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Data Structures and Algorithms Multiple Choice Questions
SET 10
1. Consider
a perfect binary tree of height 5. Which of the following are the minimum and
maximum number of nodes in the right subtree of the root?
a) 32
b) 31
c) 16
d) 9
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Ans : (b)
Answer: (b) 31
A
perfect binary tree is a
binary tree in which all interior nodes have two children and all leaves have the same depth or same level. In this tree each level
contains the maximum number of nodes, ie., every level is completely full of
nodes.
The
number of nodes in a perfect binary tree = 2^{h+1}1
As
per the question, we need to find the number of nodes in the right subtree
alone. Also, the right subtree is at height less than that of original tree.
Hence, the number of nodes = 2^{h}1.
For a perfect binary tree, the minimum and
maximum number of nodes will be 2^{h+1}1. Hence, for the right
subtree alone, they are 2^{h}1.

2. Rank the
following functions by increasing order of growth; (For example, the correct
ordering of n2, n4, n, n3 is n, n2, n3, n4.)
f1
= (n!)^{1/n}

f2
= ((n)^{n})^{1/2}

f3
= log n^{n}

f4
= n log n

a) f1, f2, f3, f4
b) f1, f3, f4, f2
c) f1, f2, f4, f3
d) f2, f1, f3, f4
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Ans : (b)
Answer: (b) f1,
f3, f4, f2

3. What is a
collision in a hash table implementation of a symbol table? Choose the most
appropriate one.
a) Two keyvalue
pairs that have equal keys but different values.
b) Two keyvalue
pairs that have different keys and hash to different indices.
c) Two keyvalue
pairs that have different keys but hash to the same index.
d) Two keyvalue
pairs that have equal keys but hash to different indices.
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Ans : (c)
Answer: (c) Two
keyvalue pairs that have different keys but hash to the same index
A
collision occurs when two keyvalue pairs have different keys but hash to the
same index.

4. A linearprobing
hash table of length 10 uses the hash function h(x) = x mod 10. After inserting
six integer keys into an initially empty hash table, the array of keys is:
Which of the following
insertion sequences resulting in the above hash table? Assume that the length
of the hash table does not change during the insertions.
a) 46, 42, 34, 52,
23, 33
b) 34, 42, 23, 52,
33, 46
c) 46, 34, 42, 23,
52, 33
d) 42, 46, 33, 23,
34, 52
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Ans : (c)
Answer: (c) 46,
34, 42, 23, 52, 33
46
mod 10 = 6. Key 46 is stored at index 6
34
mod 10 = 4. Key 34 is stored at index 4
42
mod 10 = 2. Key 42 is stored at index 2
23
mod 10 = 3. Key 23 is stored at index 3
52
mod 10 = 2. Index 2 not empty. Linear hash the key ( (i+1) mod 10).
(52+1)
mod 10 = 3. Index 3 not empty. Linear probe the key until find an index which
is empty. The next free index is 5. Hence, key 52 is stored at index 5.
33
mod 10 = 3. Index 3 not empty. Linear probe to find the next free space.
Key
33 is stored at index 7.

5. Which of the
following algorithms is parsimonious?
a) Insertion sort
b) Selection sort
c) Heap sort
d) All of the above
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Ans : (a)
Answer: (a) Insertion
sort
A
sorting algorithm is said to be parsimonious if it never compare the same
pair of input values twice (Assuming that all input values are distinct).
Insertion
sort is parsimonious.

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