Runtime of python's if substring in string

Question

What is the big O of the following if statement?

if \"pl\" in \"apple\":
   ...

What is the overall big O of how python determ

Answer 1

The time complexity is O(N) on average, O(NM) worst case (N being the length of the longer string, M, the shorter string you search for).

The same algorithm is used for str.index(), str.find(), str.__contains__() (the in operator) and str.replace(); it is a simplification of the Boyer-Moore with ideas taken from the Boyer–Moore–Horspool and Sunday algorithms.

See the original stringlib discussion post, as well as the fastsearch.h source code; the base algorithm has not changed since introduction in Python 2.5 (apart from some low-level optimisations and corner-case fixes).

The post includes a Python-code outline of the algorithm:

def find(s, p):
    # find first occurrence of p in s
    n = len(s)
    m = len(p)
    skip = delta1(p)[p[m-1]]
    i = 0
    while i <= n-m:
        if s[i+m-1] == p[m-1]: # (boyer-moore)
            # potential match
            if s[i:i+m-1] == p[:m-1]:
                return i
            if s[i+m] not in p:
                i = i + m + 1 # (sunday)
            else:
                i = i + skip # (horspool)
        else:
            # skip
            if s[i+m] not in p:
                i = i + m + 1 # (sunday)
            else:
                i = i + 1
    return -1 # not found

as well as speed comparisons.