lunduniversity.lu.se

# Computer Science

## Faculty of Engineering, LTH

1. Write a class `Rational` that describes rational numbers, i.e., numbers like 22/3 or –5/6. All numbers should be in their simplest forms, e.g., 1/2 instead of 2/4 or 3/6. Implement constructs so the program in testrational.cc works correctly, (To convert a number to its simplest form, you must compute the greatest common divisor of the numerator and the denominator. The classical GCD algorithm is Euclid's algorithm, but there are faster algorithms that don't use division. See, for example, Binary GCD.)
2. In shapetest.cc three objects `aShape`, `aSqua`, and `aCircle` are created, and the `print()` function is used to check the identity (type) of each object. Everything seems to work correctly, but when object types are checked in another way the results are wrong. Explain the results and correct the classes so both checks produce the same results.
3. In shapearraytest.cc we assume that we have fixed the error from assignment 2. We now store a mix of `Square` and `Circle` objects in a vector. The results are wrong -- the objects seem to lose their type again. Explain why this happens and fix the error,