16. Developing Efficient Algorithms - 21 Questions

# 16. Developing Efficient Algorithms

21 Questions
Created by Y. Daniel Liang
Free
##### Algorithms have been commonly defined in simple terms as "instructions for completing a task". They've also been called "recipes". In The Social Network, an algorithm is what Zuckerberg needed to make Facemash work. If you saw the movie, you probably remember seeing what looked like a scribbly equation on a window in Mark's dorm room. But what does that scribbly algebra have to do with Mark's simple "hot or not" site?
1. Estimating algorithm efficiency is ________

to measure their actual execution time.
to estimate their execution time.
to estimate their growth function.
none of these

2. An input that results in the shortest execution time is called the _____________.

best-case input
worst-case input
average-case input
none of these

3. Why is the analysis often for the worst case?

1. Best-case is not representative.
2. Worst-case is not representative, but worst-case analysis is very useful. You can show that the algorithm will never be slower than the worst-case.
3. Average-case analysis is ideal, but difficult to perform, because it is hard to determine the relative probabilities and distributions of various input instances for many problems.

1 & 2
2 & 3
3
1, 2 & 3

4.  Which of the following complexity is O(nlogn) ?

1. 300n + 400n*n
2. 23nlogn + 50
3. 45n + 45nlogn + 503
4. n*n*n + nlogn

1 & 2
2 & 3
3 & 4
1 & 4

5. On an average, linear search searches

the whole list
half of the list
just one element in the list
one fourth of the list

6. What is the number of iterations in the following loop:

int count = 5;
while (count < n) {
count = count + 3;
}

n - 3
n / 3 - 1
(n - 5) / 3
the ceiling of (n - 5) / 3

7. For a sorted list of 1024 elements, a binary search takes at most _______ comparisons. Note that to check whether an element is greater than, equal to, or less than the other element is considered as one comparison here.

11
100
512
6

8. O(1) is ________.

constant time
logarithmic time
linear time
log-linear time

9. The time complexity for the Towers of Honoi algorithm in the text is ________.

O(n)
O(n^2)
O(n^3)
O(2^n)

10. The time complexity for the selection sort algorithm in the text is ________.

O(nlogn)
O(n^2)
O(logn)
O(2^n)

11. The time complexity for the insertion sort algorithm in the text is ________.

O(nlogn)
O(n^2)
O(logn)
O(2^n)

12. ______________ approach is the process of solving subproblems, then combining the solutions of the subproblems to obtain an overall solution. This naturally leads to a recursive solution. However, it would be inefficient to use recursion, because the subproblems overlap. The key idea behind dynamic programming is to solve each subproblem only once and store the results for subproblems for later use to avoid redundant computing of the subproblems.

Divide-and-conqure
Dynamic programming
Brutal-force
Backtracking

13. The time complexity for the recursive Fibnacci algorithm in the text is ________.

O(nlogn)
O(n^2)
O(logn)
O(2^n)

14. The time complexity for the algorithm using the dynamic programming approach is ________.

O(n)
O(n^2)
O(logn)
O(2^n)

15.  The time complexity for the Euclid?s algorithm is ________.

O(n)
O(n^2)
O(logn)
O(2^n)

16. The time complexity for the Sieve of Eratosthenes algorithm is ________.

O(n)
O(n^(1.5)/logn)
O(logn)
O(2^n)

17. The time complexity for the the closest pair of points problem using divide-and-conquer is ________.

O(n)
O(nlogn)
O(logn)
O(2^n)

18. ______________ approach divides the problem into subproblems, solves the subproblems, then combines the solutions of the subproblems to obtain the solution for the entire problem. Unlike the ________ approach, the subproblems in the divide-and-conquer approach don?t overlap. A subproblem is like the original problem with a smaller size, so you can apply recursion to solve the problem.

Divide-and-conqure/dynamic programming
Dynamic programming/divide-and-conqure
Brutal-force/divide-and-conqure
Backtracking/dynamic programming

19. The ________ approach searches for a candidate solution incrementally, abandoning that option as soon as it determines that the candidate cannot possibly be a valid solution, and then looks for a new candidate.

Divide-and-conqure
Dynamic programming
Brutal-force
Backtracking

20. The gift-wrapping algorithm for finding a convex hull takes ______________ time.

O(n)
O(nlogn)
O(logn)
O(n^2)