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Mentoring

Problem and Challenges

The problem asks you to classify triangle types, encoded as a list of three side lengths.

Reasonable Solution

def is_valid(sides):
    if not sides[0]:
        return False
    return all(side * 2 < sum(sides) for side in sides)


def equilateral(sides):
    return is_valid(sides) and len(set(sides)) == 1


def isosceles(sides):
    return is_valid(sides) and len(set(sides)) < 3


def scalene(sides):
    return is_valid(sides) and len(set(sides)) == 3

Note: This exercise appears fairly early in the concept tree so students may not yet be familiar with generators.

Talking Points

Sets and unique values

This exercise could be solved by explicitly comparing various sides against each other. For example, equilateral could be solved using all(side == sides[0] for side in sides). However, len(set()) provides a quick way to count unique values in an iterable. Recognizing that counting the number of unique side lengths can be used to solve this simplifies the problem greatly. Using sets also solves the need to handle different ways of combining various sides.

Validation

Given that all three functions require validation, having a separate function for validation avoids code duplication.

Side validation can be done by computing all the side combinations and checking one_side < sum(other_sides). However, that requires computing different combinations of sides. Instead, given the condition one_side < sum(other_sides), add one_side to both sides of the comparison. This gives one_side + one_side < sum(other_sides) + one_side or 2 * one_side < sum(sides). Alternatively, all(side < sum(sides) - side for side in sides).

Decorators

Validation can be taken one step further in the form of a decorator, if the student is comfortable with decorators:

# Decorator function.
def is_valid(func):

    def wrapped(sides):
        if not sides[0]:
            return False
        if not all(side * 2 < sum(sides) for side in sides):
            return False
        return func(sides)

    return wrapped


# Decorator in use.
@is_valid
def equilateral(sides):
    return len(set(sides)) == 1