A good hash function h(x) behaves in practice very close to the uniform hashing assumption analyzed in class, but is a deterministic function. That is, h(x) = k each time x is used as an argument to h(). Designing good hash functions is hard, and a bad hash function can cause a hash table to quickly exit the sparse loading regime by overloading some buckets and under-loading others. Good hash functions often rely on beautiful and complicated insights from number theory, and have deep connections to pseudorandom number generators and cryptographic functions. In practice, most hash functions are moderate to poor approximations of uniform hashing. Consider the following hash function. Let U be the universe of strings composed of the characters from the alphabet = [A,...,Z], and let the function f(xi) return the index of a letter xi , e.g., f(A) = 1 and f(Z) = 26. Finally, for an m-character string x m, dene h(x) = ([Pm i=1 f(xi)] mod `), where ` is the number of buckets in the hash table. That is, our hash function sums up the index values of the characters of a string x and maps that value onto one of the ` buckets.

1.Using strings as input, that are choosen uniformly random from a text file we get 50% of the file and then hash them using h(x). Produce a histogram showing the corresponding distribution of hash locations when L = 175. Label the axes of your gure. Briey describe what the gure shows about h(x), and justify your results in terms of the behavior of h(x).