MadeEasy Subject Test 2019: Programming & DS - Binary Tree

Question

four vertices {A,B,C,D} is given which has only vertex D as a leaf total number of binary tree are possible when every binary tree has four node!

Comments

See, if A is root node, then B or C anyone can be child of A and it can be a left or child to A.
Lets child of root node A is B and its left child of A, ok
now, C will be child of B and it can be left or right child , rght?

say left child of B is C and then D will be leaf node and D can be left or right child of C

and It'll with root node A, we can make combinations with root B and diff child

hope you are geting my point

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i got that , see if you make a->b->c->d either as all being left child or right child or as left and right combination wont that be same imean isomorphic..

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@arvin 

But in binary tree, both are different right?

 

Answer 1

https://gateoverflow.in/277870/me-test-series

Check my solution there

Answer 2

Its mentioned that node D will always be leaf node and tree has always 1 leaf node also. Hence we are left with 3 nodes.

At 1^st level we can have 3C1 choices to select node

At 2^nd level we have 2 nodes left so we can select 2C1  *2   as either we can put the node at right or left

at 3^rd we have 1 node left and we can place it at either left or right so 2 

at left D can be also placed at right or left so 2

so 3C1 * 2C1 *2  *2 *2   = 48 BT