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. For an tree T, let LR(T) be no of nodes which are the only children of their
parent and n be total no of nodes in the tree. We define LT(T) = LR(T)/n
. Which of the following statements are true ?
(a) For any non empty AVL tree T, LT(T) =
(b) For any binary tree T, if LT(T) =
then height(T) = O(log(n))
(c) For any binary tree T, if there are ?(n) nodes which are the only children
of their parents, all of which are leaves, then height(T) = O(log(n))
(d) None of these
2. How many distinct Max Heap can be made from 5, 6, 7 distinct integers
(a) 8, 20, 80
(b) 8, 20, 76
(c) 8, 18, 80
(d) 7, 18, 76
3. Select the correct statements.
(a) A node u is an proper ancestor of a node v if v is contained in the
subtree rooted at u.
(b) The depth of a node is the number of edges in the unique path from
the root to the node.
(c) The height of a node is the length of the longest path from node to a
(d) A full binary tree is a tree in which every node other than the leaves
has two children
4. For a 2-3 tree in which 10 unique values are inserted, find the maximum and
the minimum number of splits that may happen during insertions .
5. Starting with an empty AVL tree, following operations were performed on
the tree: Inserting elements : 10.20.15,25,30,16,18,19 followed by deleting 30
from the tree. Answer the question with the root of the resultant tree and
the leaves in increasing order.
6. Select the correct statements.
(a) Given two heaps with n elements each, it is possible to construct a single
heap comprising all 2n elements in O(n) time.
(b) Building a heap with n elements can be done in O(n) time.
(c) Maximum element in min heap can always be found in O(logn) time.
(d) In a heap of depth d, there must be at least 2d
elements. (Assume depth
of root is zero)
7. A priority queue can be implemented as a heap because: (Priority Queue is
an extension of queue with every item has a priority associated with it and
always element with high priority is dequeued before an element with low