sorted strings are keysand the values are arrays of the corresponding strings from the original input def find_anagrams dictionary )sorted_string_to_anagrams collections defaultdict (listfor in dictionary sorts the string uses it as key and then appends the original string as another value into hash table sorted_string_to_anagrams ['joinsorted ( ))append (sreturn group for group in sorted_string_to_anagrams values (if lengroup > the computation consists of calls to sort and insertions into the hash table sorting all the keys has time complexity (nm log mthe insertions add time complexity of (nm)yielding (nm log mtime complexity in total design of hashable class consider class that represents contacts for simplicityassume each contact is string suppose it is hard requirement that the individual contacts are to be stored in list and it' possible that the list contains duplicates two contacts should be equal if they contain the same set of stringsregardless of the ordering of the strings within the underlying list multiplicity is not importanti three repetitions of the same contact is the same as single instance of that contact in order to be able to store contacts in hash tablewe first need to explicitly define equalitywhich we can do by forming sets from the lists and comparing the sets in our contextthis implies that the hash function should depend on the strings presentbut not their orderingit should also consider only one copy if string appears in duplicate form it should be pointed out that the hash function and equals methods below are very inefficient in practiceit would be advisable to cache the underlying set and the hash coderemembering to void these values on updates class contactlist def __init__ (self names )''names is list of strings ''self names names def __hash__ (self)conceptually we want to hash the set of names since the set type is mutable it cannot be hashed therefore we use frozenset return hashfrozenset (self names )def __eq__ (self other )return set(self names =setother names def merge_contact_lists contacts )