Question IV $[$Hashing$]$: Suppose we have a hash table of size $7,$ and a simple hash function defined as

$h(k)=$kmod$7$

We need to insert the following sequence of keys: $10,22,31,4,15,28,17.$

$(4$ points$)$ Using separate chaining, show how these keys would be inserted into the hash table. Draw the structure of each linked list in each slot after all keys are inserted.

$(8$ points$)$ Using open addressing with linear probing, show the resulting table after inserting all keys. For each insertion, indicate how the position was determined.

$(3$ points$)$ Compare the results: Based on the filled table structures, discuss the advantages and disadvantages of separate chaining versus linear probing in this case.