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Engineering LibreTexts

19.5: Sets

  • Page ID
    40847
  • In Section 13.6 I use dictionaries to find the words that appear in a document but not in a word list. The function I wrote takes d1, which contains the words from the document as keys, and d2, which contains the list of words. It returns a dictionary that contains the keys from d1 that are not in d2.

    def subtract(d1, d2):
        res = dict()
        for key in d1:
            if key not in d2:
                res[key] = None
        return res
    

    In all of these dictionaries, the values are None because we never use them. As a result, we waste some storage space.

    Python provides another built-in type, called a set, that behaves like a collection of dictionary keys with no values. Adding elements to a set is fast; so is checking membership. And sets provide methods and operators to compute common set operations.

    For example, set subtraction is available as a method called difference or as an operator, -. So we can rewrite subtract like this:

    def subtract(d1, d2):
        return set(d1) - set(d2)
    

    The result is a set instead of a dictionary, but for operations like iteration, the behavior is the same.

    Some of the exercises in this book can be done concisely and efficiently with sets. For example, here is a solution to has_duplicates, from Exercise 10.15.7, that uses a dictionary:

    def has_duplicates(t):
        d = {}
        for x in t:
            if x in d:
                return True
            d[x] = True
        return False
    

    When an element appears for the first time, it is added to the dictionary. If the same element appears again, the function returns True.

    Using sets, we can write the same function like this:

    def has_duplicates(t):
        return len(set(t)) < len(t)
    

    An element can only appear in a set once, so if an element in t appears more than once, the set will be smaller than t. If there are no duplicates, the set will be the same size as t.

    We can also use sets to do some of the exercises in Chapter 9. For example, here’s a version of uses_only with a loop:

    def uses_only(word, available):
        for letter in word: 
            if letter not in available:
                return False
        return True
    

    uses_only checks whether all letters in word are in available. We can rewrite it like this:

    def uses_only(word, available):
        return set(word) <= set(available)
    

    The <= operator checks whether one set is a subset of another, including the possibility that they are equal, which is true if all the letters in word appear in available.

    As an exercise, rewrite avoids using sets.

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