Recursive functions for sorting

Question

I made a few recursive functions for learning purposes which do a variety of tasks. Here is my current and functioning code:

def separate(p,l):
    ''' recursive function when is passed a predicate and a list returns a 2-tuple
    whose 0 index is a list of all the values in the argument list for which the     
    predicate returns True,and whose 1 index is a list of all the values in the  
    argument list for which the predicate returns False.'''
    if len(l) == 0:
        return ([],[])
    else:
        (true_list, false_list) = separate(p,l[1:])
        if p(l[0]):
            return ([l[0]] + true_list, false_list)
        else:
            return (true_list, [l[0]] + false_list)


def is_sorted(s):
    ''' recursive function when passed a list returns a bool telling whether or not 
    the values in the list are in non-descending order: lowest to highest allowing 
    repetitions. '''
    if len(s) <= 1:
        return True
    elif s[0] < s[1]:
        return is_sorted(s[1:])
    else:
        return False


def sort(l):
    ''' recursive function when passed a list; it returns a new list (not mutating 
    the passed one) with every value in the original list, but ordered in non-
    descending order. '''
    if len(l) == 0:
        return []
    else:
        (before, after) = separate(lambda i: i < l[0], l[1:])
        return sort(before) + [l[0]] + sort(after)


def compare(a,b):
    ''' a recursive function when is passed two str arguments; it returns one of 
    three str values: '<’, '=’, or '>’ which indicates the relationship between the 
    first and second parameter.'''
    if a == '' and b == '':
        return '='
    if a == '' and b != '':
        return '<'
    if a != '' and b == '':
        return '>'
    if a[0] > b[0]:
        return '>'
    if a[0] < b[0]:
        return '<'
    else:
        return compare(a[1:],b[1:])

Is there a way to write these recursive functions in a cleaner/concise way? Any help would be great.

Answer 1

is_sorted() does not behave as described or as expected. It requires elements to be strictly increasing rather than non-descending.

The implementation and docstring could be shorter as well.

def is_sorted(list):
    """Recursively checks if the elements in the list are in non-descending order."""
    return len(list) <= 1 or (list[0] <= list[1] and is_sorted(list[1:]))

I'd expect that trimming lists at the end would be more efficient (though the code definitely looks weirder):

def is_sorted(list):
    """Recursively checks if the elements in the list are in non-descending order."""
    return len(list) <= 1 or (list[-2] <= list[-1] and is_sorted(list[:-1]))

---

compare() has some redundant checks.

Here, I feel that the else is incongruous. Either rely on the early returns, or use else in conjunction with elif everywhere.

def compare(a,b):
    """Lexicographically compares strings a and b, returning '<', '=', or '>'."""
    if a == '' and b == '':
        return '='
    if a == '':
        return '<'
    if b == '':
        return '>'
    if a[0] > b[0]:
        return '>'
    if a[0] < b[0]:
        return '<'
    return compare(a[1:], b[1:])

Instead of checking for == '', consider checking the length, so that the function can operate on lists as well.

Answer 2

I recommend you be more consistent in not combining if followed by a statement sequence ending in return with an else (I left out the comments):

def separate(p,l):
    if len(l) == 0:
        return ([],[])
    (true_list, false_list) = separate(p,l[1:])
    if p(l[0]):
        return ([l[0]] + true_list, false_list)
    return (true_list, [l[0]] + false_list)

as you do e.g. in compare().

In compare() I would nest the conditions (arbitrarily based on a):

def compare(a,b):
    if a == '':
        if b == '':
            return '='
        return '<'
    if a != '':
        if b == '':
            return '>'
    if a[0] > b[0]:
        return '>'
    if a[0] < b[0]:
        return '<'
    return compare(a[1:],b[1:])

That way it is more clear to me that compare() never ends without a return value.

Your comments should at least use triple double quotes (PEP8) and you should try to conform to PEP 257 (docstring conventions).