Program to Find the Total Number of Possible Binary Search Trees with N Keys

Q. Program to find the total number of possible Binary Search Trees with n keys.

Explanation

In this program, we need to find out the total number of binary search trees can be constructed with n values. Below diagram shows a possible binary search tree with the key value as 3. So, we can construct a total of five binary search trees. When we choose node 1 as the root node, we get two trees. Similarly, one tree with 2 as root node and two trees when we select 3 as the root node.

This approach involves selecting a node recursively as the root node and create possible binary search tree.

An easy way to calculate the total number of possible binary search trees are through Catalan number:

Program to find the total number of possible Binary Search Trees with n keys

Algorithm

Define Node class which has three attributes namely: data left and right. Here, left represents the left child of the node and right represents the right child of the node.
When a node is created, data will be passed to the data attribute of the node and both left and right will be set to null.
Define another class which has an attribute root.
1. Root represents the root node of the tree and initialize it to null.
numOfBST() will find out total possible binary search tree for given key:
1. It will calculate the Catalan number for given key by making a call to factorial().
2. Catalan number can be calculated using the formula:
  Cn = (2n)! / n! *(n+1)!
3. Factorial() will calculate factorial of a given number.

Solution

Python

  #Represent a node of binary tree  class Node:      def __init__(self,data):          #Assign data to the new node, set left and right children to None          self.data = data;          self.left = None;          self.right = None;     class BinarySearchTree:      def __init__(self):          #Represent the root of binary tree          self.root = None;                #factorial() will calculate the factorial of given number      def factorial(self, num):          fact = 1;          if(num == 0):              return 1;          else:              while(num > 1):                  fact = fact * num;                  num = num – 1;              return fact;            #numOfBST() will calculate the total number of possible BST by calculating Catalan Number for given key      def numOfBST(self, key):          catalanNumber = self.factorial(2 * key)/(self.factorial(key + 1) * self.factorial(key));          return int(catalanNumber);     bt = BinarySearchTree();     #Display the total number of possible binary search tree with key 5  print(“Total number of possible Binary Search Trees with given key: ” + str(bt.numOfBST(5)));  

Output:

Total number of possible Binary Search Trees with given key: 42

C

  #include <stdio.h>  #include <stdlib.h>     //Represent a node of binary tree  struct node{      int data;      struct node *left;      struct node *right;  };     //Represent the root of binary tree  struct node *root = NULL;     //createNode() will create a new node  struct node* createNode(int data){      //Create a new node      struct node *newNode = (struct node*)malloc(sizeof(struct node));      //Assign data to newNode, set left and right child to NULL      newNode->data = data;      newNode->left = NULL;      newNode->right = NULL;      return newNode;  }     //factorial() will calculate the factorial of given number  int factorial(int num) {      int fact = 1;      if(num == 0)          return 1;      else {          while(num > 1) {              fact = fact * num;              num–;          }          return fact;      }  }     //numOfBST() will calculate the total number of possible BST by calculating Catalan Number for given key  int numOfBST(int key) {      int catalanNumber = factorial(2 * key)/(factorial(key + 1) * factorial(key));      return catalanNumber;  }        int main(){            //Display total number of possible binary search tree with key 5      printf(“Total number of possible Binary Search Trees with given key: %d”, numOfBST(5));            return 0;  }  

Output:

Total number of possible Binary Search Trees with given key: 42

JAVA

  public class BinarySearchTree {            //Represent the node of binary tree      public static class Node{          int data;          Node left;          Node right;                    public Node(int data){              //Assign data to the new node, set left and right children to null              this.data = data;              this.left = null;              this.right = null;              }          }            //Represent the root of binary tree      public Node root;            public BinarySearchTree(){          root = null;      }            //factorial() will calculate the factorial of given number      public int factorial(int num) {          int fact = 1;          if(num == 0)              return 1;          else {              while(num > 1) {                  fact = fact * num;                  num–;              }              return fact;          }      }            //numOfBST() will calculate the total number of possible BST by calculating Catalan Number for given key      public int numOfBST(int key) {          int catalanNumber = factorial(2 * key)/(factorial(key + 1) * factorial(key));          return catalanNumber;      }            public static void main(String[] args) {                    BinarySearchTree bt = new BinarySearchTree();                    //Display total number of possible binary search tree with key 5          System.out.println(“Total number of possible Binary Search Trees with given key: ” + bt.numOfBST(5));        }  }  

Output:

Total number of possible Binary Search Trees with given key: 42

C#

  using System;  namespace Tree   {                           public class Program      {          //Represent a node of binary tree          public class Node<T>{              public T data;              public Node<T> left;              public Node<T> right;                            public Node(T data) {                  //Assign data to the new node, set left and right children to null                  this.data = data;                  this.left = null;                  this.right = null;              }          }                    public class BinarySearchTree<T>{              //Represent the root of binary tree              public Node<T> root;                 public BinarySearchTree(){                  root = null;              }                        //factorial() will calculate the factorial of given number              public int factorial(int num) {                  int fact = 1;                  if(num == 0)                      return 1;                  else {                      while(num > 1) {                          fact = fact * num;                          num–;                      }                      return fact;                  }              }                 //numOfBST() will calculate the total number of possible BST by calculating Catalan Number for given key              public int numOfBST(int key) {                  int catalanNumber = factorial(2 * key)/(factorial(key + 1) * factorial(key));                  return catalanNumber;              }          }                    public static void Main()          {              BinarySearchTree<int> bt = new BinarySearchTree<int>();                        //Display total number of possible binary search tree with key 5              Console.WriteLine(“Total number of possible Binary Search Trees with given key: ” + bt.numOfBST(5));                          }          }  

Output:

Total number of possible Binary Search Trees with given key: 42

PHP

  <!DOCTYPE html>  <html>  <body>  <?php  //Represent a node of binary tree  class Node{      public $data;      public $left;      public $right;            function __construct($data){          //Assign data to the new node, set left and right children to NULL          $this->data = $data;          $this->left = NULL;          $this->right = NULL;      }  }  class BinarySearchTree{      //Represent the root of binary tree      public $root;      function __construct(){          $this->root = NULL;      }            //factorial() will calculate the factorial of given number      function factorial($num) {          $fact = 1;          if($num == 0)              return 1;          else {              while($num > 1) {                  $fact = $fact * $num;                  $num–;              }              return $fact;          }      }            //numOfBST() will calculate the total number of possible BST by calculating Catalan Number for given key      function numOfBST($key) {          $catalanNumber = $this->factorial(2 * $key)/($this->factorial($key + 1) * $this->factorial($key));          return $catalanNumber;      }  }     $bt = new BinarySearchTree();            //Display total number of possible binary search tree with key 5  print “Total number of possible Binary Search Trees with given key: ” . $bt->numOfBST(5);        ?>  </body>  </html>  

Output:

Total number of possible Binary Search Trees with given key: 42

Next TopicPrograms List

Q. Program to find the total number of possible Binary Search Trees with n keys.

Explanation

Algorithm

Solution

Python

C

JAVA

C#

PHP

Potential Energy

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