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# Binary Tree (Array implementation)

Given an array that represents a tree in such a way that array indexes are values in tree nodes and array values give the parent node of that particular index (or node). The value of the root node index would always be -1 as there is no parent for root. Construct the standard linked representation of given Binary Tree from this given representation. Do refer in order to understand how to construct binary tree from given parent array representation.

Ways to represent:

Trees can be represented in two ways as listed below:

1. Dynamic Node Representation (Linked Representation).
2. Array Representation (Sequential Representation).

Now, we are going to talk about the sequential representation of the trees.  In order to represent a tree using an array, the numbering of nodes can start either from 0–(n-1) or 1– n, consider the below illustration as follows:

Illustration:

```       A(0)
/   \
B(1)  C(2)
/   \      \
D(3)  E(4)   F(6)
OR,
A(1)
/   \
B(2)  C(3)
/   \      \
D(4)  E(5)   F(7)  ```

Procedure:

Note: father, left_son and right_son are the values of indices of the array.

Case 1: (0—n-1)

```if (say)father=p;
then left_son=(2*p)+1;
and right_son=(2*p)+2;```

Case 2: 1—n

```if (say)father=p;
then left_son=(2*p);
and right_son=(2*p)+1; ```

Implementation:

## C++

 `// C++ implementation of tree using array` `// numbering starting from 0 to n-1.` `#include` `using` `namespace` `std;` `char` `tree;` `int` `root(``char` `key) {` `  ``if` `(tree != ``'\0'``)` `    ``cout << ``"Tree already had root"``;` `  ``else` `    ``tree = key;` `  ``return` `0;` `}`   `int` `set_left(``char` `key, ``int` `parent) {` `  ``if` `(tree[parent] == ``'\0'``)` `    ``cout << ``"\nCan't set child at "` `    ``<< (parent * 2) + 1` `    ``<< ``" , no parent found"``;` `  ``else` `    ``tree[(parent * 2) + 1] = key;` `  ``return` `0;` `}`   `int` `set_right(``char` `key, ``int` `parent) {` `  ``if` `(tree[parent] == ``'\0'``)` `    ``cout << ``"\nCan't set child at "` `    ``<< (parent * 2) + 2` `    ``<< ``" , no parent found"``;` `  ``else` `    ``tree[(parent * 2) + 2] = key;` `  ``return` `0;` `}`   `int` `print_tree() {` `  ``cout << ``"\n"``;` `  ``for` `(``int` `i = 0; i < 10; i++) {` `    ``if` `(tree[i] != ``'\0'``)` `      ``cout << tree[i];` `    ``else` `      ``cout << ``"-"``;` `  ``}` `  ``return` `0;` `}`   `// Driver Code` `int` `main() {` `  ``root(``'A'``);` `  ``set_left(``'B'``,0);` `  ``set_right(``'C'``, 0);` `  ``set_left(``'D'``, 1);` `  ``set_right(``'E'``, 1);` `  ``set_right(``'F'``, 2);` `  ``print_tree();` `  ``return` `0;` `}`

## Java

 `// JAVA implementation of tree using array` `// numbering starting from 0 to n-1.`   `// Importing required classes` `import` `java.io.*;` `import` `java.lang.*;` `import` `java.util.*;`   `// Class 1` `// Helper class (Node class)` `public` `class` `Tree {`   `    ``// Main driver method` `    ``public` `static` `void` `main(String[] args)` `    ``{`   `        ``// Creating object of class 2 inside main() method` `        ``Array_imp obj = ``new` `Array_imp();`   `        ``// Setting root node` `        ``obj.Root(``"A"``);` `        ``obj.set_Left(``"B"``, ``0``);` `        ``obj.set_Right(``"C"``, ``0``);` `        ``obj.set_Left(``"D"``, ``1``);` `        ``obj.set_Right(``"E"``, ``1``);` `        ``obj.set_Right(``"F"``, ``2``);` `        ``obj.print_Tree();` `    ``}` `}`   `// Class 2` `// Helper class` `class` `Array_imp {`   `    ``// Member variables of this class` `    ``static` `int` `root = ``0``;` `    ``static` `String[] str = ``new` `String[``10``];`   `    ``// Method 1` `    ``// Creating root node` `    ``public` `void` `Root(String key) { str[``0``] = key; }`   `    ``// Method 2` `    ``// Creating left son of root` `    ``public` `void` `set_Left(String key, ``int` `root)` `    ``{` `        ``int` `t = (root * ``2``) + ``1``;`   `        ``if` `(str[root] == ``null``) {` `            ``System.out.printf(` `                ``"Can't set child at %d, no parent found\n"``,` `                ``t);` `        ``}` `        ``else` `{` `            ``str[t] = key;` `        ``}` `    ``}`   `    ``// Method 3` `    ``// Creating right son of root` `    ``public` `void` `set_Right(String key, ``int` `root)` `    ``{` `        ``int` `t = (root * ``2``) + ``2``;`   `        ``if` `(str[root] == ``null``) {` `            ``System.out.printf(` `                ``"Can't set child at %d, no parent found\n"``,` `                ``t);` `        ``}` `        ``else` `{` `            ``str[t] = key;` `        ``}` `    ``}`   `    ``// Method 4` `    ``// To print our tree` `    ``public` `void` `print_Tree()` `    ``{`   `        ``// Iterating using for loop` `        ``for` `(``int` `i = ``0``; i < ``10``; i++) {` `            ``if` `(str[i] != ``null``)` `                ``System.out.print(str[i]);` `            ``else` `                ``System.out.print(``"-"``);` `        ``}` `    ``}` `}`

