elegant find sub-list in list

An iterator-based approach that is still based on the naive algorithm, but tries to do as much implicit looping as possible making use of .index():

def find_pivot(seq, subseq):
    n = len(seq)
    m = len(subseq)
    stop = n - m + 1
    if n > 0:
        item = subseq[0]
        i = 0
        try:
            while i < stop:
                i = seq.index(item, i)
                if seq[i:i + m] == subseq:
                    yield i
                i += 1
        except ValueError:
            return

compared to a couple of others approaches with various degrees of explicit looping:

def find_loop(seq, subseq):
    n = len(seq)
    m = len(subseq)
    for i in range(n - m + 1):
        if all(seq[i + j] == subseq[j] for j in (range(m))):
            yield i

def find_slice(seq, subseq):
    n = len(seq)
    m = len(subseq)
    for i in range(n - m + 1):
        if seq[i:i + m] == subseq:
            yield i

def find_mix(seq, subseq):
    n = len(seq)
    m = len(subseq)
    for i in range(n - m + 1):
        if seq[i] == subseq[0] and seq[i:i + m] == subseq:
            yield i

one would get:

a = list(range(10))
print(a)
# [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

b = list(range(5, 10))
print(b)
# [5, 6, 7, 8, 9]

funcs = find_pivot, find_loop, find_slice, find_mix, 
for func in funcs:
    print()
    print(func.__name__)
    print(list(func(a * 10, b)))
    aa = a * 100
    %timeit list(func(aa, b))
    random.shuffle(aa)
    %timeit list(func(aa, b))

# find_pivot
# [5, 15, 25, 35, 45, 55, 65, 75, 85, 95]
# 10000 loops, best of 3: 49.6 µs per loop
# 10000 loops, best of 3: 50.1 µs per loop

# find_loop
# [5, 15, 25, 35, 45, 55, 65, 75, 85, 95]
# 1000 loops, best of 3: 712 µs per loop
# 1000 loops, best of 3: 680 µs per loop

# find_slice
# [5, 15, 25, 35, 45, 55, 65, 75, 85, 95]
# 10000 loops, best of 3: 162 µs per loop
# 10000 loops, best of 3: 162 µs per loop

# find_mix
# [5, 15, 25, 35, 45, 55, 65, 75, 85, 95]
# 10000 loops, best of 3: 82.2 µs per loop
# 10000 loops, best of 3: 83.9 µs per loop

Note that this is ~30% faster than the currently accepted answer with the tested input.

This will get the "bonus" part of your question:

pattern = [1, 2, 3, 4]
search_list = [7,2,1,2,3,4,2,1,2,3,4,9,9,1,2,3,4,7,4,3,1,2,3,5]
cursor = 0
found = []
for i in search_list:
    if i == pattern[cursor]:
        cursor += 1
        if cursor == len(pattern):
            found.append(pattern)
            cursor = 0
    else:
        cursor = 0

For non-bonus:

pattern = [1, 2, 3, 4]
search_list = [7,2,1,2,3,4,2,1,2,3,4,9,9,1,2,3,4,7,4,3,1,2,3,5]
cursor = 0
found = []
for i in search_list:
    if i != pattern[cursor]:
        if cursor > 0:
            found.append(pattern[:cursor])
        cursor = 0
    else:
        cursor += 1

Finally, this one handles overlaps:

def find_matches(pattern_list, search_list):
    cursor_list = []
    found = []
    for element in search_list:
        cursors_to_kill = []
        for cursor_index in range(len(cursor_list)):
            if element == pattern_list[cursor_list[cursor_index]]:
                cursor_list[cursor_index] += 1
                if cursor_list[cursor_index] == len(pattern_list):
                    found.append(pattern_list)
                    cursors_to_kill.append(cursor_index)
            else:
                cursors_to_kill.append(cursor_index)
        cursors_to_kill.reverse()
        for cursor_index in cursors_to_kill:
            cursor_list.pop(cursor_index)
        if element == pattern_list[0]:
            cursor_list.append(1)
    return found

I know this question is 5 months old and already "accepted", but googling a very similar problem brought me to this question and all the answers seem to have a couple of rather significant problems, plus I'm bored and want to try my hand at a SO answer, so I'm just going to rattle off what I've found.

The first part of the question, as I understand it, is pretty trivial: just return the original list with all the elements not in the "pattern" filtered out. Following that thinking, the first code I thought of used the filter() function:

def subfinder(mylist, pattern):
    return list(filter(lambda x: x in pattern, mylist))

I would say that this solution is definitely more succinct than the original solution, but it's not any faster, or at least not appreciably, and I try to avoid lambda expressions if there's not a very good reason for using them. In fact, the best solution I could come up with involved a simple list comprehension:

def subfinder(mylist, pattern):
    pattern = set(pattern)
    return [x for x in mylist if x in pattern]

This solution is both more elegant and significantly faster than the original: the comprehension is about 120% faster than the original, while casting the pattern into a set first bumps that up to a whopping 320% faster in my tests.

Now for the bonus: I'll just jump right into it, my solution is as follows:

def subfinder(mylist, pattern):
    matches = []
    for i in range(len(mylist)):
        if mylist[i] == pattern[0] and mylist[i:i+len(pattern)] == pattern:
            matches.append(pattern)
    return matches

This is a variation of Steven Rumbalski's "inefficient one liner", that, with the addition of the "mylist[i] == pattern[0]" check and thanks to python's short-circuit evaluation, is significantly faster than both the original statement and the itertools version (and every other offered solution as far as I can tell) and it even supports overlapping patterns. So there you go.