【PTA】【数据结构与算法】NP问题

判断题

1.The sum and composition of two polynomials are always polynomials.

T	F

2.A non-deterministic algorithm is said to be non-deterministic polynomial if the time-efficiency of its verification stage is polynomial.

T	F

3.所有可判定问题都是NP问题。

T	F

4.所有NP问题都可以在一台非确定性机器上用多项式时间解决。

T	F

5.已知问题A是NP完全的。如果问题B是NP问题，并且可以在多项式时间内划归到问题A，则问题B是NP完全的。

T	F

选择题

1.The worst-case efficiency of solving a problem in polynomial time is?

	选项
A	O(p(n))
B	O(p( n log n))
C	O(p(n2))
D	O(p(m log n))

2.Problems that can be solved in polynomial time are known as?

	选项
A	intractable
B	tractable
C	decision
D	complete

3._ is the class of decision problems that can be solved by non-deterministic polynomial algorithms?

	选项
A	NP
B	P
C	Hard
D	Complete

4.Problems that cannot be solved by any algorithm are called?

	选项
A	tractable problems
B	intractable problems
C	undecidable problems
D	decidable problems

5.The Euler’s circuit problem can be solved in?

	选项
A	O(N)
B	O( N logN)
C	O(log N)
D	O(N2)

6.To which class does the Euler’s circuit problem belong?

	选项
A	P class
B	NP class
C	Partition class
D	Complete class

7.Halting problem is an example for?

	选项
A	decidable problem
B	undecidable problem
C	complete problem
D	trackable problem

8.How many stages of procedure does a non-deterministic algorithm consist of?

	选项
A	1
B	2
C	3
D	4

9.How many conditions have to be met if an NP- complete problem is polynomially reducible?

	选项
A	1
B	2
C	3
D	4

10.To which of the following class does a CNF-satisfiability problem belong?

	选项
A	NP class
B	P class
C	NP complete
D	NP hard

11.How many steps are required to prove that a decision problem is NP complete?

	选项
A	1
B	2
C	3
D	4

12.Which of the following problems is not NP complete?

	选项
A	Hamiltonian circuit
B	Bin packing
C	Partition problem
D	Halting problem

13.The choice of polynomial class has led to the development of an extensive theory called __

	选项
A	computational complexity
B	time complexity
C	problem complexity
D	decision complexity

14.下列问题中，哪个不是NP完全问题？

	选项
A	顶点覆盖问题
B	哈密顿圈问题
C	停机问题
D	可满足性问题

15.设Q是一个NP问题，但不一定是NP完全问题。则以下哪句是错的？

	选项
A	若SAT问题有多项式时间解法，则必定意味着Q有多项式时间解法
B	若Q有多项式时间解法，则必定意味着SAT问题有多项式时间解法
C	若Q ∉P，则P≠NP
D	若Q是NP难问题，则Q一定是NP完全问题