Course topic 13 exercises¶

Open Hashing¶

[JSAV Placeholder: open_hashing]

Hash tables¶

 int y(x, buckets) {
   int result = 0;
   while ( x != 0 ){
     // Multiply the first and last digits of x and add it to result.
     result += last_digit(x) * first_digit(x)
     x = remove_first_and_last_digit(x)
     }
 return (result mod buckets)
 }

Question 1

What bucket will the key 12345678 hash into, when the hash function is the y shown above and there are 100 buckets?

Question 2

Which one of the following hash functions distributes the following items {”Eetu”, ”Kai”, ”Nelli”, ”Kaisa”, ”Elias”} most evenly, if there are 9 buckets? (Note. All of the hash functions given are actually quite bad.)

the first letter’s running number in the alphabet mod 9.

the length of the key mod 9.

the first letter’s running number in the alphabet multiplied by the length of the key mod 9.

Question 3

What is the load factor of the hash table from the previous question? Give your answer as a fraction.