Get relative path from comparing two absolute paths

os.path.commonprefix() and os.path.relpath() are your friends:

>>> print os.path.commonprefix(['/usr/var/log', '/usr/var/security'])
'/usr/var'
>>> print os.path.commonprefix(['/tmp', '/usr/var'])  # No common prefix: the root is the common prefix
'/'

You can thus test whether the common prefix is one of the paths, i.e. if one of the paths is a common ancestor:

paths = […, …, …]
common_prefix = os.path.commonprefix(list_of_paths)
if common_prefix in paths:
    …

You can then find the relative paths:

relative_paths = [os.path.relpath(path, common_prefix) for path in paths]

You can even handle more than two paths, with this method, and test whether all the paths are all below one of them.

PS: depending on how your paths look like, you might want to perform some normalization first (this is useful in situations where one does not know whether they always end with '/' or not, or if some of the paths are relative). Relevant functions include os.path.abspath() and os.path.normpath().

PPS: as Peter Briggs mentioned in the comments, the simple approach described above can fail:

>>> os.path.commonprefix(['/usr/var', '/usr/var2/log'])
'/usr/var'

even though /usr/var is not a common prefix of the paths. Forcing all paths to end with '/' before calling commonprefix() solves this (specific) problem.

PPPS: as bluenote10 mentioned, adding a slash does not solve the general problem. Here is his followup question: How to circumvent the fallacy of Python's os.path.commonprefix?

PPPPS: starting with Python 3.4, we have pathlib, a module that provides a saner path manipulation environment. I guess that the common prefix of a set of paths can be obtained by getting all the prefixes of each path (with PurePath.parents()), taking the intersection of all these parent sets, and selecting the longest common prefix.

PPPPPS: Python 3.5 introduced a proper solution to this question: os.path.commonpath(), which returns a valid path.

os.path.relpath:

Return a relative filepath to path either from the current directory or from an optional start point.

>>> from os.path import relpath
>>> relpath('/usr/var/log/', '/usr/var')
'log'
>>> relpath('/usr/var/log/', '/usr/var/sad/')
'../log'

So, if relative path starts with '..' - it means that the second path is not descendant of the first path.

In Python3 you can use PurePath.relative_to:

Python 3.5.1 (default, Jan 22 2016, 08:54:32)
>>> from pathlib import Path

>>> Path('/usr/var/log').relative_to('/usr/var/log/')
PosixPath('.')

>>> Path('/usr/var/log').relative_to('/usr/var/')
PosixPath('log')

>>> Path('/usr/var/log').relative_to('/etc/')
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/usr/local/Cellar/python3/3.5.1/Frameworks/Python.framework/Versions/3.5/lib/python3.5/pathlib.py", line 851, in relative_to
    .format(str(self), str(formatted)))
ValueError: '/usr/var/log' does not start with '/etc'

Another option is

>>> print os.path.relpath('/usr/var/log/', '/usr/var')
log

A write-up of jme's suggestion, using pathlib, in Python 3.

from pathlib import Path
parent = Path(r'/a/b')
son = Path(r'/a/b/c/d')            

if parent in son.parents or parent==son:
    print(son.relative_to(parent)) # returns Path object equivalent to 'c/d'

Pure Python2 w/o dep:

def relpath(cwd, path):
    """Create a relative path for path from cwd, if possible"""
    if sys.platform == "win32":
        cwd = cwd.lower()
        path = path.lower()
    _cwd = os.path.abspath(cwd).split(os.path.sep)
    _path = os.path.abspath(path).split(os.path.sep)
    eq_until_pos = None
    for i in xrange(min(len(_cwd), len(_path))):
        if _cwd[i] == _path[i]:
            eq_until_pos = i
        else:
            break
    if eq_until_pos is None:
        return path
    newpath = [".." for i in xrange(len(_cwd[eq_until_pos+1:]))]
    newpath.extend(_path[eq_until_pos+1:])
    return os.path.join(*newpath) if newpath else "."

Get relative path from comparing two absolute paths

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