how to generate the shortest string from two string - python-3.x

Question

I would like to write a function to return the shortest string C from two string, A, B and make sure string A, B is substring of C. But the key is length of A does not have to longer than B
ex:
A: 'abcd', B: 'cde' = > C: 'abcde' # c,d is duplicated
A: 'abcd', B: 'ecd' = > C: 'abcdecd' #no character duplicated so C is A + B
A: 'abc', B: 'cdeab' = > C: 'cdeabc'
A: 'bce', B: 'eabc' = > C: 'eabce' #length of eabcd is 5, length of bceabc is 6
A: '', B: 'abc' = > C: 'abc'
A: 'abc', B: '' = > C: 'abc'
I have following function but it seems like it is not correct
def checksubstring(A, B):
if not A or not B: return A if not B else B
index, string = 0, ''
for i, c in enumerate(A):
index = index + 1 if c == B[index] else 0
string += c
return string + B[index:]

Answer 1

You can back up from the end looking for a match like:
Code:
def shortest_substring(a, b):
def checksubstring(a, b):
if not a or not b:
return b or a
for i in range(1, len(b)):
if a[len(a) - i:] == b[:i]:
return a + b[i:]
return a + b
x = checksubstring(a, b)
y = checksubstring(b, a)
return x if len(x) <= len(y) else y
Test Code:
results = [
{'A': 'abcd', 'B': 'cde', 'C': 'abcde'},
{'A': 'abcd', 'B': 'ecd', 'C': 'abcdecd'},
{'A': 'abc', 'B': 'cdeab', 'C': 'cdeabc'},
{'A': 'bce', 'B': 'eabc', 'C': 'eabce'},
{'A': '', 'B': 'abc', 'C': 'abc'},
{'A': 'abc', 'B': '', 'C': 'abc'},
]
for result in results:
assert result['C'] == shortest_substring(result['A'], result['B'])

Answer 2

You must check A,B and B,A, and after this check their results:
def checksubstring(A, B):
if not A or not B: return A if not B else B
index, string = 0, ''
for i, c in enumerate(A):
index = index + 1 if c == B[index] else 0
string += c
return string + B[index:]
def test(A, B):
s1 = checksubstring(A, B)
s2 = checksubstring(B, A)
if len(s1) > len(s2):
return s2
else:
return s1
print(test('abcd', 'cde')) # = > C: 'abcde' # c,d is duplicated
print(test('abcd', 'ecd')) # = > C: 'abcdecd' #no character duplicated so C is A + B
print(test('abc', 'cdeab')) # = > C: 'cdeabc'
print(test('bce', 'eabc')) # = > C: 'eabce' #length of eabcd is 5, length of bceabc is 6
print(test('', 'abc')) # = > C: 'abc'
print(test('abc', '')) # = > C: 'abc'