Two strings are isomorphic if we can find a two-way mapping between their characters that makes the two strings identical. We keep two maps to validate the two-way mapping.
Two maps we maintain are: s -> t and t -> s. For s[i] and t[i], either they have not been mapped yet or s[i] has been mapped to t[i] and t[i] has been mapped to s[i].
Time: 
class Solution:
def isIsomorphic(self, s: str, t: str) -> bool:
s_t_map, t_s_map = {}, {}
for a, b in zip(s, t):
if (a not in s_t_map) != (b not in t_s_map):
return False
if a not in s_t_map:
s_t_map[a] = b
t_s_map[b] = a
continue
if s_t_map[a] != b or t_s_map[b] != a:
return False
return True
unreasonably effective 
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