GATE CS 2005 Q35 — Binary Search Trees

Which of the following statement(s) is/are TRUE for any binary search tree (BST) having $n$ distinct integers?

Suppose the values $10,-4,15,30,20,5,60,19$ are inserted in that order into an initially empty binary search tree. Let $T$ be the resulting binary search tree. The number of edges in the path from the node containing $19$ to the root node of $T$ is _________. (Answer in integer)

​​​​​​You are given a set $V$ of distinct integers. A binary search tree $T$ is created by inserting all elements of $V$ one by one, starting with an empty tree. The tree $T$ follows the convention that, at each node, all values stored in the left subtree of the node are smaller than the value stored at the node. You are not aware of the sequence in …

Suppose a binary search tree with $1000$ distinct elements is also a complete binary tree. The tree is stored using the array representation of binary heap trees. Assuming that the array indices start with $0,$ the $3^{\text{rd}}$ largest element of the tree is stored at index ______________ .

A binary search tree $T$ contains $n$ distinct elements. What is the time complexity of picking an element in $T$ that is smaller than the maximum element in $T$?

The preorder traversal of a binary search tree is $15, 10, 12, 11, 20, 18, 16, 19$. Which one of the following is the postorder traversal of the tree?