Algorithm: Determine if an array of arrays of characters can be concatenated in order, into a substring of haystack.


[['a','A','@'], ['b','B','8'], ['c','(','[']]

This list can be combined by selecting from each of the subarrays in order, such as:

abc, ab(, ab[, Abc, Ab( etc.

Are any of these combinations substrings of the search string?

"123 easy as Ab(" # True
"123 easy as Abb" # False
"123 easy as @b(" # True
"123 easy as Abc" # False

Python 3

combos = [['a','A','@'], ['b','B','8'], ['c','(','[']]
search = "123 easy as Ab(" # True

def find_mutated_string(offset, combos, search):
    for i, char in enumerate(search):
        for mutant in combos[offset]:
            if mutant == char:
                if len(combos) == (offset+1):
                    # Last letter combo found
                    return True
                    return find_mutated_string(offset+1, combos, search[i+1:])
    # Didn't find mutant char in search string
    return False

print(find_mutated_string(0, combos, search))


You don't reset the offset when there is a mismatch, so "123 easy as b(" also returns True. Just add:

        offset = 0

optional parameter offset

The caller of the function should not care about the offset if he wants to check whether a combination is part of the string. I would change the method signature to def find_mutated_string2(combos, search, offset=0). Then your user doesn't need to worry about this


Python has the in statement.

Your code says

    for mutant in combos[offset]:
        if mutant == char:

but actually mean: if char in combos[offset]

Since in in a list traverses the list to look for a match, while set uses a lookup, defining the combos as sets helps here

combos = [{"@", "A", "a"}, {"8", "B", "b"}, {"(", "[", "c"}]

def find_mutated_string2(combos, search, offset=0):
    for i, char in enumerate(search):
        if char in combos[offset]:
            if len(combos) == (offset + 1):
                return True
                return find_mutated_string2(combos, search[i+1:], offset+1)
            offset = 0
    return False

match substring

You could write a helper function that takes a substring and checks whether this matches the combo's

def matches_combos(substring, combos):
    return len(substring) == len(combos) and all(
        char in combo for char, combo in zip(substring, combos)

This can be easily tested:

test_cases = {
    "abc": True,
    "Ab[": True,
    "abd": False,
    "ab": False,
    "abcd": False,
for substring, answer in test_cases.items():
    result = matches_combos(substring, combos)
    assert result == answer


If your string is long, you will run into the recursion limit.

for i in range(10000):
        _ = find_mutated_string2(combos, "a"*i)
    except RecursionError:
        print(f"fails for string length: {i}")
fails for string length: 5921

for a recursionlimit of 3000

You can easily rewrite this proble iteratively

def find_mutated_string3(combos, search):
    if len(search) < len(combos):
        return False
    for i in range(len(search) - 2):
        substring = search[i : i + len(combos)]
        if matches_combos(substring, combos):
            return True

or using any

def find_mutated_string4(combos, search):
    if len(search) < len(combos):
        return False
    return any(
        matches_combos(search[i : i + len(combos)], combos)
        for i in range(len(search) - 2)
  • \$\begingroup\$ Thanks a bunch! How likely am I to hit the recursion limit? I guess the search string must be at least 998 characters or so for this to happen? \$\endgroup\$ – deed02392 May 8 at 16:01

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