SORTIRANJE STABLA

Vrsta stabla je algoritam sortiranja koji se temelji na Stablo binarnog pretraživanja struktura podataka. Prvo stvara binarno stablo pretraživanja od elemenata ulaznog popisa ili niza, a zatim izvodi redoslijedno obilaženje kreiranog binarnog stabla pretraživanja kako bi se elementi dobili sortiranim redoslijedom.

Algoritam:

Korak 1:Uzmite elemente unesene u polje.Korak 2:Stvorite stablo binarnog pretraživanja umetanjem podatkovnih stavki iz polja u binarno stablo pretraživanja .Korak 3:Izvršite redoslijedno obilaženje na stablu da biste dobili elemente poredanim redoslijedom.

Primjene vrste stabla:

Njegova je najčešća upotreba za uređivanje elemenata na mreži: nakon svake instalacije skup do sada viđenih objekata dostupan je u strukturiranom programu.
Ako upotrebljavate splay stablo kao binarno stablo pretraživanja, rezultirajući algoritam (zvan splaysort) ima dodatno svojstvo da je prilagodljivo sortiranje što znači da je njegovo radno vrijeme brže od O (n log n) za virtualne ulaze.

U nastavku je implementacija gornjeg pristupa:

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<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__(selfitem = 0): self.key = item self.leftself.right = NoneNone # 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

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>

Izlaz

2 4 5 7 11

Analiza složenosti:

Prosječna složenost slučaja: O(n log n) Dodavanje jedne stavke stablu binarnog pretraživanja u prosjeku traje O(log n) vremena. Stoga će dodavanje n stavki trajati O(n log n) vremena

Vremenska složenost u najgorem slučaju: Na²). Vremenska složenost sortiranja stabla u najgorem slučaju može se poboljšati upotrebom samobalansirajućeg binarnog stabla pretraživanja kao što je AVL stablo Red Black Tree. Korištenje samobalansirajućeg sortiranja stabla binarnog stabla trebat će O(n log n) vremena za sortiranje niza u najgorem slučaju.

Pomoćni prostor: Na)

TechCodeview

Algoritam:

Primjene vrste stabla:

Analiza složenosti: