MyLab Programming with Pearson eText -- Access Card -- for Introduction to Java Programming and Data Structures, Comprehensive Version
11th Edition
ISBN: 9780134672816
Author: Liang
Publisher: PEARSON
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Chapter 22, Problem 22.15PE
(Geometry: noncrossed polygon) Write a program that enables the user to add or remove points by clicking the left or light mouse button and displays a noncrossed polygon that links all the points, as shown in Figure 22.11a, A polygon is crossed if two or more sides intersect, as shown in Figure 22.11b. Use the following
FIGURE 22.11 (a)
Step 1: Given a set of points S, select the rightmost lowest point p0 in the set S.
Step 2: Sort the points in S angularly along the x-axis with p0 as the center. If there is a tie and two points have the same angle, the one that is closer to p0 is considered greater. The points in S are now sorted as p0, p1, p2, ..., Pn-1 .
Step 3: The sorted points form a noncrossed polygon.
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1. Consider the NFA defined by the state diagram below. Follow the algorithm seen in
class and in our textbook to construct an equivalent DFA. Please only include the
states reachable (in one or more transitions) from the start state. (Your solution can
be either the table or the state diagram, or both if you wish.)
a
ε, b
b
a
a
92
91
8
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a, b
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a) Answer these Theoretical Questions:
1. Explain the rule of thumb for the Big O. Provide at least one example of applying each rule.
2. What is the Big O of each of the following functions?
a) (n + 1)³/n
b) (n³ + logзn) ³/n
c) n + 100n³ + n
d) 3n+ 100n3 + 3n
*
e) n 3n+ n * 33n
3. Describe an algorithm for finding the occurrence of the max element in an array. Analyze the
complexity of the algorithm.
4. What is Divide-and-Conquer? What is the difference between Divide-and-Conquer and Dynamic
Programming? What are the benefits of using one over another if any?
5. Is it possible to design an algorithm for finding the max element in a list using Divide-and-Conquer?
What is the complexity of this algorithm?
Hint: In this approach, the initial array is divided into two halves...
b) Programming assignment:
Implement initiative / naïve method to find a max element in an array.
Implement the method that uses the Divide-and-Conquer approach to find the max element in an array.
Test both…
9. Given the following Boolean Function:
F(P, Q, R) = PQ+QR+PR
F(P,Q,R)
(i) Derive the canonical SOP (sum of minterms) for F.
(ii) Derive the canonical POS (product of maxterms) for F.
(iii) Draw the truth table, clearly marking which rows are minterms of F and
which rows correspond to maxterms of F.
10) For n Boolean variables, how many distinct Boolean functions exist? Give the answer as a
function of n and briefly justify it.
Chapter 22 Solutions
MyLab Programming with Pearson eText -- Access Card -- for Introduction to Java Programming and Data Structures, Comprehensive Version
Ch. 22.2 - Prob. 22.2.1CPCh. 22.2 - What is the order of each of the following...Ch. 22.3 - Count the number of iterations in the following...Ch. 22.3 - How many stars are displayed in the following code...Ch. 22.3 - Prob. 22.3.3CPCh. 22.3 - Prob. 22.3.4CPCh. 22.3 - Example 7 in Section 22.3 assumes n = 2k. Revise...Ch. 22.4 - Prob. 22.4.1CPCh. 22.4 - Prob. 22.4.2CPCh. 22.4 - Prob. 22.4.3CP
Ch. 22.4 - Prob. 22.4.4CPCh. 22.4 - Prob. 22.4.5CPCh. 22.4 - Prob. 22.4.6CPCh. 22.5 - Prob. 22.5.1CPCh. 22.5 - Why is the recursive Fibonacci algorithm...Ch. 22.6 - Prob. 22.6.1CPCh. 22.7 - Prob. 22.7.1CPCh. 22.7 - Prob. 22.7.2CPCh. 22.8 - Prob. 22.8.1CPCh. 22.8 - What is the difference between divide-and-conquer...Ch. 22.8 - Prob. 22.8.3CPCh. 22.9 - Prob. 22.9.1CPCh. 22.9 - Prob. 22.9.2CPCh. 22.10 - Prob. 22.10.1CPCh. 22.10 - Prob. 22.10.2CPCh. 22.10 - Prob. 22.10.3CPCh. 22 - Program to display maximum consecutive...Ch. 22 - (Maximum increasingly ordered subsequence) Write a...Ch. 22 - (Pattern matching) Write an 0(n) time program that...Ch. 22 - (Pattern matching) Write a program that prompts...Ch. 22 - (Same-number subsequence) Write an O(n) time...Ch. 22 - (Execution time for GCD) Write a program that...Ch. 22 - (Geometry: gift-wrapping algorithm for finding a...Ch. 22 - (Geometry: Grahams algorithm for finding a convex...Ch. 22 - Prob. 22.13PECh. 22 - (Execution time for prime numbers) Write a program...Ch. 22 - (Geometry: noncrossed polygon) Write a program...Ch. 22 - (Linear search animation) Write a program that...Ch. 22 - (Binary search animation) Write a program that...Ch. 22 - (Find the smallest number) Write a method that...Ch. 22 - (Game: Sudoku) Revise Programming Exercise 22.21...Ch. 22 - (Bin packing with smallest object first) The bin...Ch. 22 - Prob. 22.27PE
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