Q. Consider the following nested representation of binary trees indicates y and z are the left right subtrees, respectively, of node x. Note that y and z may be NULL or further nested. Which of the following represents a valid binary tree?

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Q. B+- trees are preferred to binary trees in databases because

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Q. A full binary tree with n non-leaf nodes contains

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Q. The depth of a complete binary tree with 'n nodes is (log is to be base two)

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Q. Which of the below diagram is following AVL tree property?

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Q. Is the below tree representation of 50,100,400,300,280 correct way to represent cartesian tree?

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Q. What is the condition for a tree to be weight balanced. where a is factor and n is a node?

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Q. What are the operations that can be performed on weight balanced tree?

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Q. Consider a weight balanced tree such that, the number of nodes in the left sub tree is at least half and at most twice the number of nodes in the right sub tree. The maximum possible height (number of nodes on the path from the root to the farthest leaf) of such a tree on k nodes can be described as

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Q. What does the below definations convey?

i. A binary tree is balanced if for every node it is gonna hold that the number of inner nodes in the left subtree and the number of inner nodes in the right subtree differ by at most 1.
ii. A binary tree is balanced if for any two leaves the difference of the depth is at most 1.

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Q. Elements in a tree can be indexed by its position under the ordering of the keys and the ordinal position of an element can be determined, both with good efficiency.

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Q. What is the special property of red-black trees and what root should always be?

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Q. Why do we impose restrictions like
. root property is black
. every leaf is black
. children of red node are black
. all leaves have same black

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Q. Cosider the below formations of red-black tree. All the below formations are incorrect for it to be a redblack tree. Then what may be the correct order?

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Q. What are the operations that could be performed in O(logn) time complexity by red-black tree?

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Q. Which of the following is an application of Red-black trees and why?

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Q. When it would be optimal to prefer Red-black trees over AVL trees?

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Q. Why Red-black trees are preferred over hash tables though hash tables have constant time complexity?

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Q. How can you save memory when storing color information in Red-Black tree?

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Q. When to choose Red-Black tree, AVL tree and B-trees?

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