Substrings

Your task is to count how many distinct substrings there are in a given string.

For example, the string abab has $7$ distinct substrings: a, b, ab, ba, aba, bab and abab.

In a file substrings.py, implement the function count_substrings that returns the number of substrings in the string given as a parameter.

The function will be tested in various situations, where the string is of length at most $20$ and consists of the characters a–z. The function should be efficient in all such situations.

def count_substrings(string):
    # TODO

if __name__ == "__main__":
    print(count_substrings("aaaa")) # 4
    print(count_substrings("abab")) # 7
    print(count_substrings("abcd")) # 10
    print(count_substrings("abbbbbb")) # 13
    print(count_substrings("aybabtu")) # 26
    print(count_substrings("saippuakauppias")) # 110