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 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 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# 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
<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>
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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