Distribution

Your task is to computer the length distribution of the distinct substrings of a given string.

For example, the distinct substrings of the string abab are a, b, ab, ba, aba, bab and abab. Their length distribution is as follows:

• length $1$: substring count $2$
• length $2$: substring count $2$
• length $3$: substring count $2$
• length $4$: substring count $1$

In a file distribution.py, implement the function create_distribution that returns the distinct substring length distribution for the string given as a parameter. The distribution must be returned as a dictionary as shown in the examples.

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 create_distribution(string):
    # TODO

if __name__ == "__main__":
    print(create_distribution("aaaa"))
    # {1: 1, 2: 1, 3: 1, 4: 1}
    
    print(create_distribution("abab"))
    # {1: 2, 2: 2, 3: 2, 4: 1}
    
    print(create_distribution("abcd"))
    # {1: 4, 2: 3, 3: 2, 4: 1}

    print(create_distribution("abbbbbb"))
    # {1: 2, 2: 2, 3: 2, 4: 2, 5: 2, 6: 2, 7: 1}

    print(create_distribution("aybabtu"))
    # {1: 5, 2: 6, 3: 5, 4: 4, 5: 3, 6: 2, 7: 1}