Complexity Theory
1.

Choose the correct answer for the following statements:

I. The theory of NP–completeness provides a method of obtaining a polynomial time for NP algorithms.

II. All NP-complete problem are NP-Hard.

A.  I is FALSE and II is TRUE B.  I is TRUE and II is FALSE C.  Both are TRUE D.  Both are FALSE
2.

The following are the statements regarding the NP problems. Chose the right option from the following options:

I. All NP-complete problems are not NP-hard.

II. Some NP-hard problems are not known to be NP-complete.

A.  Both (I) and (II) are true B.  Both (I) and (II) are false C.  Only (I) is true D.  Only (II) is true
3. The time complexity of the shortest path algorithm can be bounded by
A.  O(n2) B.  O(n4) C.  O(n3) D.  O(n) E.  O(n log n ).
4. The time taken by NP-class sorting algorithm is
A.  O(1) B.  O(log n) C.  O(n2) D.  O(n)
5. A problem L is NP-complete iff L is NP-hard and
A.  L ≈ NP B.  L α NP C.  L ε NP D.  L = NP
6.

The term ________ refers to all state space search methods in which all children of the E–nodes are generated before any other live node can become the E-node.

A.  Backtacking B.  Depth First Search C.  Branch and Bound D.  Breadth First Search
7.

Which of the following case does not exist in complexity theory?

A.

Best case

B.

Worst case

C.

Average case

D.

Null case

8.

The complexity of linear search algorithm is _________

A.

O(n)

B.

O(log n)

C.

O(n2)

D.

O(n log n)

9.

The complexity of Binary search algorithm is _________

A.

O(n)

B.

O(log)

C.

O(n2)

D.

O(n log n)

10.

The complexity of merge sort algorithm is _________

A.

O(n)

B.

O(log n)

C.

O(n2)

D.

O(n log n)