# Construct a complete binary tree from given array in level order fashion

Given an array of elements, our task is to construct a complete binary tree from this array in a level order fashion. That is, elements from the left in the array will be filled in the tree level-wise starting from level 0.
Examples:

`Input  :  arr[] = {1, 2, 3, 4, 5, 6}Output : Root of the following tree                  1                 / \                2   3               / \ /              4  5 6Input: arr[] = {1, 2, 3, 4, 5, 6, 6, 6, 6, 6}Output: Root of the following tree                   1                  / \                 2   3                / \ / \               4  5 6  6              / \ /             6  6 6`

If we observe carefully we can see that if the parent node is at index i in the array then the left child of that node is at index (2*i + 1) and the right child is at index (2*i + 2) in the array.
Using this concept, we can easily insert the left and right nodes by choosing their parent node. We will insert the first element present in the array as the root node at level 0 in the tree and start traversing the array and for every node, we will insert both children left and right in the tree.
Below is the recursive program to do this:

## C++

 `// CPP program to construct binary ` `// tree from given array in level` `// order fashion Tree Node` `#include ` `using` `namespace` `std;`   `/* A binary tree node has data, ` `pointer to left child and a` `pointer to right child */` `struct` `Node` `{` `    ``int` `data;` `    ``Node* left, * right;` `};`   `/* Helper function that allocates a` `new node */` `Node* newNode(``int` `data)` `{` `    ``Node* node = (Node*)``malloc``(``sizeof``(Node));` `    ``node->data = data;` `    ``node->left = node->right = NULL;` `    ``return` `(node);` `}`   `// Function to insert nodes in level order` `Node* insertLevelOrder(``int` `arr[],` `                       ``int` `i, ``int` `n)` `{` `      ``Node *root = nullptr;` `    ``// Base case for recursion` `    ``if` `(i < n)` `    ``{` `        ``root = newNode(arr[i]);` `        `  `        ``// insert left child` `        ``root->left = insertLevelOrder(arr,` `                   ``2 * i + 1, n);`   `        ``// insert right child` `        ``root->right = insertLevelOrder(arr,` `                  ``2 * i + 2, n);` `    ``}` `    ``return` `root;` `}`   `// Function to print tree nodes in` `// InOrder fashion` `void` `inOrder(Node* root)` `{` `    ``if` `(root != NULL)` `    ``{` `        ``inOrder(root->left);` `        ``cout << root->data <<``" "``;` `        ``inOrder(root->right);` `    ``}` `}`   `// Driver program to test above function` `int` `main()` `{` `    ``int` `arr[] = { 1, 2, 3, 4, 5, 6, 6, 6, 6 };` `    ``int` `n = ``sizeof``(arr)/``sizeof``(arr[0]);` `    ``Node* root = insertLevelOrder(arr, 0, n);` `    ``inOrder(root);` `}`   `// This code is contributed by Chhavi and improved by Thangaraj`

## Java

 `// Java program to construct binary tree from` `// given array in level order fashion`   `public` `class` `Tree {` `    ``Node root;`   `    ``// Tree Node` `    ``static` `class` `Node {` `        ``int` `data;` `        ``Node left, right;` `        ``Node(``int` `data)` `        ``{` `            ``this``.data = data;` `            ``this``.left = ``null``;` `            ``this``.right = ``null``;` `        ``}` `    ``}`   `    ``// Function to insert nodes in level order` `    ``public` `Node insertLevelOrder(``int``[] arr, ``int` `i)` `    ``{` `          ``Node root = ``null``;` `        ``// Base case for recursion` `        ``if` `(i < arr.length) {` `            ``root = ``new` `Node(arr[i]);`   `            ``// insert left child` `            ``root.left = insertLevelOrder(arr, ``2` `* i + ``1``);`   `            ``// insert right child` `            ``root.right = insertLevelOrder(arr, ``2` `* i + ``2``);` `        ``}` `        ``return` `root;` `    ``}`   `    ``// Function to print tree nodes in InOrder fashion` `    ``public` `void` `inOrder(Node root)` `    ``{` `        ``if` `(root != ``null``) {` `            ``inOrder(root.left);` `            ``System.out.print(root.data + ``" "``);` `            ``inOrder(root.right);` `        ``}` `    ``}`   `    ``// Driver program to test above function` `    ``public` `static` `void` `main(String args[])` `    ``{` `        ``Tree t2 = ``new` `Tree();` `        ``int` `arr[] = { ``1``, ``2``, ``3``, ``4``, ``5``, ``6``, ``6``, ``6``, ``6` `};` `        ``t2.root = t2.insertLevelOrder(arr, ``0``);` `        ``t2.inOrder(t2.root);` `    ``}` `}`

