Consider inserting the keys 10, 22, 31, 4, 15, 28, 17, 88, 59 into a hash table of

length m = 11 using open addressing with the primary hash function h(k) = k mod m.

Illustrate the result of inserting these keys using the following probing methods; draw the hash

table after each insertion.

a) Linear probing with = 1.

b) Quadratic probing with = 3 and = 1.

c) Double hashing with h₂(k) = 1 + (k mod (m - 1)).