Find length of smallest window that contains all the characters of a string in another string

Question

Recently i have been interviewed. I didn\'t do well cause i got stuck at the following question

suppose a sequence is given : A D C B D A B C D A C D and search seq

Answer 1

Here is my solution in Python. It returns the indexes assuming 0-indexed sequences. Therefore, for the given example it returns (9, 11) instead of (10, 12). Obviously it's easy to mutate this to return (10, 12) if you wish.

def solution(s, ss):
    S, E = [], []
    for i in xrange(len(s)):
        if s[i] == ss[0]:
            S.append(i)
        if s[i] == ss[-1]:
            E.append(i)
    candidates = sorted([(start, end) for start in S for end in E
                        if start <= end and end - start >= len(ss) - 1],
                        lambda x,y: (x[1] - x[0]) - (y[1] - y[0]))
    for cand in candidates:
        i, j = cand[0], 0
        while i <= cand[-1]:
            if s[i] == ss[j]:
                j += 1
            i += 1
        if j == len(ss):
            return cand

Usage:

>>> from so import solution
>>> s = 'ADCBDABCDACD'
>>> solution(s, 'ACD')
(9, 11)
>>> solution(s, 'ADC')
(0, 2)
>>> solution(s, 'DCCD')
(1, 8)
>>> solution(s, s)
(0, 11)
>>> s = 'ABC'
>>> solution(s, 'B')
(1, 1)
>>> print solution(s, 'gibberish')
None

I think the time complexity is O(p log(p)) where p is the number of pairs of indexes in the sequence that refer to search_sequence[0] and search_sequence[-1] where the index for search_sequence[0] is less than the index forsearch_sequence[-1] because it sorts these p pairings using an O(n log n) algorithm. But then again, my substring iteration at the end could totally overshadow that sorting step. I'm not really sure.

It probably has a worst-case time complexity which is bounded by O(n*m) where n is the length of the sequence and m is the length of the search sequence, but at the moment I cannot think of an example worst-case.