## Python3

 `# Python3 program to construct binary ` `# tree from given array in level ` `# order fashion Tree Node `   `# Helper function that allocates a ` `#new node` `class` `newNode:` `    ``def` `__init__(``self``, data):` `        ``self``.data ``=` `data ` `        ``self``.left ``=` `self``.right ``=` `None`   `# Function to insert nodes in level order ` `def` `insertLevelOrder(arr, i, n):` `    ``root ``=` `None` `    ``# Base case for recursion ` `    ``if` `i < n:` `        ``root ``=` `newNode(arr[i]) `   `        ``# insert left child ` `        ``root.left ``=` `insertLevelOrder(arr, ``2` `*` `i ``+` `1``, n)`   `        ``# insert right child ` `        ``root.right ``=` `insertLevelOrder(arr, ``2` `*` `i ``+` `2``, n)` `        `  `    ``return` `root`   `# Function to print tree nodes in ` `# InOrder fashion ` `def` `inOrder(root):` `    ``if` `root !``=` `None``:` `        ``inOrder(root.left) ` `        ``print``(root.data,end``=``" "``) ` `        ``inOrder(root.right)`   `# Driver Code` `if` `__name__ ``=``=` `'__main__'``:` `    ``arr ``=` `[``1``, ``2``, ``3``, ``4``, ``5``, ``6``, ``6``, ``6``, ``6``]` `    ``n ``=` `len``(arr)` `    ``root ``=` `None` `    ``root ``=` `insertLevelOrder(arr, ``0``, n) ` `    ``inOrder(root)` `    `  `# This code is contributed by PranchalK and Improved by Thangaraj`

## C#

 `// C# program to construct binary tree from` `// given array in level order fashion` `using` `System;` `    `  `public` `class` `Tree` `{` `    ``Node root;`   `    ``// Tree Node` `    ``public` `class` `Node ` `    ``{` `        ``public` `int` `data;` `        ``public` `Node left, right;` `        ``public` `Node(``int` `data)` `        ``{` `            ``this``.data = data;` `            ``this``.left = ``null``;` `            ``this``.right = ``null``;` `        ``}` `    ``}`   `    ``// Function to insert nodes in level order` `    ``public` `Node insertLevelOrder(``int``[] arr, ``int` `i)` `    ``{` `          ``Node root = ``null``;` `        ``// Base case for recursion` `        ``if` `(i < arr.Length) ` `        ``{` `            ``root = ``new` `Node(arr[i]);`   `            ``// insert left child` `            ``root.left = insertLevelOrder(arr, 2 * i + 1);`   `            ``// insert right child` `            ``root.right = insertLevelOrder(arr, 2 * i + 2);` `        ``}` `        ``return` `root;` `    ``}`   `    ``// Function to print tree` `    ``// nodes in InOrder fashion` `    ``public` `void` `inOrder(Node root)` `    ``{` `        ``if` `(root != ``null``) ` `        ``{` `            ``inOrder(root.left);` `            ``Console.Write(root.data + ``" "``);` `            ``inOrder(root.right);` `        ``}` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `Main(String []args)` `    ``{` `        ``Tree t2 = ``new` `Tree();` `        ``int` `[]arr = { 1, 2, 3, 4, 5, 6, 6, 6, 6 };` `        ``t2.root = t2.insertLevelOrder(arr, 0);` `        ``t2.inOrder(t2.root);` `    ``}` `}`   `// This code is contributed Rajput-Ji and improved by Thangaraj`

## Javascript

 ``

Output

```6 4 6 2 5 1 6 3 6

```

Time Complexity: O(n), where n is the total number of nodes in the tree.

Space Complexity: O(n) for calling recursion using stack.

Approach 2: Using queue

Create a TreeNode struct to represent a node in the binary tree.
Define a function buildTree that takes the nums array as a parameter.
If the nums array is empty, return NULL.
Create the root node with the value at index 0 and push it into a queue.
Initialize an integer i to 1.
Loop while the queue is not empty:
Pop the front node from the queue and assign it to curr.
If i is less than the size of the nums array, create a new node with the value at index i and set it as the left child of curr. Increment i by 1. Push the left child node into the queue.
If i is less than the size of the nums array, create a new node with the value at index i and set it as the right child of curr. Increment i by 1. Push the right child node into the queue.
Return the root node.
Define a printTree function to print the values of the tree in preorder traversal order.
Call the buildTree function with the given nums array to construct the complete binary tree.
Call the printTree function to print the values of the tree.

Time complexity: The buildTree function has to visit every element in the nums array once, so the time complexity is O(n), where n is the size of the nums array.

## C++

 `#include ` `using` `namespace` `std;`   `struct` `TreeNode {` `    ``int` `val;` `    ``TreeNode *left, *right;` `    ``TreeNode(``int` `x) : val(x), left(NULL), right(NULL) {}` `};`   `TreeNode* buildTree(vector<``int``>& nums) {` `    ``if` `(nums.empty()) {` `        ``return` `NULL;` `    ``}` `    ``TreeNode* root = ``new` `TreeNode(nums[0]);` `    ``queue q;` `    ``q.push(root);` `    ``int` `i = 1;` `    ``while` `(i < nums.size()) {` `        ``TreeNode* curr = q.front();` `        ``q.pop();` `        ``if` `(i < nums.size()) {` `            ``curr->left = ``new` `TreeNode(nums[i++]);` `            ``q.push(curr->left);` `        ``}` `        ``if` `(i < nums.size()) {` `            ``curr->right = ``new` `TreeNode(nums[i++]);` `            ``q.push(curr->right);` `        ``}` `    ``}` `    ``return` `root;` `}`   `void` `printTree(TreeNode* root) {` `    ``if` `(!root) {` `        ``return``;` `    ``}` `      ``printTree(root->left);` `    ``cout << root->val << ``" "``;` `  `  `    ``printTree(root->right);` `}`   `int` `main() {` `    ``vector<``int``> nums = { 1, 2, 3, 4, 5, 6, 6, 6, 6 };` `    ``TreeNode* root = buildTree(nums);` `    ``printTree(root);` `    ``return` `0;` `}`

## Java

 `import` `java.util.*;`   `class` `TreeNode {` `    ``int` `val;` `    ``TreeNode left, right;` `    `  `    ``TreeNode(``int` `x) {` `        ``val = x;` `        ``left = ``null``;` `        ``right = ``null``;` `    ``}` `}`   `class` `Main {` `    ``public` `static` `TreeNode buildTree(``int``[] nums) {` `        ``if` `(nums == ``null` `|| nums.length == ``0``) {` `            ``return` `null``;` `        ``}` `        ``TreeNode root = ``new` `TreeNode(nums[``0``]);` `        ``Queue q = ``new` `LinkedList<>();` `        ``q.add(root);` `        ``int` `i = ``1``;` `        ``while` `(i < nums.length) {` `            ``TreeNode curr = q.remove();` `            ``if` `(i < nums.length) {` `                ``curr.left = ``new` `TreeNode(nums[i++]);` `                ``q.add(curr.left);` `            ``}` `            ``if` `(i < nums.length) {` `                ``curr.right = ``new` `TreeNode(nums[i++]);` `                ``q.add(curr.right);` `            ``}` `        ``}` `        ``return` `root;` `    ``}`   `    ``public` `static` `void` `printTree(TreeNode root) {` `        ``if` `(root == ``null``) {` `            ``return``;` `        ``}` `        ``printTree(root.left);` `        ``System.out.print(root.val + ``" "``);` `        ``printTree(root.right);` `    ``}`   `    ``public` `static` `void` `main(String[] args) {` `        ``int``[] nums = { ``1``, ``2``, ``3``, ``4``, ``5``, ``6``, ``6``, ``6``, ``6` `};` `        ``TreeNode root = buildTree(nums);` `        ``printTree(root);` `    ``}` `}`

