Question

With three unlabeled nodes what is the maximum.Number of binary trees that can be created

Answer 1

@SOLUTION;__✍️

BST(n) = C(2*n , n) / (n+1)

Therefore Unlabeled BT(n) = C(2*n , n) / (n+1)

Therefore number of unlabeled BT with 3 nodes is given by:—

=> C(2*3, 3) /(3+1)

=> C(6,3)/4

=> 6!/(3!*3!*4)

=> 6*5/6

=> 5

So the number of unlabeled Binary Tree with 3 nodes is 5.

Answer 2

Answer:

Number of binary trees that can be created is 5.

Step-by-step explanation:

Given:

• Nodes are unlabeled. If the nodes are labeled, we get more number of trees.

• Use  Catalan number to find number of binary tree :

Here n = 3

• Number of binary tree = $\frac{^{2n} C_{n}}{(n+1)} = \frac{^{2*3C_{3} } }{4+1} =5$

Number of binary trees that can be created is 5.