Judging the tree from post order

#1

i am not able to understand how to write in order traversal from the post order traversal

moreover the question and answer in the quiz don’t match
ques—
Postorder traversal of a given binary search tree is:
10, 3, 2, 5, 6, 4, 8, 11, 9, 15, 20, 19, 12, 7
find the inorder traversal
and the correct answer according to them is

2, 3, 4, 5, 6, 7, 8 , 9, 11, 12, 15, 19, 20
where is 10 in this !!!
plzz explain me the approach for these kind of problems.

and 1 more doubt
For a perfect binary tree of height h and n nodes the sum of heights of all the nodes is:

ans is O(n)

plz explain it to me? How?

#2

doubt 1:
we can’t tell inorder traversal if only postorder is given or only preorder is given
any two should be given then only we can tell third one

doubt 2:
ans is wrong
sum of height of all node is sum of levels of a tree
because height is nothing but level of tree in reverse order for complete tree

#3

then sir in doubt 1
one option was answer not unique then that will be the answer?

and in doubt 2
they are asking for some of height of all nodes
then if at level 4 of total height 10
height will be 4-3*(10/4)
right!!
then what would be the general way to calculate it??

and sir if there are wrong answers how would we even realise that
it might implant wrong concepts in our mind :frowning: