reading-notes

Hash Tables

What is a Hashtable?

Terminology:

• Hash - A hash is the result of some algorithm taking an incoming string and converting it into a value that could be used for either security or some other purpose. In the case of a hashtable, it is used to determine the index of the array.
• Buckets - A bucket is what is contained in each index of the array of the hashtable. Each index is a bucket. An index could potentially contain multiple key/value pairs if a collision occurs.
• Collisions - A collision is what happens when more than one key gets hashed to the same location of the hashtable.

Why do we use them?

1. Hold unique values
2. Dictionary
3. Library

What Are they?

• Hashtables are a data structure that utilize key value pairs. This means every Node or Bucket has both a key, and a value.
• The basic idea of a hashtable is the ability to store the key into this data structure, and quickly retrieve the value. This is done through what we call a hash. A hash is the ability to encode the key that will eventually map to a specific location in the data structure that we can look at directly to retrieve the value.
• Since we are able to hash our key and determine the exact location where our value is stored, we can do a lookup in an O(1) time complexity. This is ideal when quick lookups are required.

Structure

Hashing

• Basically, a hash code turns a key into an integer. It’s very important that hash codes are deterministic: their output is determined only by their input. Hash codes should never have randomness to them. The same key should always produce the same hash code.

Creating a Hash

• A hashtable traditionally is created from an array. I always like the size 1024. this is important for index placement. After you have created your array of the appropriate size, do some sort of logic to turn that “key” into a numeric number value. Here is a simplistic hashing algorithm:
  1. Add or multiply all the ASCII values together.
  2. Multiply it by a prime number such as 599.
  3. Use modulo to get the remainder of the result, when divided by the total size of the array.

  4. Insert into the array at that index.

      Key = "Cat"
      Value = "Josie"
     
      67 + 97 + 116 = 280
     
      280 * 599 = 69648
     
      69648 % 1024 = 16
     
      # Key gets placed in index of 16. 
     

• We now know that our key Cat maps to index 16 of the array. We can view into this index and find “Josie”, our value quickly. NOTE: Production systems will have much more robust hashing algorithms that ensure even distribution of values across all buckets and avoid unnecessary collisions.
• Each index of the array can hold many types of values. The trick is how the values are stored in comparison to efficiency. Each Index of the array contain “buckets”. Each of these “buckets” holds one key/value pair combination. When there is no entry in a specific bucket, the buckets (each index of the array) all start null. The hash table starts each bucket empty and overwrites their value once a key generates a hashCode that corresponds with an index.

Collisions

• A collision occurs when more than one key hashes to the same index in an array. As mentioned earlier, a “perfect hash” will never have any collisions. To put this into perspective, the worst possible hash is one that hashes every single key to the same exact index of an array. The more keys you have hashed to a specific index, the more key/value pair combos you can potentially have.
• What would happen if two different keys resolved to be the same index of the array? This is called a collision. The hash map needs to be able to handle two keys resolving to the same index.
• If two keys ever ultimately resolved to the same index, then two calls to .Add(key, val) with different keys would overwrite each other.
• Collisions are solved by changing the initial state of the buckets. Instead of starting them all as null we can initialize a LinkedList in each one! Now if two keys resolve to the same index in the array then their key/value pairs can be stored as a node in a linked list. Each index in the array is called a “bucket” because it can store multiple key/value pairs.
• Since different keys can lead to the same bucket it’s important to store the entire key/value pair in the bucket, not just the value. The key must be stored with the value! If only values were stored in buckets then it would be impossible to determine which value to return when a key led you to a bucket.

• Here’s an actual example of just one bucket in a real hash map. In this example the two different keys "Pioneer Square" and "Alki Beach" happen to ultimately resolve to the same bucket. When we look at the bucket we see a representation of the Linked List that exists there. Pioneer Square was added first, so it’s at the front of the list. Then there’s Alki Beach as the second element in the linked list. Notice that both of them store the entire key/value pair.

  hashMap.Add("Pioneer Square", 98104);
  hashMap.Add("Alki Beach", 98116);
  Bucket 92: [{Pioneer Square: 98104} --> {Alki Beach: 98116}]
  

• If we didn’t store the key, the bucket would look like this. Accessing .get("Pioneer Square") or .get("Alki Beach") would hash the keys and still lead to bucket 92, but it would be impossible to tell which of the zip code values there to return.

  Bucket 92: [{98104} --> {98116}]
  

Storing and Reading Values

Hash maps do this to store values:

• accept a key
• calculate the hash of the key
• use modulus to convert the hash into an array index
• store the key with the value by appending both to the end of a linked list

Hash maps do this to read value:

• accept a key
• calculate the hash of the key
• use modulus to convert the hash into an array index
• use the array index to access the short LinkedList representing a bucket
• search through the bucket looking for a node with a key/value pair that matches the key you were given

Bucket Sizes

• Hash Maps can have any number of buckets. If a hash map has only a few buckets it will be densely full and have many collisions. If a hash map has more buckets it will be more sparsely populated, there will be less collisions, but there may be a lot of extra empty space.
• It’s possible to compute the “load factor” of a hash table. The load factor tells us something about how full the hash table is. A hash table can start with only a few buckets, calculate it’s own load factor, recognize when it gets too full and automatically grow and add more buckets to itself to accommodate more data.
• Recognize: calculating load factors and choosing the optimal number of buckets, and determining the best hash functions is not within the scope of this class. This class intends to introduce you to what a hash table is, how it’s implemented, what hash codes are, how to handle collisions and how to reason generally about what it means for a hash table to be more empty or more full. This class does not intend to calculate theoretical optimal performance limits for how to best balance a Hash Table.
• Here’s an example: the first hash table only has 7 buckets. The second has 100 buckets. Even though the second hash table has 100 buckets there are still some collisions. Collisions are ok! We just don’t want every key to hash to the exact same index.

Methods

• set() - When adding a new key/value pair to a hashtable:
  1. send the key to the hash() method.
  2. Once you determine the index of where it should be placed, go to that index.
  3. Check if something exists at that index already, if it doesn’t, add it with the key/value pair.
  4. If something does exist, add the new key/value pair to the data structure within that bucket.
• get() - The get() method takes in a key, gets the Hash, and goes to the index location specified. Once at the index location is found in the array, it is then the responsibility of the algorithm the iterate through the bucket and see if the key exists and return the value.
• has() - The has() method will accept a key, and return a bool on if that key exists inside the hashtable. The best way to do this is to have the contains call the hash() method and check the hashtable if the key exists in the table given the index returned.
• keys() - The keys() method returns a collection (array) of unique hash keys.
• hash() - The hash() method will accept a key as a string, conduct the hash, and then return the index of the array where the key/value should be placed.

What I Want to Know More About?

• I’m excited to try these!