In this project, we will need to implement a Java class for hash tables which are equipped with the search,

insertion, and deletion methods with respect to the following techniques for resolving collisions:

Separate chaining. The index for a key $x$ is obtained by the hashing function:

$h(x)=x$@ $TABL{E}_S$IZE

$(10$ points$)$ Search: To check if a specific key $x$ exists within the hash table, locate its list using

$h(x)$ and traverse it$.$ If such an element with key $x$ is found, the search is successful; otherwise, it

indicates that the key does not exist within the table.

$(15$ points$)$ Insertion: To insert an element in a hash table, the algorithm locates the list with the

corresponding hash index $h(x).$ If the element isn't already in this list, it is added to the beginning.

This approach allows multiple keys with the same hash index to be stored without issues.

$(15$ points$)$ Deletion: To remove a key from a hash table, first find the list at the hash index $h(x).$

If the list has the key, remove it$.$ If not, do nothing.

Linear probing. The index for a key $x$ is obtained by the hashing function

$h_i(x)=(x$: $TABL{E}_S$IZE $+i)TABL{E}_S$IZE

$(10$ points$)$ Search: To determine if key $x$ exists, iteratively probe from the initial hash index $h(x)$

until an empty slot or the starting index is encountered. If found, return the index of $x$; if not, the

search fails.

$(15$ points$)$ Insertion: This method follows the search method but inserts $x$ into the first unoccupied

slot. If it cycles back to the initial hash without finding an open slot, insertion fails.

$(15$ points$)$ Deletion: Proceed with the search to locate $x.$ Upon finding $x,$ remove it just by

marking this slot out of the hash table and return.

The content of each element is a positive integer key$-$value pair. You may use the type int to represent

the key$-$value pair.

$(10$ points$)$ You are also required to provide a method to display the content of the hash table. Your

display should show not only the keys but also the associated values.

$(5$ points$)$ Implementing the following test case using the separate chaining technique.

Creating an empty hash table of size $11.$

Consecutively insert the following keys into the hash table and display the table content after each

insertion.

$54,19,23,34,125,37,45,42$

$$ Deleting the key $125$ and displaying the table content.

$$ Searching the key $45$ and displaying the table content.

$$ Inserting the key $68$ and displaying the table content.

$4.(5$ points$)$ Implementing the above test case using the linear probing hashing technique