## C#

 `// C# implementation of tree using array` `// numbering starting from 0 to n-1.` `using` `System;`   `public` `class` `Tree {` `    ``public` `static` `void` `Main(String[] args)` `    ``{` `        ``Array_imp obj = ``new` `Array_imp();` `        ``obj.Root(``"A"``);` `        ``obj.set_Left(``"B"``, 0);` `        ``obj.set_Right(``"C"``, 0);` `        ``obj.set_Left(``"D"``, 1);` `        ``obj.set_Right(``"E"``, 1);` `        ``obj.set_Right(``"F"``, 2);` `        ``obj.print_Tree();`   `    ``}` `}`   `class` `Array_imp {` `    ``static` `int` `root = 0;` `    ``static` `String[] str = ``new` `String;`   `    ``/*create root*/` `    ``public` `void` `Root(String key)` `    ``{` `        ``str = key;` `    ``}`   `    ``/*create left son of root*/` `    ``public` `void` `set_Left(String key, ``int` `root)` `    ``{` `        ``int` `t = (root * 2) + 1;`   `        ``if` `(str[root] == ``null``) {` `            ``Console.Write(``"Can't set child at {0}, no parent found\n"``, t);` `        ``}` `        ``else` `{` `            ``str[t] = key;` `        ``}` `    ``}`   `    ``/*create right son of root*/` `    ``public` `void` `set_Right(String key, ``int` `root)` `    ``{` `        ``int` `t = (root * 2) + 2;`   `        ``if` `(str[root] == ``null``) {` `            ``Console.Write(``"Can't set child at {0}, no parent found\n"``, t);` `        ``}` `        ``else` `{` `            ``str[t] = key;` `        ``}` `    ``}`   `    ``public` `void` `print_Tree()` `    ``{` `        ``for` `(``int` `i = 0; i < 10; i++) {` `            ``if` `(str[i] != ``null``)` `                ``Console.Write(str[i]);` `            ``else` `                ``Console.Write(``"-"``);` `        ``}` `    ``}` `}`   `// This code contributed by Rajput-Ji`

## Python3

 `# Python3 implementation of tree using array` `# numbering starting from 0 to n-1.` `tree ``=` `[``None``] ``*` `10`     `def` `root(key):` `    ``if` `tree[``0``] !``=` `None``:` `        ``print``(``"Tree already had root"``)` `    ``else``:` `        ``tree[``0``] ``=` `key`     `def` `set_left(key, parent):` `    ``if` `tree[parent] ``=``=` `None``:` `        ``print``(``"Can't set child at"``, (parent ``*` `2``) ``+` `1``, ``", no parent found"``)` `    ``else``:` `        ``tree[(parent ``*` `2``) ``+` `1``] ``=` `key`     `def` `set_right(key, parent):` `    ``if` `tree[parent] ``=``=` `None``:` `        ``print``(``"Can't set child at"``, (parent ``*` `2``) ``+` `2``, ``", no parent found"``)` `    ``else``:` `        ``tree[(parent ``*` `2``) ``+` `2``] ``=` `key`     `def` `print_tree():` `    ``for` `i ``in` `range``(``10``):` `        ``if` `tree[i] !``=` `None``:` `            ``print``(tree[i], end``=``"")` `        ``else``:` `            ``print``(``"-"``, end``=``"")` `    ``print``()`     `# Driver Code` `root(``'A'``)` `set_left(``'B'``, ``0``)` `set_right(``'C'``, ``0``)` `set_left(``'D'``, ``1``)` `set_right(``'E'``, ``1``)` `set_right(``'F'``, ``2``)` `print_tree()`       `# This code is contributed by Gaurav Kumar Tailor`

## Javascript

 `// JavaScript implementation of tree using array` `// numbering starting from 0 to n-1.` `const tree = Array(10).fill(``null``);`   `function` `root(key) {` `    ``if` `(tree != ``null``) {` `        ``console.log(``"Tree already had root"``);` `    ``} ``else` `{` `        ``tree = key;` `    ``}` `}`   `function` `setLeft(key, parent) {` `    ``if` `(tree[parent] == ``null``) {` `        ``console.log(`Can``'t set child at \${(parent * 2) + 1}, no parent found
`);` `    ``} else {` `        ``tree[(parent * 2) + 1] = key;` `    ``}` `}`   `function setRight(key, parent) {` `    ``if (tree[parent] == null) {` `        ``console.log(`Can'``t set child at \${(parent * 2) + 2}, no parent found
`);` `    ``} ``else` `{` `        ``tree[(parent * 2) + 2] = key;` `    ``}` `}`   `function` `printTree() {` `    ``for` `(let i = 0; i < 10; i++) {` `        ``if` `(tree[i] != ``null``) {` `            ``console.log(tree[i]);` `        ``} ``else` `{` `            ``console.log(``"-"``);` `        ``}` `    ``}` `}`   `// Driver Code` `root(``"A"``);` `setLeft(``"B"``, 0);` `setRight(``"C"``, 0);` `setLeft(``"D"``, 1);` `setRight(``"E"``, 1);` `setRight(``"F"``, 2);` `printTree();`       `// This code is contributed by lokeshpotta20`

Output

`ABCDE-F---`

Time complexity: O(log n) since using heap to create a binary tree
Space complexity: O(1)

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