hw2solns.pdf - CMPS 101 Homework Assignment 2 Solutions 1...

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CMPS 101
Homework Assignment 2
Solutions
.
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2. p. 53: 3.1-4
Determine whether the following statements are true or false.
a. 2
𝑛+1
= 𝑂(2
𝑛
)
.
b. 2
2𝑛
= 𝑂(2
𝑛
■
)
■
3. p.61: 3-2abcdef
Indicate, for each pair of expressions ( A , B ) in the table below, whether A is O , o , Ω , 𝜔 , or Θ
Assume that 𝑘 ≥ 1 , 𝜀 > 0 , and 𝑐 > 1 are constants. Place 'yes' or 'no' in each of the empty cells below,
and justify your answers.
of B .
A B O o
Ω 𝜔 Θ
a. lg
𝑘
? ?
𝜀
yes yes no no no
b.
?
𝑘
𝑐
𝑛 yes yes no no no
c.