Chapter 0: Q1E (page 1)

Question: Answer each part TRUE or FALSE.
$a . 2 n = O (n) b . n^{2} = O (n) \cdot A c . n^{2} = O (n l o g 2 n) \cdot A d . n l o g n = O (n^{2}) e . 3 n = 2 O (n) f . 2^{2 n} = O (2^{2 n})$

Short Answer

Expert verified

(a) $2 n = O (n)$ is True.

(b) $n^{2} = O (n)$ isFalse.

(d) $n \log n = O (n^{2})$ isTrue.

(e) $3 n = O (2 n)$ isFalse.

(f) $2^{2 n} = O (2^{2 n})$ is True.

Step by step solution

To check whether 2n = O(n) True or false

a) $2 n = O (n)$ isTrue

Suppose. $c = 2 2 n ⩽ c n = 2 n f o r a l l n > = 1$

Thus Big-O holds.

To check whether O(n)n2=O(n) True or false

b) $n^{2} = O (n)$ isFalse

$n^{2} = c n n^{2} < = c n f o r a l l n > = n_{0}$ doesn’t hold.

To check whether n2=O(nlog2n) True or false

c) $n^{2} = O (n \log^{2} n)$ isFalse

There doesn’t exist positive constants $n_{0}$ and c such that $n^{2} ⩽ c n \log^{2} n f o r a l l n > = n_{0}$ .

To Find whether nlogn=O(n2) True or false

d) $n \log n = O (n^{2})$ isTrue

$l o g n = O (n)$ there exist positive constants c and n0 such that log $n ⩽ c n f o r a l l n > = n_{0}$ .

To Find whether n = 2O(n) True or false

e) $3 n = 2 O (n)$ isFalse

there doesn’t exist constants c and n0 such that $3 n ⩽ c^{2} n f o r a l l n > = n_{0}$ .

To Find whether 22n=O(22n) True or false

f) $2^{2 n} = O (2^{2 n})$ isTrue

We know any function $f (n) i s O (f (n))$ .

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Question: Answer each part TRUE or FALSE.
$a . 2 n = O (n) b . n^{2} = O (n) \cdot A c . n^{2} = O (n l o g 2 n) \cdot A d . n l o g n = O (n^{2}) e . 3 n = 2 O (n) f . 2^{2 n} = O (2^{2 n})$

Short Answer

Step by step solution

To check whether 2n = O(n) True or false

To check whether O(n)n2=O(n) True or false

To check whether n2=O(nlog2n) True or false

To Find whether nlogn=O(n2) True or false

To Find whether n = 2O(n) True or false

To Find whether 22n=O(22n) True or false

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Most popular questions from this chapter

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Question: Answer each part TRUE or FALSE.a.2n=O(n)b.n2=O(n)·Ac.n2=O(nlog2n)·Ad.nlogn=O(n2)e.3n=2O(n)f.22n=O(22n)

Short Answer

Step by step solution

To check whether 2n = O(n) True or false

To check whether O(n)n2=O(n) True or false

To check whether n2=O(nlog2n) True or false

To Find whether nlogn=O(n2) True or false

To Find whether n = 2O(n) True or false

To Find whether 22n=O(22n) True or false

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Computer Science Textbooks

Big Data

Databases

Issues in Computer Science

Computer Systems

Functional Programming

Problem Solving Techniques

Study anywhere. Anytime. Across all devices.

Question: Answer each part TRUE or FALSE.
$a . 2 n = O (n) b . n^{2} = O (n) \cdot A c . n^{2} = O (n l o g 2 n) \cdot A d . n l o g n = O (n^{2}) e . 3 n = 2 O (n) f . 2^{2 n} = O (2^{2 n})$