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.

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 inoder 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);     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

Output:

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.

Auxiliary Space : O(n)

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

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