Solution: Double hashing is one of the best methods for open addressing because the permutations produced have many characteristics of randomly chosen permutations.

Solution: Double hashing uses a hash function of the form (h1(k) + i*h2(k))mod m where h1 and h2 are auxiliary hash functions and m is the size of the hash table.

Solution: The probe sequence depends in upon the key k since the initial probe position, the offset or both may vary.

Solution: The value h2(k) must be relatively prime to the hash table size m for the entire hash table to be searched. It can be ensured by having m in powers of 2 and designing h2 so that it produces an odd number.

Solution: The values h1(k) and h2(k) are k mod m and 1+(k mod m’) respectively where m is a prime number and m’ is chosen slightly less than m. (m’=m-1).

Solution: The running time of double hashing is Theta(m) since each possible (h1(k), h2(k)) pair yields a distinct probe sequence. Hence the performance of double hashing is better.

Solution: Double hashing has the greatest number of probe sequences thereby efficiently resolves hash collision problems.

Solution: The number 72 must be inserted at index 6.
H(k)=k mod m
H(72)= 72 mod 11
H(72)= 6.

Solution: Here the hash table is of size 13 with h1(k) = k mod 13 and h2(k) = 1 + k mod 11. Since 14 = 1 (mod 13) and 14 = 3 (mod 11), the key 14 is inserted into empty slot 9.

Solution: The value of m’ is chosen as a prime number slightly less than the value of m. Here the value of m is 19, hence the value of m’ can be chosen as 17.