A collision occurs when you have two values that hash to the same location. There are several methods for dealing with collisions. Here are the two most common:

Open Addressing $-$ Also called closed hashing

Chaining $-$ also called open hashing

Fortunately for you and this exercise you are not going to have to worry about implementing either of these.

$(18)$

To reduce the number of collisions several hash function have been introduced:

Knuth Hash Function

The Knuth hash function flows something like this:

Initialize the return value to the size of the string

For each character within the string

Rotate the return value left by five bits

XOR the return value with the character being examined

Modulus the return value by the number of elements in the array $($hash table$)$

Bernstein Hash Function

D$.$J$.$ Bernstein is a research professor at the University of Illinois at Chicago. His hash function is as follows:

Initialize the return value to $5381$

For each character in the string

Multiply the return value by $33$

Add the character

Modulus the return value by the number of spaces in the hash table

You may wonder why $5381$ is used to initialize the return value. You will find these kinds of "magic numbers" in most hash algorithms. The reason is that through testing these numbers were found to have far less collisions.

Here is an example of the Bernstein hash function: