For technical reasons, some of the requirements below may be the same as what you have done in previous assignments. If so, don't worry about it, just make sure the requirement is met, even if it means just copying code you wrote before. Here are the client program, data file, and correct output. This week you'll be making the following refinements to the class that you wrote last week. Reduce Fractions [5 points] Add a private "simplify()" function to your class and call it from the appropriate member functions. (If you write your code the way that 90% of students write it, there will be 6 places where you need to call it. But if you call it a different number of times and your class works, that's also fine.) The best way to do this is to make the function a void function with no parameters that reduces the calling object. Recall that "simplifying" or "reducing" a fraction is a separate task from converting it from an improper fraction to a mixed number. Make sure you keep those two tasks separate in your mind. For now (until you get down to the part of the assignment where you improve your insertion operator) your fractions will still be printed as improper fractions, not mixed numbers. In other words, 19/3 will still be 19/3, not 6+1/3. Make sure that your class will reduce ANY fraction, not just the fractions that are tested in the provided client program. Fractions should not be simply reduced upon output, they should be stored in reduced form at all times. In other words, you should ensure that all fraction objects are reduced before the end of any member function. To put it yet another way: each member function must be able to assume that all fraction objects are in simple form when it begins execution. You must create your own algorithm for reducing fractions. Don't look up an already existing algorithm for reducing fractions or finding GCF. The point here is to have you practice solving the problem on your own. In particular, don't use Euclid's algorithm. Don't worry about being efficient. It's fine to have your function check every possible factor, even if it would be more efficient to just check prime numbers. Just create something of your own that works correctly on ANY fraction. Your simplify() function should also ensure that the denominator is never negative. If the denominator is negative, fix this by multiplying numerator and denominator by -1. Better Insertion Operator [10 points] Now modify your overloaded << operator so that improper fractions are printed as mixed numbers. Whole numbers should print without a denominator (e.g. not 3/1 but just 3). Improper fractions should be printed as a mixed number with a + sign between the two parts (2+1/2). Negative fractions should be printed with a leading minus sign. Note that your class should have only two data members. Fractions will be stored as improper fractions. The << operator is responsible for printing the improper fraction as a mixed number. Also, the '+' in mixed numbers does not mean add. It is simply a separator (to separate the integer part from the fraction part of the number). So the fraction "negative two and one-sixth" would be written as -2+1/6, even though -2 plus 1/6 is not what we mean. Extraction Operator [10 points] You should be able to read any of the formats described above (mixed number, negative number, whole numbers, etc.). You may assume that there are no spaces or formatting errors in the fractions that you read. You may need to exceed 15 lines for this function. My solution is about 20 lines long. Since your extraction operator should not consume anything after the end of the fraction being read, you will probably want to use the .peek() function to look ahead in the input stream and see what the next character is after the first number is read. If it's not either a '/'' or a '+', then you are done reading and should read no further. I have something like this: int temp; in >> temp; if (in.peek() == '+'){ doSomething... } else if (in.peek() == '/'){ doSomethingElse... } else { doThirdOption } Hint: You don't need to detect or read the minus operator as a separate character. When you use the extraction operator to read an int, it will interpret a leading minus sign correctly. So, for example, you shouldn't have "if (in.peek() == '-')" Hint: The peek() function does not consume the character from the input stream, so after you use it to detect what the next character is, the first thing you need to do is get past that character. One good way to do that would be to use in.ignore(), which ignores one single character in the input stream. Three Files and Namespaces [10 points] Split the project up into three files: client file, implementation file, and header (specification) file. Also, place the