CSCI 1730 – Programming Assignment 3

Description

1. Create a class, called Complex, for modeling complex numbers, a + bi, and some complex number arithmetic/comparison operations.

Here is what should be included within this class:
• Include a no-argument constructor (to initialize a complex number to 0+0i).
• Include public member functions to perform these complex number tasks:
o Addition of complex numbers
o Subtraction of complex numbers
o Multiplication of complex numbers
o Division of complex numbers
o User input of a complex number
o Display of a complex number
o Conversion of a real number, r, to a complex number, r + 0i
o Check for equality of two complex numbers

Then, write a C++ program that will use the Complex class to repeatedly do one of the following tasks:
a) Perform a complex number arithmetic operation. For this option, the program will ask the user to enter a complex number, an arithmetic operation (+, –, *, /), and a second complex number, and will then calculate and display the result of performing the arithmetic operation on the two input complex numbers.
b) Determine if a complex number is a solution of a quadratic equation. For this option, the program will prompt for and read in the real number coefficients, a, b, and c, of a quadratic equation, ax2+bx+c=0. Next, it will prompt for and read in a complex number, z. Then, it will determine if z is a solution of the quadratic equation.

• Note: When checking for equality of two complex numbers, do not use the “is equal to” operator on the float values – instead, determine if the absolute value of the float values are smaller than a threshold value (something small, like 0.000001).
• To extract input of a complex number a + bi from keyboard, do the following:
double a, b;
char i;
cin >>a >> b >> i;

Complex Number Review:
A complex number is a number of the form a + bi where a and b are real numbers and i is the imaginary unit, .

• Addition/Subtraction:
• Multiplication:
• Division:

Here is output from a sample run of the program (user input in bold):

Select an option – (1) perform complex number arithmetic
(2) check for quadratic equation solution
(3) exit
1
Enter a complex number a+bi: 2+3i
Enter an operation (+, -, *, /): +
Enter a complex number a+bi: 4-8i
2+3i + 4-8i = 6-5i

Select an option – (1) perform complex number arithmetic
(2) check for quadratic equation solution
(3) exit
1
Enter a complex number a+bi: 2+9i
Enter an operation (+, -, *, /): –
Enter a complex number a+bi: 4+5i
2+9i – 4+5i = -2+4i

Select an option – (1) perform complex number arithmetic
(2) check for quadratic equation solution
(3) exit
1
Enter a complex number a+bi: 4+2i
Enter an operation (+, -, *, /): *
Enter a complex number a+bi: 4-2i
4+2i * 4-2i = 20+0i

Select an option – (1) perform complex number arithmetic
(2) check for quadratic equation solution
(3) exit
1
Enter a complex number a+bi: 4+8i
Enter an operation (+, -, *, /): /
Enter a complex number a+bi: 1-1i
4+8i / 1-1i = -2+6i

Select an option – (1) perform complex number arithmetic
(2) check for quadratic equation solution
(3) exit
2
Enter the coefficients of a quadratic equation: 1 -2 5
Enter a complex number a+bi: 1+2i
The complex number: 1+2i is a solution of the quadratic equation

Select an option – (1) perform complex number arithmetic
(2) check for quadratic equation solution
(3) exit
2
Enter the coefficients of a quadratic equation: 1 -2 5
Enter a complex number a+bi: 2+3i
The complex number: 2+3i is not a solution of the quadratic equation

Select an option – (1) perform complex number arithmetic
(2) check for quadratic equation solution
(3) exit
3

2. Modify the Complex class from problem #1 and replace all arithmetic and relational operator member functions with appropriate overloaded operators (+, -, *, /, ==). In addition, add friend functions to overload the insertion and extraction operators (<< and >>) for use with the Complex class. Then modify the main function and any other stand-alone functions that make use of Complex objects to make use of the new overloaded operators.

