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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 sub-tree of the root?
a) 32
b) 31
c) 16
d) 9
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 sub-tree alone. Also, the right sub-tree 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 sub-tree 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
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 key-value pairs that have equal keys but different values.
b) Two key-value pairs that have different keys and hash to different indices.
c) Two key-value pairs that have different keys but hash to the same index.
d) Two key-value pairs that have equal keys but hash to different indices.
Answer: (c) Two key-value pairs that have different keys but hash to the same index A collision occurs when two key-value pairs have different keys but hash to the same index. |
4. A linear-probing 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
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
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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