Tree Sort

Tree sort is a sorting algorithm that is based on Binary Search Tree data structure. It first creates a binary search tree from the elements of the input list or array and then performs an in-order traversal on the created binary search tree to get the elements in sorted order.

Algorithm:

• Step 1: Take the elements input in an array.
• Step 2: Create a Binary search tree by inserting data items from the array into the binary search tree.
• Step 3: Perform in-order traversal on the tree to get the elements in sorted order.

Applications of Tree sort:

• Its most common use is to edit the elements online: after each installation, a set of objects seen so far is available in a structured program.
• If you use a splay tree as a binary search tree, the resulting algorithm (called splaysort) has an additional property that it is an adaptive sort, which means its working time is faster than O (n log n) for virtual inputs.

Below is the implementation for the above approach:

C++

 `// C++ program to implement Tree Sort ` `#include ` ` `  `using` `namespace` `std; ` ` `  `struct` `Node ` `{ ` `    ``int` `key; ` `    ``struct` `Node *left, *right; ` `}; ` ` `  `// A utility function to create a new BST Node ` `struct` `Node *newNode(``int` `item) ` `{ ` `    ``struct` `Node *temp = ``new` `Node; ` `    ``temp->key = item; ` `    ``temp->left = temp->right = NULL; ` `    ``return` `temp; ` `} ` ` `  `// Stores inorder traversal of the BST ` `// in arr[] ` `void` `storeSorted(Node *root, ``int` `arr[], ``int` `&i) ` `{ ` `    ``if` `(root != NULL) ` `    ``{ ` `        ``storeSorted(root->left, arr, i); ` `        ``arr[i++] = root->key; ` `        ``storeSorted(root->right, arr, i); ` `    ``} ` `} ` ` `  `/* A utility function to insert a new ` `   ``Node with given key in BST */` `Node* insert(Node* node, ``int` `key) ` `{ ` `    ``/* If the tree is empty, return a new Node */` `    ``if` `(node == NULL) ``return` `newNode(key); ` ` `  `    ``/* Otherwise, recur down the tree */` `    ``if` `(key < node->key) ` `        ``node->left  = insert(node->left, key); ` `    ``else` `if` `(key > node->key) ` `        ``node->right = insert(node->right, key); ` ` `  `    ``/* return the (unchanged) Node pointer */` `    ``return` `node; ` `} ` ` `  `// This function sorts arr[0..n-1] using Tree Sort ` `void` `treeSort(``int` `arr[], ``int` `n) ` `{ ` `    ``struct` `Node *root = NULL; ` ` `  `    ``// Construct the BST ` `    ``root = insert(root, arr[0]); ` `    ``for` `(``int` `i=1; i

Java

 `// Java program to  ` `// implement Tree Sort ` `class` `GFG  ` `{ ` ` `  `    ``// Class containing left and ` `    ``// right child of current  ` `    ``// node and key value ` `    ``class` `Node  ` `    ``{ ` `        ``int` `key; ` `        ``Node left, right; ` ` `  `        ``public` `Node(``int` `item)  ` `        ``{ ` `            ``key = item; ` `            ``left = right = ``null``; ` `        ``} ` `    ``} ` ` `  `    ``// Root of BST ` `    ``Node root; ` ` `  `    ``// Constructor ` `    ``GFG()  ` `    ``{  ` `        ``root = ``null``;  ` `    ``} ` ` `  `    ``// This method mainly ` `    ``// calls insertRec() ` `    ``void` `insert(``int` `key) ` `    ``{ ` `        ``root = insertRec(root, key); ` `    ``} ` `     `  `    ``/* A recursive function to  ` `    ``insert a new key in BST */` `    ``Node insertRec(Node root, ``int` `key)  ` `    ``{ ` ` `  `        ``/* If the tree is empty, ` `        ``return a new node */` `        ``if` `(root == ``null``)  ` `        ``{ ` `            ``root = ``new` `Node(key); ` `            ``return` `root; ` `        ``} ` ` `  `        ``/* Otherwise, recur ` `        ``down the tree */` `        ``if` `(key < root.key) ` `            ``root.left = insertRec(root.left, key); ` `        ``else` `if` `(key > root.key) ` `            ``root.right = insertRec(root.right, key); ` ` `  `        ``/* return the root */` `        ``return` `root; ` `    ``} ` `     `  `    ``// A function to do  ` `    ``// inorder traversal of BST ` `    ``void` `inorderRec(Node root)  ` `    ``{ ` `        ``if` `(root != ``null``)  ` `        ``{ ` `            ``inorderRec(root.left); ` `            ``System.out.print(root.key + ``" "``); ` `            ``inorderRec(root.right); ` `        ``} ` `    ``} ` `    ``void` `treeins(``int` `arr[]) ` `    ``{ ` `        ``for``(``int` `i = ``0``; i < arr.length; i++) ` `        ``{ ` `            ``insert(arr[i]); ` `        ``} ` `         `  `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String[] args)  ` `    ``{ ` `        ``GFG tree = ``new` `GFG(); ` `        ``int` `arr[] = {``5``, ``4``, ``7``, ``2``, ``11``}; ` `        ``tree.treeins(arr); ` `        ``tree.inorderRec(tree.root); ` `    ``} ` `} ` ` `  `// This code is contributed ` `// by Vibin M `