## Python3

 `class` `TreeNode:` `    ``def` `__init__(``self``, x):` `        ``self``.val ``=` `x` `        ``self``.left ``=` `None` `        ``self``.right ``=` `None`   `def` `buildTree(nums):` `    ``if` `not` `nums:` `        ``return` `None` `    ``root ``=` `TreeNode(nums[``0``])` `    ``q ``=` `[root]` `    ``i ``=` `1` `    ``while` `i < ``len``(nums):` `        ``curr ``=` `q.pop(``0``)` `        ``if` `i < ``len``(nums):` `            ``curr.left ``=` `TreeNode(nums[i])` `            ``q.append(curr.left)` `            ``i ``+``=` `1` `        ``if` `i < ``len``(nums):` `            ``curr.right ``=` `TreeNode(nums[i])` `            ``q.append(curr.right)` `            ``i ``+``=` `1` `    ``return` `root`   `def` `printTree(root):` `    ``if` `not` `root:` `        ``return` `    ``printTree(root.left)` `    ``print``(root.val, end``=``" "``)` `    ``printTree(root.right)`   `nums ``=` `[``1``, ``2``, ``3``, ``4``, ``5``, ``6``, ``6``, ``6``, ``6``]` `root ``=` `buildTree(nums)` `printTree(root)`

## C#

 `using` `System;` `using` `System.Collections.Generic;`   `// creating a tree node` `public` `class` `TreeNode` `{` `    ``public` `int` `val;` `    ``public` `TreeNode left, right;`   `    ``public` `TreeNode(``int` `x)` `    ``{` `        ``val = x;` `        ``left = ``null``;` `        ``right = ``null``;` `    ``}` `}`   `public` `class` `MainClass` `{` `    ``public` `static` `TreeNode BuildTree(``int``[] nums)` `    ``{` `        ``if` `(nums == ``null` `|| nums.Length == 0)` `        ``{` `            ``return` `null``;` `        ``}` `      `  `        ``TreeNode root = ``new` `TreeNode(nums[0]);` `      `  `      ``// taking a queue` `        ``Queue q = ``new` `Queue();` `        ``q.Enqueue(root);` `        ``int` `i = 1;` `        ``while` `(i < nums.Length)` `        ``{` `            ``TreeNode curr = q.Dequeue();` `            ``if` `(i < nums.Length)` `            ``{` `              ``// traversing left` `                ``curr.left = ``new` `TreeNode(nums[i++]);` `                ``q.Enqueue(curr.left);` `            ``}` `            ``if` `(i < nums.Length)` `            ``{` `              ``// traversing right` `                ``curr.right = ``new` `TreeNode(nums[i++]);` `                ``q.Enqueue(curr.right);` `            ``}` `        ``}` `        ``return` `root;` `    ``}`   `    ``public` `static` `void` `PrintTree(TreeNode root)` `    ``{` `        ``if` `(root == ``null``)` `        ``{` `            ``return``;` `        ``}` `        ``PrintTree(root.left);` `        ``Console.Write(root.val + ``" "``);` `        ``PrintTree(root.right);` `    ``}`   `  ``// Driver code` `    ``public` `static` `void` `Main(``string``[] args)` `    ``{` `        ``int``[] nums = { 1, 2, 3, 4, 5, 6, 6, 6, 6 };` `        ``TreeNode root = BuildTree(nums);` `        ``PrintTree(root);` `    ``}` `}`

## Javascript

 `class TreeNode {` `    ``constructor(val) {` `        ``this``.val = val;` `        ``this``.left = ``null``;` `        ``this``.right = ``null``;` `    ``}` `}`   `function` `buildTree(nums) {` `    ``if` `(nums.length === 0) {` `        ``return` `null``;` `    ``}` `    ``let root = ``new` `TreeNode(nums[0]);` `    ``let q = [root];` `    ``let i = 1;` `    ``while` `(i < nums.length) {` `        ``let curr = q.shift();` `        ``if` `(i < nums.length) {` `            ``curr.left = ``new` `TreeNode(nums[i++]);` `            ``q.push(curr.left);` `        ``}` `        ``if` `(i < nums.length) {` `            ``curr.right = ``new` `TreeNode(nums[i++]);` `            ``q.push(curr.right);` `        ``}` `    ``}` `    ``return` `root;` `}`   `function` `printTree(root) {` `    ``if` `(!root) {` `        ``return``;` `    ``}` `    ``printTree(root.left);` `    ``console.log(root.val + ``" "``);` `    ``printTree(root.right);` `}`   `let nums = [1, 2, 3, 4, 5, 6, 6, 6, 6];` `let root = buildTree(nums);` `printTree(root);`

Output

```6 4 6 2 5 1 6 3 6

```

Time Complexity: O(n), where n is the total number of nodes in the tree.

Auxiliary Space: O(n)

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