Self Doubt

Question

The Total Combinations Possible of Min heap with 8 Distinct elements are ?

Answer 1

It should be 210.

Answer 2

Since

For calculating number of total min/max heaps of some n elements

T(n) =(n-1)Ck*T(k)*T(n-k)

Where n is number of elements given and k is number of child in right subtree

By bottom up approach we can see the structure of heap with 8 elements

                    1

            2              3

   4           5       6         7    

8

We can see that right subtree will have 3 nodes

So

k= 3   and n= 8

Putting these values in above formula

T(8)=7C3*T(3)*T(4)

By same method we calcute T(3) and T(4)

we get

T(8) = 35*2*3= 210