The keys $5,28,19,15,26,33,12,17,10$ are inserted into a hash table using the hash function $h(k)=k \bmod 9$. The collisions are resolved by chaining. After all the keys are inserted, the length of the longest chain is $\_\_\_\_$ . (answer in integer)

Consider a hash table $P[0,1, \ldots, 10]$ that is initially empty. The hash table is maintained using open addressing with linear probing. The hash function used is $h(x)=(x+7) \bmod 11$. Consider the following sequence of insertions performed on $P$ :

$$ 1,13,22,15,11,24 $$

Which of the following positions in the hash table is/are empty after these insertions are performed?

An algorithm has to store several keys generated by an adversary in a hash table. The adversary is malicious who tries to maximize the number of collisions. Let $$k$$ be the number of keys, $$m$$ be the number of slots in the hash table, and $$k > m$$. Which one of the following is the best hashing strategy to counteract the adversary?

Suppose we are given n keys, m has table slots, and two simple uniform hash functions h₁ and h₂. Further suppose our hashing scheme uses h₁ for the odd keys and h₂ for the even keys. What is the expected number of keys in a slot?