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Tree Sort

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  • Difficulty Level : Easy
  • Last Updated : 23 Jun, 2022
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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<bits/stdc++.h>
 
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<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 functions
int 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




// 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




<script>
 
// Javascript program to
// implement Tree Sort
 
// Class containing left and
// right child of current
// node and key value
class Node {
 
  constructor(item) {
    this.key = item;
    this.left = this.right = null;
  }
}
 
// Root of BST
let root = new Node();
 
root = null;
 
// This method mainly
// calls insertRec()
function insert(key) {
  root = insertRec(root, key);
}
 
/* A recursive function to
insert 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 BST
function 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>

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)
 

https://www.youtube.com/watch?v=n2MLjGeK7qA

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References: https://en.wikipedia.org/wiki/Tree_sort

This article is contributed by Harsh Agarwal. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 


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