Suppose we would like to insert a sequence of numbers into a hash table with table size 8 using the three open addressing methods, with the primary hash function h1(k) = k mod 8, the secondary hash function h2(k) = 1 + (k mod 7), and the constants c1 = c2 = 1/2 (in quadratic probing).

(a)(10 points) If the sequence of numbers is , please successively insert these numbers into the following tables.

(b)(3 points) For the hashing functions and table size we used in part (a), does the linear probing fully utilize the table? How about the quadratic probing and double hashing ?

index linear L double quadratic