**Compare and contrast a hash table and an STL map. How is hash table implemented? If the number of inputs is small, which data structure options can be used instead of a hash table?**

Hash table:

1. In a hash table, a value is stored by calling a hash function on a key. Values are not stored in sorted order.

2. An insert or lookup can be done in amortized O(1) time(assuming few collisions in the hash table).

3. In hash table, one must also handle potential collisions. This is often done by chaining, which means to create a linked list of all the values whose keys map to a particular index.

STL map:

1. STL map inserts the key/value pairs into a binary search tree based on the keys. There is no need to handle collisions.

2. Since the tree is balanced, the insert and lookup time is guaranteed to be O(log N).

**How is a hash table implemented?**

A hash table is traditionally implemented with an array of linked lists. When we want to insert a key/value pair, we map the key to an index in the array using a hash function. The function is then inserted into the linked list at that position.

Note that the elements in a linked list at a particular index of the array do not have the same key. Rather, hashFunction(key) is the same for these values. Therefore, in order to retrieve the value for a specific key, we need to store in each node both the exact key and the value.

To summarize, the hash table will be implemented with an array of linked lists, where each node in the linked list holds two pieces of data: the value and the original key. In addition, we will want to node the following design criteria:

1. We want to use a good hash function to ensure that the keys are well distributed. If they are not well distributed, then we would get a log of collisions and the speed to find an element would decline.

2. No matter how good our hash function is we will still have collisions, so we need a method for handling them. This often means chaining via a linked list, bit it’s not the only way.

3. We may also wish to implement methods to dynamically increase or decrease the hash table size depending on capacity. For example, when the ratio of the number of elements to the table size exceeds a certain threshold , we may wish to increase the hash table size. This would mean creating a new hash table and transferring the entries from the old table to the new table. Because this is an expensive operation, we want to be careful to not do it too often.

**What can be used instead of a hash table, if the number of inputs is small?**

One can use an STL map or a binary tree. Although this takes O(log(n)) time, the number of inputs may be small enough to make this time negligible.