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Complexity Questions

NA
SHSTTON
80
Solv. Corr.
74
Solv. In. Corr.
154
Attempted
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Avg. Time

21 / 48

Choose the correct option.

Hash tree is used in data synchronisation. In the worst case the data synchronisation takes ______ time.


AO(logn)

BO(n2)

CO(nlogn)

DO(n)

Answer: Option D

Explanation:

In average scenarios, the synchronisation takes O(logn) because it is based on the traversal and searching. The worst case occurs when there are no nodes in common, so the synchronisation takes O(n) time.

Workspace

NA
SHSTTON
149
Solv. Corr.
52
Solv. In. Corr.
201
Attempted
0 M:0 S
Avg. Time

22 / 48

Choose the correct option.

What is the time complexity to insert an element into the direct address table?


AO(n)

BO(logn)

CO(nlogn)

DO(1)

Answer: Option D

Explanation:

As every key has a unique array position, it takes constant time to insert an element.

Workspace

NA
SHSTTON
164
Solv. Corr.
34
Solv. In. Corr.
198
Attempted
0 M:0 S
Avg. Time

23 / 48

Choose the correct option.

What is the time complexity to delete an element from the direct address table?


AO(n)

BO(logn)

CO(nlogn)

DO(1)

Answer: Option D

Explanation:

As every key has a unique array position, it takes constant time to delete an element, although the deleted position must be specified by nil.

Workspace

NA
SHSTTON
47
Solv. Corr.
116
Solv. In. Corr.
163
Attempted
0 M:0 S
Avg. Time

24 / 48

Choose the correct option.

What is the space complexity of searching in a heap?


AO(logn)

BO(n)

CO(1)

DO(nlogn)

Answer: Option B

Explanation:

The space complexity of searching an element in heap is O (n). Heap consists of n elements and we need to compare every element. Here no addition or deletion of elements takes place. Hence space complexity is O (n).

Workspace

NA
SHSTTON
74
Solv. Corr.
82
Solv. In. Corr.
156
Attempted
0 M:0 S
Avg. Time

25 / 48

Choose the correct option.

What is the best case complexity in building a heap?


AO(nlogn)

BO(n2)

CO(n*longn *logn)

DO(n)

Answer: Option D

Explanation:

The best case complexity occurs in bottom-up construction when we have a sortes array given.

Workspace

NA
SHSTTON
61
Solv. Corr.
79
Solv. In. Corr.
140
Attempted
0 M:0 S
Avg. Time

26 / 48

Choose the correct option.

State the complexity of algorithm given below.

complexity-1


Ao(n)

BO(logn)

CO(1)

DO(n logn)

Answer: Option C

Explanation:

Deletion in a min-heap is in O(1) time.

Workspace

NA
SHSTTON
60
Solv. Corr.
80
Solv. In. Corr.
140
Attempted
0 M:0 S
Avg. Time

27 / 48

Choose the correct option.

An array consists of n elements. We want to create a heap using the elements. The time complexity of building a heap will be in order of


AO(n*n*logn)

BO(n*logn)

CO(n*n)

DO(n *logn *logn)

Answer: Option B

Explanation:

The total time taken will be N times the complexity of adding a single element to the heap. And adding a single element takes logN time, so That is equal to N*logN.

Workspace

NA
SHSTTON
45
Solv. Corr.
75
Solv. In. Corr.
120
Attempted
0 M:0 S
Avg. Time

28 / 48

Choose the correct option.

What is the complexity of given function of insertion.

complexity-2


AO(logn)

Bamortized O(1)

CO(n)

DO (n*logn)

Answer: Option B

Explanation:

Use a buffer array to store a fixed number of elements when the buffer is full the content of buffer is moved to heap.As a result the complexity
is amotized O(1).

Workspace

NA
SHSTTON
38
Solv. Corr.
88
Solv. In. Corr.
126
Attempted
0 M:0 S
Avg. Time

29 / 48

Choose the correct option.

What is the amortized efficiency of skew merge?


AO(N)

BO(log N)

CO(N log N)

DO(N2)

Answer: Option B

Explanation:

The amortized efficiency of a skew heap is mathematically found to be O( log N).

Workspace

NA
SHSTTON
42
Solv. Corr.
69
Solv. In. Corr.
111
Attempted
0 M:0 S
Avg. Time

30 / 48

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What is the amortized cost per operation of a skew heap?


AO(N)

BO(N log N)

CO(N2)

DO(log N)

Answer: Option D

Explanation:

The amortized cost per operation of a skew heap is O(log N) since the worst case analysis of skew heap is O(N) and splay tree is O(M log N).

Workspace

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