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

You can archive it in sublinear time by XOR'ing the rotated binary form for the input array:

1. get the binary representation of the array, input_binary
2. loop from i = 1 to len(input_array)/2, and for each loop, rotate the input_binary to the right by i bits, save it as rotated_bin, then compare the XOR of rotated_bin and input_binary.
3. The first i that yields 0, is the index to which is the desired substring.

Complete code:

def get_substring(arr):
    binary = ''.join(map(str, arr)) # join the elements to get the binary form

    for i in xrange(1, len(arr) / 2):
        # do a i bit rotation shift, get bit string sub_bin
        rotated_bin = binary[-i:] + binary[:-i]
        if int(rotated_bin) ^ int(binary) == 0:
            return arr[0:i]

    return None


if __name__ == "__main__":
    test = [1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1]
    print get_substring(test) # [1,0,1,1]