Part 1: Reduction
We have seen how to map a function across a list of data, with the return
value of each function call placed into a list of results. For example,
you summed together two lists of numbers using
map using code such as this.
ipython and type
def sum(x, y): """Function to return the sum of x and y""" return x + y a = [1, 2, 3, 4, 5] b = [6, 7, 8, 9, 10] result = map( sum, a, b ) print(result)
This returns a list of results. However, what if we want to sum every value in the returned list of results to form a single value? We could write the code by hand, e.g. type
total = 0 for i in range(0,len(result)): total += result[i] print("Total = %d" % total)
This process of summing a list of numbers into a total is an example
of “reduction”. The list of numbers has been reduced into a total by
adding each value onto a running total. Reduction is the complement
to mapping, and as such, Python has a
reduce function, e.g. type
total = reduce( sum, result ) print(total)
You should see that
reduce has returned the result
reduce takes two required arguments and one additional, optional argument:
The reduction function used to reduce a pair of arguments to a single result, e.g.
sumtakes two arguments and returns the sum of those arguments. This can be any function that accepts two arguments and returns a single result.
The list of values to be reduced.
An (optional) initial value that is used as the first value for the reduction.
For example, type
a = [1, 2, 3, 4, 5] total = reduce( sum, a, 10 ) print(total)
You should see that the total is
25. Why do you think the answer is 25?
reduce applies the reduction function (in this case
cumalatively from left to right along the items of a list. If an initial
value is supplied then this is used as the first value. Otherwise, the
first value is the result of the reduction function applied to the
first two items in the list. In the above case,
- total = 10
- total = sum(total,1)
- total = sum(total,2)
- total = sum(total,3)
- total = sum(total,4)
- total = sum(total,5)
The result is thus 25, i.e. (((((10+1)+2)+3)+4)+5).
The reduction function can be any function that accepts two arguments
and returns a single value. For example, let’s now use
to calculate the product of all of the values
in the list. To do this, we need to create a new function that
will take in two arguments and return their product. Type into
def multiply(x, y): """Return the product of the two arguments""" return x*y total = reduce( multiply, a ) print(total)
You should see that the product is
120. Is this
what you expected? In this case,
- total = multiply(1, 2)
- total = multiply(total, 3)
- total = multiply(total, 4)
- total = multiply(total, 5)
i.e. it set
total equal to ((((1x2)x3)x4)x5) = 120.
Note that the reduction function is not limited to just numbers. You can write a reduction function to reduce any types of object together. For example, we could use reduce to join together some strings. Type into ipython;
def join_strings(x, y): return "%s %s" % (x,y) a = [ "cat", "dog", "mouse", "fish" ] result = reduce( join_strings, a ) print(result)
You should see the result
cat dog mouse fish.
countlines.py script so that, in addition
to printing out the total number of lines in each
it also uses
reduce to print out the total number of
lines in all Shakespeare plays.
If you get stuck or want some inspiration, a possible answer is given here.