Problems

All of these problems are for practice. You are freely encouraged to work together and you do not need to submit any of this work for a grade.

1. Python's abs(x) function accepts a single argument that can be an integer or floating-point number. Given the beginning of a hypothetical implementation of such a function that validates the parameter.

   Spoiler: my code

2. The random module includes a function randint(a, b) that produces a random integer in the open interval $[a,b]$. Those parameters must be integer and it must be that $a \leq b$. Give the presumed beginning of the implementation of such a function that validates the parameters.

   Spoiler: my code

3. Python's fractions module provides a function gcd(a,b) to compute the greatest common divisor of integers a and b (since that is a common subtask when simplifying a fraction).

   We will not concern ourselves with the algorithm for computing that gcd (typically Euclid's algorithm), nor will we concern ourselves with how gcd's are defined when negative values are given. Instead, assume we were to author our own version of such a function and insist that both parameters be nonnegative integers. Give the beginning of the function body that validates those parameters.

   Spoiler: my code

4. Python's int constructor can also be used to compute the integer value associated with a string in a non-decimal base. For example, in base 8 (i.e., octal) the string '132' represents the decimal value 90, as it represents $1 \cdot 8^2 + 3 \cdot 8^1 + 2 \cdot 8^0 = 64 + 24 + 2$. You can determine this in Python by sending the base as a second optional parameter to the constructor, as in int('132', 8) which returns 90. Of course, when working in base 8, you are only allowed to use digits 0 through 7 (just as in decimal you are only allowed to use digits 0 through 9). A call to int('139', 8) will raise a ValueError.

   We will not concern ourselves with the logic of doing such a base conversion (though it is an interesting exercise). Instead, we look at the task of rigorously error checking the parameters to determine if they are legitimate. Instead of using the int constructor, assume we want to design a function with signature

   def toDecimal(value, base):

   such that base is an integer between 2 and 10 (inclusive), and value is a nonemptystring that is composed entirely of valid digits for the given base. Your task is to write the beginning of such a function body to perform the appropriate error-checking.

   Spoiler: my code

5. We have previously considered the implementation of a function longest(words) which accepts a nonempty sequence of strings and returns the longest among them. Assuming that the sequence must be either a list of strings or a tuple of strings, give the beginning of the implementation of such a function that validates the input.

   Spoiler: my code

6. For the previous problem, we considered tuples or lists as the way to describe a sequence, but functions such as Python's max will accept more general objects (such as sets, ranges, comprehension generators) that are not actually lists or tuples. For such a parameter to be valid, it must simply support the for-loop syntax.

   Knowing that an attempt at a for-loop over a non-iterable object raises a TypeError, redo the previous problem to allow for this more general type of iterable parameter.

   Spoiler: my code