Question

I’ve been learning functional programming for some time, but I haven’t read somewhere about sorting with the functional programming languages.

I know the sorting algorithms that are based on value exchanges are hard to implement with the functional idea, but I want to know that are there any sorting algorithms for use in functional programming? What are they?

Thank you.

Answer 1

In a functional language you write a function that given a list returns a sorted list, not touching (of course) the input.

Consider for example merge sorting… first you write a function that given two already sorted lists returns a single sorted list with the elements of both in it. For example:

def merge(a, b):
    if len(a) == 0:
        return b
    elif len(b) == 0:
        return a
    elif a[0] < b[0]:
        return [a[0]] + merge(a[1:], b)
    else:
        return [b[0]] + merge(a, b[1:])

then you can write a function that sorts a list by merging the resulting of sorting first and second half of the list.

def mergesort(x):
    if len(x) < 2:
        return x
    else:
        h = len(x) // 2
        return merge(mergesort(x[:h]), mergesort(x[h:]))

About Python syntax:

• L[0] is the first element of list L
• L[1:] is the list of all remaining elements
• More generally L[:n] is the list of up to the n-th element, L[n:] the rest
• A + B if A and B are both lists is the list obtained by concatenation
• [x] is a list containing just the single element x

PS: Note that python code above is just to show the concept… in Python this is NOT a reasonable approach. I used Python because I think it’s the easiest to read if you know any other common imperative language.