Trees & BST

The height of a binary tree is the number of edges in the longest path from the root to a leaf in the tree. The maximum possible height of a full binary tree with 23 nodes is _________. (*answer in integer*)

Let $P$ be the set of all integers from 1 to 15. Consider any order of insertion of the elements of $P$ into a binary search tree that creates a complete binary tree. Which one of the following elements can NEVER be the third element that is inserted?

The following sequence corresponds to the preorder traversal of a binary search tree $T$: $$50, 25, 13, 40, 30, 47, 75, 60, 70, 80, 77$$ The position of the element 60 in the postorder traversal of $T$ is ______. (*answer in integer*) *Note:* The position begins with 1.

The set T represents various traversals over binary tree. The set S represents the order of visiting nodes during a traversal.

T                   S
I:   Inorder        L: left subtree, node, right subtree
II:  Preorder       M: node, left subtree, right subtree
III: Postorder      N: left subtree, right subtree, node

Which one of the following is the correct match from T to S?

Consider a binary search tree (BST) with $n$ leaf nodes ($n > 0$). Given any node $V$, the key present in the node is denoted as $Val(V)$. All the keys present in the given BST are distinct. The keys belong to the set of real numbers. For a node $V$, let $Suc(V)$ denote the node that is its inorder successor. If a node $V$ does not have an inorder successor, then $Suc(V)$ is $NULL$. As there are no duplicates, if $Suc(V)$ is not $NULL$, then $Val(V) < Val(Suc(V))$. Corresponding to every leaf node $L_i$ that has a non-NULL $Suc(L_i)$, a new key $k_i$ with the following property is to be inserted into the BST. $$Val(L_i) < k_i < Val(Suc(L_i))$$ Let $K$ represent the list of all such new keys to be inserted into the BST. Which of the following statements is/are true?