` `static` `void` `inorderRec(Node root)` `    ``{` `        ``if` `(root != ``null``) {` `            ``inorderRec(root.left);` `            ``System.out.print(root.data);` `              ``System.out.print(``" "``);` `            ``inorderRec(root.right);` `        ``}` `    ``}`   `    ``// Driver Code` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``int``[] nodeData = { ``10``, ``5``, ``1``, ``7``, ``40``, ``50` `};`   `        ``for` `(``int` `i = ``0``; i < nodeData.length; i++) {` `            ``create(nodeData[i]);` `        ``}` `        ``inorderRec(node);` `    ``}` `}`

## Python3

 `# Construct a BST from given pre-order traversal` `# 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`     `class` `Node:` `    ``data ``=` `0` `    ``left ``=` `None` `    ``right ``=` `None`   `    ``def` `__init__(``self``, data):` `        ``self``.data ``=` `data` `        ``self``.left ``=` `None` `        ``self``.right ``=` `None`     `class` `CreateBSTFromPreorder:` `    ``node ``=` `None` `    ``# This will create the BST`   `    ``@staticmethod` `    ``def` `createNode(node,  data):` `        ``if` `(node ``=``=` `None``):` `            ``node ``=` `Node(data)` `        ``if` `(node.data > data):` `            ``node.left ``=` `CreateBSTFromPreorder.createNode(node.left, data)` `        ``if` `(node.data < data):` `            ``node.right ``=` `CreateBSTFromPreorder.createNode(node.right, data)` `        ``return` `node`   `    ``# A wrapper function of createNode` `    ``@staticmethod` `    ``def` `create(data):` `        ``CreateBSTFromPreorder.node ``=` `CreateBSTFromPreorder.createNode(` `            ``CreateBSTFromPreorder.node, data)`   `    ``# A function to print BST in inorder` `    ``@staticmethod` `    ``def` `inorderRec(root):` `        ``if` `(root !``=` `None``):` `            ``CreateBSTFromPreorder.inorderRec(root.left)` `            ``print``(root.data)` `            ``CreateBSTFromPreorder.inorderRec(root.right)`   `    ``# Driver Code` `    ``@staticmethod` `    ``def` `main(args):` `        ``nodeData ``=` `[``10``, ``5``, ``1``, ``7``, ``40``, ``50``]` `        ``i ``=` `0` `        ``while` `(i < ``len``(nodeData)):` `            ``CreateBSTFromPreorder.create(nodeData[i])` `            ``i ``+``=` `1` `        ``CreateBSTFromPreorder.inorderRec(CreateBSTFromPreorder.node)`     `if` `__name__ ``=``=` `"__main__"``:` `    ``CreateBSTFromPreorder.main([])`   `# This code is contributed by mukulsomukesh`

## C#

 `/*Construct a BST from given pre-order traversal` `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 */` `using` `System;` `public` `class` `Node {` `    ``public` `int` `data;` `    ``public` `Node left, right;` `    ``public` `Node(``int` `data)` `    ``{` `        ``this``.data = data;` `        ``this``.left = ``this``.right = ``null``;` `    ``}` `}`   `public` `class` `CreateBSTFromPreorder {` `    ``private` `static` `Node node;`   `    ``// This will create the BST` `    ``public` `static` `Node createNode(Node node, ``int` `data)` `    ``{` `        ``if` `(node == ``null``)` `            ``node = ``new` `Node(data);`   `        ``if` `(node.data > data)` `            ``node.left = createNode(node.left, data);` `        ``if` `(node.data < data)` `            ``node.right = createNode(node.right, data);`   `        ``return` `node;` `    ``}`   `    ``// A wrapper function of createNode` `    ``public` `static` `void` `create(``int` `data)` `    ``{` `        ``node = createNode(node, data);` `    ``}`   `    ``// A function to print BST in inorder` `    ``public` `static` `void` `inorderRec(Node root)` `    ``{` `        ``if` `(root != ``null``) {` `            ``inorderRec(root.left);` `            ``Console.Write(root.data);` `              ``Console.Write(``" "``);` `            ``inorderRec(root.right);` `        ``}` `    ``}`   `    ``// Driver Code` `    ``public` `static` `void` `Main(String[] args)` `    ``{` `        ``int``[] nodeData = { 10, 5, 1, 7, 40, 50 };` `        ``for` `(``int` `i = 0; i < nodeData.Length; i++) {` `            ``create(nodeData[i]);` `        ``}` `        ``inorderRec(node);` `    ``}` `}`   `// This code is contributed by Rajput-Ji`

## Javascript

 ``

Output

```1
5
7
10
40
50```

Time Complexity: O(N * log N)
Auxiliary Space: O(N)

Efficient Approach: To solve the problem follow the below idea:

The trick is to set a range {min .. max} for every node.

Follow the below steps to solve the problem:

• Initialize the range as {INT_MIN .. INT_MAX}
• The first node will definitely be in range, so create a root node.
• To construct the left subtree, set the range as {INT_MIN …root->data}.
• If a value is in the range {INT_MIN .. root->data}, the values are part of the left subtree.
• To construct the right subtree, set the range as {root->data..max .. INT_MAX}.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach` `#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);`   `    ``printInorder(root);`   `    ``return` `0;` `}`   `// This code is contributed by rathbhupendra`

## C

 `// C program for the above approach` `#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);`   `    `  `    ``printInorder(root);`   `    ``return` `0;` `}`

## Java

 `// 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);` `        `  `        ``tree.printInorder(root);` `    ``}` `}`   `// This code has been contributed by Mayank Jaiswal`

## Python3

 `# Python3 program for the above approach`   `INT_MIN ``=` `-``float``(``"inf"``)` `INT_MAX ``=` `float``(``"inf"``)`   `# 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, end``=``" "``)` `    ``printInorder(node.right)`     `# Driver code` `pre ``=` `[``10``, ``5``, ``1``, ``7``, ``40``, ``50``]`   `# Function call` `root ``=` `constructTree(pre)`     `printInorder(root)`   `# This code is contributed by Nikhil Kumar Singh(nickzuck_007)`

## C#

 `// 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);` `        `  `        ``tree.printInorder(root);` `    ``}` `}`   `// This code is contributed by Shrikant13`

## Javascript

 ``

Output

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

Time Complexity: O(N)
Auxiliary Space: O(N)

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