Exercise $1$: $($Close Hashing$)$

Hashing is a widely used technique to store records in a way that allows efficient access. The idea is to use a hash function to map the unique data keys into a hash table. However, this mapping can result in collisions, i$.$e$.,$ mapping more than one key to the same value. This is resolved by using open hashing, in which linked lists are used to store them. The second approach is close hashing, in which the key is stored in an alternate location if another key has already taken its place in the table. In this lab, we will implement the close hashing approach.

Your function should look like this:

Hash$\_$table $=$ Close$\_$Hashing$($input$\_$keys, hash$\_$table$\_$size$)$

Parameters are defined below:

input$\_$keys: an array of size N containing the keys

hash$\_$table$\_$size: Size of hash table $($an Mx$1$ array where $\backslash (\backslash$mathrm$\{$M$\}>=\backslash$mathrm$\{$N$\}\backslash ))$

hash$\_$table: The output after storing each key from the input array

Write a code to implement this and paste your code below. Use the hash function mod$($key$,\backslash (\backslash$mathrm$\{$M$\})\backslash ).$ Indicate any unfilled values in the hash table by $-1.$