3. Write a class IntSet for modeling sets of integers in the range 0 through 99. A set should be represented internally as an array of type bool: The ith array element will be true whenever integer i is in the set and will be false whenever integer i is not in the set. Include a no-argument constructor that initializes a set to the so-called “empty set,” i.e., a set whose array representation contains all false values. The class should include the following overloaded operators:
+ to perform the union of two set (the union of sets A and B is the set that contains all
elements of set A or set B, or both).
* to perform the intersection of two sets (the intersection of sets A and B is the set that
contains all elements in both set A and set B.)
– to form the difference of two sets (the difference of sets A and B is the set containing those elements that are in A but not in B)
+= to add an integer into a set.
-= to delete an integer from a set.
== to determine if two sets are equal.
! to form the complement of a set (the complement of set A, denoted , is the set containing all the elements in the universal set that are not in A – the universal set for this problem is the set containing all integers between 0 and 99)
<= to determine if one set is a subset of another set (set A is a subset of set B means that for any element x in A, x is also an element of set B). << to display a set in roster notation (for example, {2, 3, 5, 9}) Requirement: The overloaded += and -= operators should check for valid integer input (in the range 0-99), or if an add-item is already in the set, or if a delete-item is not in the set. An error message for invalid input should be generated. Then, write a C++ program that uses the new IntSet class. The program should allow the user to repeatedly select from these options: • add numbers to a set • remove numbers from a set • form the union of two sets • form the intersection of two sets • form the difference of two sets • determine if two sets are equal • form the complement of an set • determine if one set is a subset of another set • display a set The program should allow for up to ten sets to be created during a given program run. Use any stand-alone functions you feel necessary. Here is output from a sample run of the program (user input in bold): Select an option: 1 - add numbers to a set 2 - remove numbers from a set 3 - form the union of two sets 4 - form the intersection of two sets 5 - form the difference of two sets 6 - determine if two sets are equal 7 - form the complement of an set 8 - determine if one set is a subset of another set 9 - display a set 10 – Exit 1 Add numbers to which sets (A, B,C, D, E, F, G, H, I, J)? :A Enter number to add: 1 Add another (y or n): y Enter number to add: 3 Add another (y or n): y Enter number to add: 8 Add another (y or n): n Select an option: 1 - add numbers to a set 2 - remove numbers from a set 3 - form the union of two sets 4 - form the intersection of two sets 5 - form the difference of two sets 6 - determine if two sets are equal 7 - form the complement of an set 8 - determine if one set is a subset of another set 9 - display a set 10 – Exit 9 Display set (A, B, C, D, E, F, G, H, I, J)? :A {1, 3, 8} Select an option: 1 - add numbers to a set 2 - remove numbers from a set 3 - form the union of two sets 4 - form the intersection of two sets 5 - form the difference of two sets 6 - determine if two sets are equal 7 - form the complement of an set 8 - determine if one set is a subset of another set 9 - display a set 10 – Exit 1 Add numbers to which sets (A, B,C, D, E, F, G, H, I, J)? :B Enter number to add: 2 Add another (y or n): y Enter number to add: 3 Add another (y or n): y Enter number to add: 7 Add another (y or n): n Select an option: 1 - add numbers to a set 2 - remove numbers from a set 3 - form the union of two sets 4 - form the intersection of two sets 5 - form the difference of two sets 6 - determine if two sets are equal 7 - form the complement of an set 8 - determine if one set is a subset of another set 9 - display a set 10 – Exit 2 Remove numbers from which set (A, B, C, D, E, F, G, H, I, J)? :A Enter number to remove: 1 Remove another (y or n): n Select an option: 1 - add numbers to a set 2 - remove numbers from a set 3 - form the union of two sets 4 - form the intersection of two sets 5 - form the difference of two sets 6 - determine if two sets are equal 7 - form the complement of an set 8 - determine if one set is a subset of another set 9 - display a set 10 – Exit 3 Sets union – specify sets to use: First set: (A, B, C, D, E, F, G, H, I, J)? :A Second set: (A, B, C, D, E, F, G, H, I, J)? :B Result set: (A, B, C, D, E, F, G, H, I, J)? :C Select an option: 1 - add numbers to a set 2 - remove numbers from a set 3 - form the union of two sets 4 - form the intersection of two sets 5 - form the difference of two sets 6 - determine if two sets are equal 7 - form the complement of an set 8 - determine if one set is a subset of another set 9 - display a set 10 – Exit 4 Set intersection – specify sets to use: First set: (A, B, C, D, E, F, G, H, I, J)? :A Second set: (A, B, C, D, E, F, G, H, I, J)? :B Result set: (A, B, C, D, E, F, G, H, I, J)? 