class declaration and implementation in a namespace. Normally one would call a namespace something more likely to be unique, but for purposes of convenience we will all call our namespace "cs_fraction". Namespaces are covered in lesson 16.15. Add Documentation [10 points] See Style Convention 1, especially Style Convention 1D. Every public member function and friend function, however simple, must have a precondition (if there is one) and a postcondition listed in the header file. Here is a two part explanation of pre- and post- conditions. You'll have to download these to view them: part 1, part 2. The most complex of your function definitions will need additional comment in the implementation file. Most of the function definitions in the implementation file will not need a comment. Name your source code files fraction.h and fraction.cpp. The below is fracttest.cpp #include #include "fraction.h" #include #include #include using namespace std; using namespace cs_fraction; void BasicTest(); void RelationTest(); void BinaryMathTest(); void MathAssignTest(); bool eof(ifstream& in); string boolString(bool convertMe); int main() { BasicTest(); RelationTest(); BinaryMathTest(); MathAssignTest(); } void BasicTest() { cout << " ----- Testing basic fraction creation & printing "; cout << "(fractions should be in reduced form, and as mixed numbers.) "; const fraction fr[] = {fraction(4, 8), fraction(-15,21), fraction(10), fraction(12, -3), fraction(), fraction(28, 6), fraction(0, 12)}; for (int i = 0; i < 7; i++){ cout << "fraction [" << i <<"] = " << fr[i] << endl; } cout << " ----- Now reading fractions from file "; ifstream in("fraction.txt"); assert(in); while (!eof(in)) { fraction f; if (in.peek() == '#') { in.ignore(128, ' '); //skip this line, it's a comment } else { in >> f; cout << "Read fraction = " << f << endl; } } } bool eof(ifstream& in) { char ch; in >> ch; in.putback(ch); return !in; } string boolString(bool convertMe) { if (convertMe) { return "true"; } else { return "false"; } } void RelationTest() { cout << " ----- Testing relational operators between fractions "; const fraction fr[] = {fraction(3, 6), fraction(1,2), fraction(-15,30), fraction(1,10), fraction(0,1), fraction(0,2)}; for (int i = 0; i < 5; i++) { cout << "Comparing " << fr[i] << " to " << fr[i+1] << endl; cout << "\tIs left < right? " << boolString(fr[i] < fr[i+1]) << endl; cout << "\tIs left <= right? " << boolString(fr[i] <= fr[i+1]) << endl; cout << "\tIs left > right? " << boolString(fr[i] > fr[i+1]) << endl; cout << "\tIs left >= right? " << boolString(fr[i] >= fr[i+1]) << endl; cout << "\tDoes left == right? " << boolString(fr[i] == fr[i+1]) << endl; cout << "\tDoes left != right ? " << boolString(fr[i] != fr[i+1]) << endl; } cout << " ----- Testing relations between fractions and integers "; fraction f(-3,6); int num = 2; cout << "Comparing " << f << " to " << num << endl; cout << "\tIs left < right? " << boolString(f < num) << endl; cout << "\tIs left <= right? " << boolString(f <= num) << endl; cout << "\tIs left > right? " << boolString(f > num) << endl; cout << "\tIs left >= right? " << boolString(f >= num) << endl; cout << "\tDoes left == right? " << boolString(f == num) << endl; cout << "\tDoes left != right ? " << boolString(f != num) << endl; fraction g(1,4); num = -3; cout << "Comparing " << num << " to " << g << endl; cout << "\tIs left < right? " << boolString(num < g) << endl; cout << "\tIs left <= right? " << boolString(num <= g) << endl; cout << "\tIs left > right? " << boolString(num > g) << endl; cout << "\tIs left >= right? " << boolString(num >= g) << endl; cout << "\tDoes left == right? " << boolString(num == g) << endl; cout << "\tDoes left != right ? " << boolString(num != g) << endl; } void BinaryMathTest() { cout << " ----- Testing binary arithmetic between fractions "; const fraction fr[] = {fraction(1, 6), fraction(1,3), fraction(-2,3), fraction(5), fraction(-4,3)}; for (int i = 0; i < 4; i++) { cout << fr[i] << " + " << fr[i+1] << " = " << fr[i] + fr[i+1] << endl; cout << fr[i] << " - " << fr[i+1] << " = " << fr[i] - fr[i+1] << endl; cout << fr[i] << " * " << fr[i+1] << " = " << fr[i] * fr[i+1] << endl; cout << fr[i] << " / " << fr[i+1] << " = " << fr[i] / fr[i+1] << endl; } cout << " ----- Testing arithmetic between fractions and integers "; fraction f(-1, 2); int num = 4; cout << f << " + " << num << " = " << f + num << endl; cout << f << " - " << num << " = " << f - num << endl; cout << f << " * " << num << " = " << f * num << endl; cout << f << " / " << num << " = " << f / num << endl; fraction g(-1, 2); num = 3; cout << num << " + " << g << " = " << num + g << endl; cout << num << " - " << g << " = " << num - g << endl; cout << num << " * " << g << " = " << num * g << endl; cout << num << " / " << g << " = " << num / g << endl; } void MathAssignTest() { cout << " ----- Testing shorthand arithmetic assignment on fractions "; fraction fr[] = {fraction(1, 6), fraction(4), fraction(-1,2), fraction(5)}; for (int i = 0; i < 3; i++) { cout << fr[i] << " += " << fr[i+1] << " = "; cout << (fr[i] += fr[i+1]) << endl; cout << fr[i] << " -= " << fr[i+1] << " = "; cout << (fr[i] -= fr[i+1]) << endl; cout << fr[i] << " *= " << fr[i+1] << " = "; cout << (fr[i] *= fr[i+1]) << endl; cout << fr[i] << " /= " << fr[i+1] << " = "; cout << (fr[i] /= fr[i+1]) << endl; } cout << " ----- Testing shorthand arithmetic assignment using integers "; fraction f(-1, 3); int num = 3; cout << f << " += " << num << " = "; cout << (f += num) << endl; cout << f << " -= " << num << " = "; cout << (f -= num) << endl; cout << f << " *= " << num << " = "; cout << (f *= num) << endl; cout << f << " /= " << num << " = "; cout << (f /= num) << endl; cout << " ----- Testing increment/decrement prefix and postfix "; fraction g(-1, 3); cout << "Now g = " << g << endl; cout << "g++ = " << g++ << endl; cout << "Now g = " << g << endl; cout << "++g = " << ++g << endl; cout << "Now g = " << g << endl; cout << "g-- = " << g-- << endl; cout << "Now g = " << g << endl; cout << "--g = " << --g << endl; cout << "Now g = " << g << endl; } The below is fraction data. # This file shows the patterns your fraction class needs to be able to # read. A fraction may be just a single integer, two integers separated by # a slash, or a mixed number which consists of an integer, followed by a + # and then two integers with a slash. A minus sign may appear in the # very first character to indicate the whole fraction is negative. # No white space is allowed in between the component parts of a fraction. # 1/3 3/6 3072/4096 -4/5 12/2 5 -8 21/15 -50/3 1+1/4 1+5/5 -4+3/12 -10+10/12 The below is fraction output. ----- Testing basic fraction creation & printing (fractions should be in reduced form, and as mixed numbers.) fraction [0] = 1/2 fraction [1] = -5/7 fraction [2] = 10 fraction [3] = -4 fraction [4] = 0 fraction [5] = 4+2/3 fraction [6] = 0 ----- Now reading fractions from file Read fraction = 1/3 Read fraction = 1/2 Read fraction = 3/4 Read fraction = -4/5 Read fraction = 6 Read fraction = 5 Read fraction = -8 Read fraction = 1+2/5 Read fraction = -16+2/3 Read fraction = 1+1/4 Read fraction = 2 Read fraction = -4+1/4 Read fraction = -10+5/6 ----- Testing relational operators between fractions Comparing 1/2 to 1/2 Is left < right? false Is left <= right? true Is left > right? false Is left >= right? true Does left == right? true Does left != right ? false Comparing 1/2 to -1/2 Is left < right? false Is left <= right? false Is left > right? true Is left >= right? true Does left == right? false Does left != right ? true Comparing -1/2 to 1/10 Is left < right? true Is left <= right? true Is left > right? false Is left >= right? false Does left == right? false Does left != right ? true Comparing 1/10 to 0 Is left < right? false Is left <= right? false Is left > right? true Is left >= right? true Does left == right? false Does left != right ? true Comparing 0 to 0 Is left < right? false Is left <= right? true Is left > right? false Is left >= right? true Does left == right? true Does left != right ? false ----- Testing relations between fractions and integers Comparing -1/2 to 2 Is left < right? true Is left <= right? true Is left > right? false Is left >= right? false Does left == right? false Does left != right ? true Comparing -3 to 1/4 Is left < right? true Is left <= right? true Is left > right? false Is left >= right? false Does left == right? false Does left != right ? true ----- Testing binary arithmetic between fractions 1/6 + 1/3 = 1/2 1/6 - 1/3 = -1/6 1/6 * 1/3 = 1/18 1/6 / 1/3 = 1/2 1/3 + -2/3 = -1/3 1/3 - -2/3 = 1 1/3 * -2/3 = -2/9 1/3 / -2/3 = -1/2 -2/3 + 5 = 4+1/3 -2/3 - 5 = -5+2/3 -2/3 * 5 = -3+1/3 -2/3 / 5 = -2/15 5 + -1+1/3 = 3+2/3 5 - -1+1/3 = 6+1/3 5 * -1+1/3 = -6+2/3 5 / -1+1/3 = -3+3/4 ----- Testing arithmetic between fractions and integers -1/2 + 4 = 3+1/2 -1/2 - 4 = -4+1/2 -1/2 * 4 = -2 -1/2 / 4 = -1/8 3 + -1/2 = 2+1/2 3 - -1/2 = 3+1/2 3 * -1/2 = -1+1/2 3 / -1/2 = -6 ----- Testing shorthand arithmetic assignment on fractions 1/6 += 4 = 4+1/6 4+1/6 -= 4 = 1/6 1/6 *= 4 = 2/3 2/3 /= 4 = 1/6 4 += -1/2 = 3+1/2 3+1/2 -= -1/2 = 4 4 *= -1/2 = -2 -2 /= -1/2 = 4 -1/2 += 5 = 4+1/2 4+1/2 -= 5 = -1/2 -1/2 *= 5 = -2+1/2 -2+1/2 /= 5 = -1/2 ----- Testing shorthand arithmetic assignment using integers -1/3 += 3 = 2+2/3 2+2/3 -= 3 = -1/3 -1/3 *= 3 = -1 -1 /= 3 = -1/3 ----- Testing increment/decrement prefix and postfix Now g = -1/3 g++ = -1/3 Now g = 2/3 ++g = 1+2/3 Now g = 1+2/3 g-- = 1+2/3 Now g = 2/3 --g = -1/3 Now g = -1/3