Question

1. Which of the following statements is true?

   The best way to study algorithm efficiency is to see how many milliseconds it takes to execute a program
   All O(log n) sort algorithms will use the same number of CPU cycles to sort identical arrays
   Big O notation is not useful for estimating the specific number of CPU cycles an algorithm will require
   A program will take the same number of millseconds to execute an algorithm each time it is run for the same data

2. We can use the assumption T(1) = 1 because

   We express complexity in relationship to 1 millisecond.
   Every algorithm performs exactly one operation when n is 1
   Since we are interested mostly in how the time required increases with n, we can arbitrarily call T(1) 1 unit of time without worrying about its actual value
   Most Java operators require 1 CPU cycle to execute

3. (Use Excel for this one if you'd like)

   Suppose n = 35. Which of the following statements is true?
   

   n log n is greater than 200
   n squared is greater than 2000
   log n is greater than 6
   2 ^ n is greater than 30 billion

4. Which of the following statements is true?

   You should choose an O(n log n) algorithm over an O(n ^ 2) algorithm
   You should choose an O(n log n) algorithm over an O(n) algorithm
   You should choose an O(n) algorithm over an O(1) algorithm
   You should choose an O(n log n) algorithm over an O(log n) algorithm

5. (If you don't see how to do this question, see the lecture slide on summations.)

   1 + 2 + 3 + 4 + 5 + ... 30 =

   930
   465
   30
   -2147483648

Answer 1

Which of the following statements is true?

You should choose an O(n log n) algorithm over an O(n ^ 2) algorithm ---> TRUE

Explanation: For all values of n, an O(n log n) takes less time than O(n²) algorithm and is more efficient.

You should choose an O(n log n) algorithm over an O(n) algorithm ---> False

Explanation: For all values of n, an O(n log n) takes more time than O(n) algorithm and is less efficient.

You should choose an O(n) algorithm over an O(1) algorithm ---> FALSE

Explanation: For all values of n, an O(n) takes more time than O(1) algorithm and is less efficient.

You should choose an O(n log n) algorithm over an O(log n) algorithm ---> TRUE

Explanation: For all values of n, an O(n log n) takes more time than O(log n) algorithm and is less efficient.

1 + 2 + 3 + 4 + 5 + ... 30 = 30 * 31/2 (Since sum of first n natural numbers is n(n+1)/2)

= 465

NOTE: As per Chegg policy, I am allowed to answer only 4 questions (including sub-parts) on a single post. I have gone ahead and answered 5. Kindly post the remaining questions separately and I will try to answer them. Sorry for the inconvenience caused.