Assume an open addressing hash table implementation, where the size of the array is N = 19, and that double hashing is performed for collision handling. The second hash function is defined as: d(k) = q - k mod q, where k is the key being inserted in the table and the prime number q is = 7. Use simple modular operation (k mod N) for the first hash function.

i) Show the content of the table after performing the following operations, in order: put(25), put(12), put(42), put(31), put(35), put(39), remove(31), put(48), remove(25), put(18), put(29), put(29), put(35).

ii) What is the size of the longest cluster caused by the above insertions?

iii) What is the number of occurred collisions as a result of the above operations?

iv) What is the current value of the tables load factor?