### Introduction to Programming Using Python, Y. Daniel Liang

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### Chapter 16 Developing Efficient Algorithms

Section 16.2 Measuring Algorithm Efficiency Using Big O Notation
16.1  Estimating algorithm efficiency is ________
A. to measure their actual execution time.
B. to estimate their execution time.
C. to estimate their growth function.

16.2  An input that results in the shortest execution time is called the _____________.
A. best-case input
B. worst-case input
C. average-case input

16.3  Why is the analysis often for the worst case?
A. Best-case is not representative.
B. 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.
C. 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.

16.4  Which of the following complexity is O(nlogn)
A. 300n + 400n*n
B. 23nlogn + 50
C. 45n + 45nlogn + 503
D. n*n*n + nlogn

16.5  On an average, linear search searches
A. the whole list
B. half of the list
C. just one element in the list
D. one fourth of the list

Section 16.3 Examples: Determining Big O
16.6  What is the number of iterations in the following loop:

int count = 5;
while (count < n) {
count = count + 3;
}
A. n - 5
B. n - 3
C. n / 3 - 1
D. (n - 5) / 3
E. the ceiling of (n - 5) / 3

Section 16.4 Analyzing Algorithm Time Complexity
16.7  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.
A. 11
B. 100
C. 512
D. 6

16.8  O(1) is ________.
A. constant time
B. logarithmic time
C. linear time
D. log-linear time

16.9  The time complexity for the Towers of Honoi algorithm in the text is ________.
A. O(n)
B. O(n^2)
C. O(n^3)
D. O(2^n)

16.10  The time complexity for the selection sort algorithm in the text is ________.
A. O(nlogn)
B. O(n^2)
C. O(logn)
D. O(2^n)

16.11  The time complexity for the insertion sort algorithm in the text is ________.
A. O(nlogn)
B. O(n^2)
C. O(logn)
D. O(2^n)

Section 16.5 Finding Fibonacci Numbers Using Dynamic Programming
16.12  ______________ 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.
A. Divide-and-conqure
B. Dynamic programming
C. Brutal-force
D. Backtracking

16.13  The time complexity for the recursive Fibnacci algorithm in the text is ________.
A. O(nlogn)
B. O(n^2)
C. O(logn)
D. O(2^n)

16.14  The time complexity for the algorithm using the dynamic programming approach is ________.
A. O(n)
B. O(n^2)
C. O(logn)
D. O(2^n)

Section 16.6 Finding Greatest Common Divisors Using Euclid?s Algorithm
16.15  The time complexity for the Euclid?s algorithm is ________.
A. O(n)
B. O(n^2)
C. O(logn)
D. O(2^n)

Section 16.7 Efficient Algorithms for Finding Prime Numbers
16.16  The time complexity for the Sieve of Eratosthenes algorithm is ________.
A. O(n)
B. O(n^(1.5)/logn)
C. O(logn)
D. O(2^n)

Section 16.8 Finding the Closest Pair of Points Using Divide-and-Conquer
16.17  The time complexity for the the closest pair of points problem using divide-and-conquer is ________.
A. O(n)
B. O(nlogn)
C. O(logn)
D. O(2^n)

16.18  ______________ 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.
A. Divide-and-conqure/dynamic programming
B. Dynamic programming/divide-and-conqure
C. Brutal-force/divide-and-conqure
D. Backtracking/dynamic programming

Section 16.9 Solving the Eight Queens Problem Using Backtracking
16.19  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.
A. Divide-and-conqure
B. Dynamic programming
C. Brutal-force
D. Backtracking

Section 16.10 Computational Geometry: Finding a Convex Hull
16.20  The gift-wrapping algorithm for finding a convex hull takes ______________ time.
A. O(n)
B. O(nlogn)
C. O(logn)
D. O(n^2)

16.21  The Graham's algorithm for finding a convex hull takes ______________ time.
A. O(n)
B. O(nlogn)
C. O(logn)
D. O(n^2)