Python3

 `# Python3 program to  ` `# implement Tree Sort ` ` `  `# Class containing left and ` `# right child of current  ` `# node and key value ` `class` `Node: ` ` `  `  ``def` `__init__(``self``,item ``=` `0``): ` `    ``self``.key ``=` `item ` `    ``self``.left,``self``.right ``=` `None``,``None` ` `  ` `  `# Root of BST ` `root ``=` `Node() ` ` `  `root ``=` `None` ` `  `# This method mainly ` `# calls insertRec() ` `def` `insert(key): ` `  ``global` `root ` `  ``root ``=` `insertRec(root, key) ` ` `  `# A recursive function to  ` `# insert a new key in BST ` `def` `insertRec(root, key): ` ` `  `  ``# If the tree is empty, ` `  ``# return a new node ` ` `  `  ``if` `(root ``=``=` `None``): ` `    ``root ``=` `Node(key) ` `    ``return` `root ` ` `  `  ``# Otherwise, recur ` `  ``# down the tree  ` `  ``if` `(key < root.key): ` `    ``root.left ``=` `insertRec(root.left, key) ` `  ``elif` `(key > root.key): ` `    ``root.right ``=` `insertRec(root.right, key) ` ` `  `  ``# return the root ` `  ``return` `root ` ` `  `# A function to do  ` `# inorder traversal of BST ` `def` `inorderRec(root): ` `  ``if` `(root !``=` `None``): ` `    ``inorderRec(root.left) ` `    ``print``(root.key ,end ``=` `" "``) ` `    ``inorderRec(root.right) ` `   `  `def` `treeins(arr): ` `  ``for` `i ``in` `range``(``len``(arr)): ` `    ``insert(arr[i]) ` ` `  `# Driver Code ` `arr ``=` `[``5``, ``4``, ``7``, ``2``, ``11``] ` `treeins(arr) ` `inorderRec(root) ` ` `  `# This code is contributed by shinjanpatra`

C#

 `// C# program to  ` `// implement Tree Sort ` `using` `System; ` `public` `class` `GFG  ` `{ ` ` `  `  ``// Class containing left and ` `  ``// right child of current  ` `  ``// node and key value ` `  ``public` `class` `Node  ` `  ``{ ` `    ``public` `int` `key; ` `    ``public` `Node left, right; ` ` `  `    ``public` `Node(``int` `item)  ` `    ``{ ` `      ``key = item; ` `      ``left = right = ``null``; ` `    ``} ` `  ``} ` ` `  `  ``// Root of BST ` `  ``Node root; ` ` `  `  ``// Constructor ` `  ``GFG()  ` `  ``{  ` `    ``root = ``null``;  ` `  ``} ` ` `  `  ``// This method mainly ` `  ``// calls insertRec() ` `  ``void` `insert(``int` `key) ` `  ``{ ` `    ``root = insertRec(root, key); ` `  ``} ` ` `  `  ``/* A recursive function to  ` `    ``insert a new key in BST */` `  ``Node insertRec(Node root, ``int` `key)  ` `  ``{ ` ` `  `    ``/* If the tree is empty, ` `        ``return a new node */` `    ``if` `(root == ``null``)  ` `    ``{ ` `      ``root = ``new` `Node(key); ` `      ``return` `root; ` `    ``} ` ` `  `    ``/* Otherwise, recur ` `        ``down the tree */` `    ``if` `(key < root.key) ` `      ``root.left = insertRec(root.left, key); ` `    ``else` `if` `(key > root.key) ` `      ``root.right = insertRec(root.right, key); ` ` `  `    ``/* return the root */` `    ``return` `root; ` `  ``} ` ` `  `  ``// A function to do  ` `  ``// inorder traversal of BST ` `  ``void` `inorderRec(Node root)  ` `  ``{ ` `    ``if` `(root != ``null``)  ` `    ``{ ` `      ``inorderRec(root.left); ` `      ``Console.Write(root.key + ``" "``); ` `      ``inorderRec(root.right); ` `    ``} ` `  ``} ` `  ``void` `treeins(``int` `[]arr) ` `  ``{ ` `    ``for``(``int` `i = 0; i < arr.Length; i++) ` `    ``{ ` `      ``insert(arr[i]); ` `    ``} ` ` `  `  ``} ` ` `  `  ``// Driver Code ` `  ``public` `static` `void` `Main(String[] args)  ` `  ``{ ` `    ``GFG tree = ``new` `GFG(); ` `    ``int` `[]arr = {5, 4, 7, 2, 11}; ` `    ``tree.treeins(arr); ` `    ``tree.inorderRec(tree.root); ` `  ``} ` `} ` ` `  `// This code is contributed by Rajput-Ji  `

Javascript

 ``

Output

`2 4 5 7 11 `

Complexity Analysis:

Average Case Time Complexity: O(n log n) Adding one item to a Binary Search tree on average takes O(log n) time. Therefore, adding n items will take O(n log n) time

Worst Case Time Complexity: O(n2). The worst case time complexity of Tree Sort can be improved by using a self-balancing binary search tree like Red Black Tree, AVL Tree. Using self-balancing binary tree Tree Sort will take O(n log n) time to sort the array in worst case.

Auxiliary Space: O(n)

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