Algorithm for grouping anagram words

Question

Given a set of words, we need to find the anagram words and display each category alone using the best algorithm.

input:

man car kile arc none like
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Answer 1

I used a Godel-inspired scheme:

Assign the primes P_1 to P_26 to the letters (in any order, but to obtain smallish hash values best to give common letters small primes).

Built a histogram of the letters in the word.

Then the hash value is the product of each letter's associated prime raised to the power of its frequency. This gives a unique value to every anagram.

Python code:

primes = [2, 41, 37, 47, 3, 67, 71, 23, 5, 101, 61, 17, 19, 13, 31, 43, 97, 29, 11, 7, 73, 83, 79, 89, 59, 53]


def get_frequency_map(word):
    map = {}

    for letter in word:
        map[letter] = map.get(letter, 0) + 1

    return map


def hash(word):
    map = get_frequency_map(word)
    product = 1
    for letter in map.iterkeys():
        product = product * primes[ord(letter)-97] ** map.get(letter, 0)
    return product

This cleverly transforms the tricky problem of finding subanagrams into the (also known to be tricky) problem of factoring large numbers...