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Engineering LibreTexts

1.7: Map, Filter and Reduce

  • Page ID
    17012
  • To add up all the numbers in a list, you can use a loop like this:

    def add_all(t):
        total = 0
        for x in t:
            total += x
        return total
    

    total is initialized to 0. Each time through the loop, x gets one element from the list. The += operator provides a short way to update a variable. This augmented assignment statement:

        total += x
    

    is equivalent to:

        total = total + x
    

    As the loop executes, total accumulates the sum of the elements; a variable used this way is sometimes called an accumulator.

    Adding up the elements of a list is such a common operation that Python provides it as a built-in function, sum:

    >>> t = [1, 2, 3]
    >>> sum(t)
    6
    

    An operation like this that combines a sequence of elements into a single value is sometimes called reduce.

    Exercise \(\PageIndex{1}\)

    Write a function called nested_sum that takes a nested list of integers and add up the elements from all of the nested lists.

    Sometimes you want to traverse one list while building another. For example, the following function takes a list of strings and returns a new list that contains capitalized strings:

    def capitalize_all(t):
        res = []
        for s in t:
            res.append(s.capitalize())
        return res
    

    res is initialized with an empty list; each time through the loop, we append the next element. So res is another kind of accumulator.

    An operation like capitalize_all is sometimes called a map because it “maps” a function (in this case the method capitalize) onto each of the elements in a sequence.

    Exercise \(\PageIndex{2}\)

    Use capitalize_all to write a function named capitalize_nested that takes a nested list of strings and returns a new nested list with all strings capitalized.

    Another common operation is to select some of the elements from a list and return a sublist. For example, the following function takes a list of strings and returns a list that contains only the uppercase strings:

    def only_upper(t):
        res = []
        for s in t:
            if s.isupper():
                res.append(s)
        return res
    

    isupper is a string method that returns True if the string contains only upper case letters.

    An operation like only_upper is called a filter because it selects some of the elements and filters out the others.

    Most common list operations can be expressed as a combination of map, filter and reduce. Because these operations are so common, Python provides language features to support them, including the built-in function map and an operator called a “list comprehension.”

    Exercise \(\PageIndex{3}\)

    Write a function that takes a list of numbers and returns the cumulative sum; that is, a new list where the ith element is the sum of the first i+1 elements from the original list. For example, the cumulative sum of [1, 2, 3] is [1, 3, 6].

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