😀 Select an option: 1 - add numbers to a set 2 - remove numbers from a set 3 - form the union of two sets 4 - form the intersection of two sets 5 - form the difference of two sets 6 - determine if two sets are equal 7 - form the complement of an set 8 - determine if one set is a subset of another set 9 - display a set 10 – Exit 5 Set difference – specify sets to use: First set: (A, B, C, D, E, F, G, H, I, J)? :A Second set: (A, B, C, D, E, F, G, H, I, J)? :B Result set: (A, B, C, D, E, F, G, H, I, J)? :E Select an option: 1 - add numbers to a set 2 - remove numbers from a set 3 - form the union of two sets 4 - form the intersection of two sets 5 - form the difference of two sets 6 - determine if two sets are equal 7 - form the complement of an set 8 - determine if one set is a subset of another set 9 - display a set 10 – Exit 6 Set equality – specify sets to compare: First set: (A, B, C, D, E, F, G, H, I, J)? :A Second set: (A, B, C, D, E, F, G, H, I, J)? :B These sets are not equal Select an option: 1 - add numbers to a set 2 - remove numbers from a set 3 - form the union of two sets 4 - form the intersection of two sets 5 - form the difference of two sets 6 - determine if two sets are equal 7 - form the complement of an set 8 - determine if one set is a subset of another set 9 - display a set 10 – Exit 7 Set complement – specify sets to use: Complement set: (A, B, C, D, E, F, G, H, I, J)? :A Result set: (A, B, C, D, E, F, G, H, I, J)? :F Select an option: 1 - add numbers to a set 2 - remove numbers from a set 3 - form the union of two sets 4 - form the intersection of two sets 5 - form the difference of two sets 6 - determine if two sets are equal 7 - form the complement of an set 8 - determine if one set is a subset of another set 9 - display a set 10 – Exit 8 Subsets – specify sets to compare: First set: (A, B, C, D, E, F, G, H, I, J)? :A Second set: (A, B, C, D, E, F, G, H, I, J)? :B The first set is not a subset of the second Select an option: 1 - add numbers to a set 2 - remove numbers from a set 3 - form the union of two sets 4 - form the intersection of two sets 5 - form the difference of two sets 6 - determine if two sets are equal 7 - form the complement of an set 8 - determine if one set is a subset of another set 9 - display a set 10 – Exit 9 Display set (A, B, C, D, E, F, G, H, I, J)? :B {2, 3, 7} Select an option: 1 - add numbers to a set 2 - remove numbers from a set 3 - form the union of two sets 4 - form the intersection of two sets 5 - form the difference of two sets 6 - determine if two sets are equal 7 - form the complement of an set 8 - determine if one set is a subset of another set 9 - display a set 10 – Exit 10 4. Write a C++ program that will read in one or more lines of text and then determine the following: • The number of uppercase letters in the text. • The number of lowercase letters in the text. • The number of digits in the text. • The number of whitespace characters (i.e., blanks or newlines) in the text. • The number of other, non-letter, non-digit, non-whitespace characters in the text. After reading the text, the program should display the text followed by a display of all of the above statistics. Suggestions and hints: • Use a string variable to read the text into (since you do not know in advance how much text will be input). • The getline function can be used to read in more than one line into a string variable. To do this, specify a special terminating character as a “flag” to indicate input termination as the third parameter to getline when it is called to read. For example, getline(cin,text,'@'); will read text into the string variable text until a '@' character is encountered. • You may assume that the text to be entered does not contain the '@' character. Output from a sample run of the program (user input is one line in bold): A string is a joy forever! Enter 3 or 4 words: Am I a palindrome? Hello friends# Is this a valid English sentence@ A string is a joy forever! Enter 3 or 4 words: Am I a palindrome? Hello friends# Is this a valid English sentence There were 113 total characters. There were 7 upper case letters. There were 78 lower case letters. There were 2 digits. There were 22 white space characters. There were 4 other characters. 5. Write a C++ program that repeatedly prompts for and reads an e-mail address and then determines and displays whether the address is valid or invalid. For purposes of this program, an e-mail address is valid if it satisfies these conditions: • The address cannot contain blanks. For example, john smith@minneapolis.edu is not a valid e-mail address. • The @ character must occur exactly once. For example, baz.cs.dpu.edu and bar@cs@dpu are not valid e-mail addresses. • The @ character cannot be the first character of the address. For example, @cs.dpu.edu is not a valid e-mail address. • Every occurrence of the dot character (.)must have a non-@, non-dot character on both side. For example, bar@cs. , .ed@comcast.net, and bar@.depaul, joe..smith@bob.com are not valid e-mail addresses. After reading an email address, the program should display it. If the address is valid, a message should be displayed stating that it is. For invalid addresses, the program should generate an error message for each of the above conditions that was violated. Suggestions and hints: • Use string class strings in your program. • Write a separate bool-valued function to check each of the four invalidity checks given above. Each should