Problem $1$: Consider inserting the keys $10,22,31,4,15,28,17,88$ into a hash table of length $m=9$ using open addressing with the auxiliary hash function $H(K)=$KmodM. Illustrate the results of inserting the keys using linear probing. $(18$ points$)$

Steps: Linear probing: When inserting a key K in a table of size M $,$ with hash function $H(K)$

Set index $=H(K)$

If table location index already contains the key, no need to insert it$.$ Done!

Else if table location index is empty, insert key there. Done!

Else collision. Set index index $+1$