How many different binary trees can be made from three nodes?

Answer 1

As far as i Know, just one.

Do you know any formula to calculate how many binary search trees are possible?

--

answer:

(2n C n) / (n+1) = ( factorial (2n) / factorial (n) * factorial (2n - n) ) / ( n + 1 )

where 'n' is number of element (integer/string)

like:

N Number of BST

1 1

2 2

3 5

4 14

5 42

6 132

and so on

Answer 2

balanced 6:

A(B,C)

A(C,B)

B(A,C)

B(C,A)

C(A,B)

C(B,A)

unbalanced 24:

A(B(C,),)

A(B(,C),)

A(,B(C,))

A(,B(,C))

A(C(B,),)

A(C(,B),)

A(,C(B,))

A(,C(,B))

...

30 total

Answer 3

Try it recursively.

for 1 nodes it is 1.

For 2 distinct nodes it is 4.

For 3 nodes, using combinationaries it is 3*(4+4+2)=30

For 4 nodes it is 4 *(30*2+2*(4*1))=272(required answer)

Here answer is for creating any binary tree with no imposed restriction upon it.

Another answer: Not allowing empty trees, it is four or less. (Allowing empty trees it is infinite.)

Answer 4

Answer is Catalan number i.e 2n!/(n!*(n+1)!) where n is number of nodes.

Answer 5

How many nodes are in a binary tree?

How many binary trees in a node?

Come on think, if this is too hard for you think about changing your courses.

Answer 6

It is 2^4 =16.

Answer 7

14

Answer 8

2n

Answer 9

12