Detect whether sequence is a multiple of a subsequence in Python

Question

I have a tuple of zeros and ones, for instance:

(1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1)

It turns out:

(1, 0, 1, 1, 1, 0, 1, 1, 1,          


        

Answer 1

The following solution is O(N^2), but has the advantage of not creating any copies (or slices) of your data, as it is based on iterators.

Depending on the size of your input, the fact you avoid making copies of the data can result in a significant speed-up, but of course, it would not scale as well for huge inputs as algorithms with lower complexity (e.g. O(N*logN)).

[This is the second revision of my solution, the first one is given below. This one is simpler to understand, and is more along the lines of OP's tuple-multiplication, only using iterators.]

from itertools import izip, chain, tee

def iter_eq(seq1, seq2):
    """ assumes the sequences have the same len """
    return all( v1 == v2 for v1, v2 in izip(seq1, seq2) )

def dup_seq(seq, n):
    """ returns an iterator which is seq chained to itself n times """
    return chain(*tee(seq, n))

def is_reps(arr, slice_size):
    if len(arr) % slice_size != 0:
        return False
    num_slices = len(arr) / slice_size
    return iter_eq(arr, dup_seq(arr[:slice_size], num_slices))

s = (1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1)
for i in range(1,len(s)):
    if is_reps(s, i):
        print i, s[:i]
        break

[My original solution]

from itertools import islice

def is_reps(arr, num_slices):
    if len(arr) % num_slices != 0:
        return False
    slice_size = len(arr) / num_slices
    for i in xrange(slice_size):
        if len(set( islice(arr, i, None, num_slices) )) > 1:
            return False
    return True

s = (1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1)
for i in range(1,len(s)):
    if is_reps(s, i):
        print i, s[:i]
        break

You can avoid the call to set() by using something like:

def is_iter_unique(seq):
    """ a faster version of testing len(set(seq)) <= 1 """
    seen = set()
    for x in seq:
        seen.add(x)
        if len(seen) > 1:
            return False
    return True

and replacing this line:

if len(set( islice(arr, i, None, num_slices) )) > 1:

with:

if not is_iter_unique(islice(arr, i, None, num_slices)):