receive the email address via a parameter and then return true if the email address is invalid according to the particular invalidity conditions. • Use a bool array of size four to store the results of calling each of these invalidity check functions. • If you have buffering problems when repeatedly reading strings and chars, make use of the function call cin.ignore(80,’\n’) to clear the buffer at appropriate times. Output from a sample run of the program (user input is one line in bold): Enter the address: john smith@minneapolis.edu You entered: john smith@minneapolis.edu Not valid – contains a blank Enter another (y or n)? y Enter the address: baz.cs.dpu.edu You entered: baz.cs.dpu.edu Not valid – not exactly one ‘@’ Enter another (y or n)? y Enter the address: bar@cs@dpu You entered: bar@cs@dpu Not valid – not exactly one ‘@’ Enter another (y or n)? y Enter the address: @cs.dpu.edu You entered: @cs.dpu.edu Not valid – ‘@’ is first character Enter another (y or n)? y Enter the address: bar@cs. You entered: bar@cs. Not valid – a dot is first or last, or preceded or followed by @ or . Enter another (y or n)? y Enter the address: .ed@comcast.net You entered: .ed@comcast.net Not valid – a dot is first or last, or preceded or followed by @ or . Enter another (y or n)? y Enter the address: bar@.depaul You entered: bar@.depaul Not valid - a dot is first or last, or preceded or followed by @ or . Enter another (y or n)? y Enter the address: joe..smith@bob.com You entered: joe..smith@bob.com Not valid - a dot is first or last, or preceded or followed by @ or . Enter another (y or n)? n 6. The following C++ main driver, along with function myFunc, uses a C++ class DynArray that models a dynamic integer array – that is, the class uses dynamic memory allocation to create a contiguous block of memory for storing a specified number of integers. The indexing for a DynArray object is the same as for a regular array. But, a DynArray can be initialized to size zero. Write the C++ DynArray class. Here is a brief description of all of the class functions that your class should include: • No-argument constructor – initializes a DynArray object to being empty. • One-argument constructor – uses dynamic memory allocation to obtain a contiguous block of memory for storing n int values, where n is its argument. • show – displays the nth element in the DynArray. If the DynArray is empty or if n is an invalid index, this function should generate an error message. • set – will set the nth element in the DynArray to x, where n is the value of its first argument and x is value of its second argument. If the DynArray is empty or if n is an invalid index, this function should generate an error message. • expand – will take an existing DynArray and expand its size by its argument, s. Hint: To expand a DynArray, allocate a new, larger block of dynamic memory, copy the values from the old DynArray to the new memory, and deallocate the old memory. • A destructor to deallocate dynamic memory when a DynArray object passes out of scope. Requirement: When accessing the dynamic array elements in the set, show and expand member functions, you must use the dereferencing operator, *, along with pointer arithmetic instead of the array indexing operator, []. Next, combine your DynArray class with the following main and myFunc code and run the resulting C++ program. The output generated from a run of your program should be similar to that shown in the output of a sample run given after the code. void myFunc(); int main() { int size,more,i; DynArray y; cout << "Enter dynamic array size: "; cin >> size;
DynArray x(size);
for(i=0;i> more;
x.expand(more);
for(i=0;i<(size+more);i++) x.set(i,5*i); for(i=0;i<(size+more);i++) x.show(i); x.show(size+more+5); //invalid index in show x.set(-2,9); //invalid index in set y.set(3,6); //empty DynArray set y.show(3); //empty DynArray show myFunc(); char ch; cin >> ch;
return 0;
}
void myFunc()
{
int i;
cout << "hi from myFunc...\n"; DynArray y(5); for(i=0;i<5;i++) y.set(i,i*i); for(i=0;i<5;i++) y.show(i); cout << "bye from myFunc...\n"; } Output from a sample run of the program (user input is in bold): Enter dynamic array size: 3 0 3 6 How much more dynamic array space do you want? 2 0 5 10 15 20 Invalid index in show Invalid index in set Cannot set - DynArray empty Cannot show - DynArray empty hi from myFunc... 0 1 4 9 16 bye from myFunc... hi from the DynArray destructor... What you need to turn in: • Source code listing: A printed copy of the source code for each problem. Remember to include the name of each group member in a comment at the top of your source code. Be sure to follow the “Code Style Guidelines” specified in class. • Source code files: E-mail me your source code as attachments. • Working in Groups: Every student will work with two other students in our class on this assignment; all members of the group must contribute to the solution. Turn in only one copy of the solution – clearly identify the name of each member on everything that you turn in. • Late Assignments: Assignments are due before class on the specified due date (both the paper copies and the e-mail copies). If you wish to turn in the paper copy of an assignment after class, place them under my office door. Assignments turned in late will be assessed a 20% penalty per class day late.