Tree Sort

23 Jun, 2022
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. 
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.
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++
Java
Python3
C#
Javascript
// C++ program to implement Tree Sort#include<bits/stdc++.h> using namespace std; struct Node{    int key;    struct Node *left, *right;}; // A utility function to create a new BST Nodestruct 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 Sortvoid treeSort(int arr[], int n){    struct Node *root = NULL;     // Construct the BST    root = insert(root, arr[0]);    for (int i=1; i<n; i++)        root = insert(root, arr[i]);     // Store inorder traversal of the BST    // in arr[]    int i = 0;    storeSorted(root, arr, i);} // Driver Program to test above functionsint main(){    //create input array    int arr[] = {5, 4, 7, 2, 11};    int n = sizeof(arr)/sizeof(arr[0]);     treeSort(arr, n);         for (int i=0; i<n; i++)       cout << arr[i] << " ";     return 0;}
// Java program to// implement Tree Sortclass 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 program to# implement Tree Sort # Class containing left and# right child of current# node and key valueclass Node:   def __init__(self,item = 0):    self.key = item    self.left,self.right = None,None  # Root of BSTroot = 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 BSTdef 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 BSTdef 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 Codearr = [5, 4, 7, 2, 11]treeins(arr)inorderRec(root) # This code is contributed by shinjanpatra
// C# program to// implement Tree Sortusing 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
<script> // Javascript program to// implement Tree Sort // Class containing left and// right child of current// node and key valueclass Node {   constructor(item) {    this.key = item;    this.left = this.right = null;  }} // Root of BSTlet root = new Node(); root = null; // This method mainly// calls insertRec()function insert(key) {  root = insertRec(root, key);} /* A recursive function toinsert a new key in BST */function insertRec(root, 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 BSTfunction inorderRec(root) {  if (root != null) {    inorderRec(root.left);    document.write(root.key + " ");    inorderRec(root.right);  }}function treeins(arr) {  for (let i = 0; i < arr.length; i++) {    insert(arr[i]);  } } // Driver Code let arr = [5, 4, 7, 2, 11];treeins(arr);inorderRec(root);  // This code is contributed// by Saurabh Jaiswal   </script>
2 4 5 7 11 
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. 
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References: https://en.wikipedia.org/wiki/Tree_sort
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