AQA A’Level Hash tables - Part 1

Summary

This video script introduces hash tables as a data structure that combines the benefits of arrays and linked lists for efficient data retrieval. It explains the concept of hashing, hash functions, and how they map keys to fixed indices in a hash table. The script also addresses collisions and their resolution through rehashing and linked lists, preventing clustering and ensuring fast access to data.

Takeaways

• 📚 **Hash Tables Overview**: The script introduces hash tables as a data structure that combines the best features of arrays and linked lists for efficient data retrieval.
• 🔑 **Key Concept**: A hash table uses a hash function to map a key to a fixed index in an array, allowing for quick data access.
• 🔄 **Collision Handling**: Collisions occur when different keys map to the same index; they are handled by techniques like rehashing.
• 📈 **Advantages of Arrays**: Arrays provide quick and easy random access to elements due to their fixed nature and direct indexing.
• 🔗 **Dynamic Nature of Linked Lists**: Linked lists can grow dynamically as they store data with pointers to the next element, but lack random access efficiency.
• 🚫 **Limitations of Arrays**: Arrays are static data structures with a fixed size, making them unsuitable for situations where data size is unpredictable.
• 🔍 **Inefficiency in Linked Lists**: Searching for an item in a linked list requires traversing from the start, which can be slow for large lists.
• 🔐 **Hash Function Role**: The hash function is crucial as it consistently generates the same hash value for a given key, facilitating data retrieval.
• 🔄 **Simple Hash Function Example**: The script demonstrates a simple hash function using modulo operation to convert keys into hash values.
• 🔄 **Collision Resolution**: When a collision occurs, the next available space in the hash table is used, which can lead to clustering if not managed properly.
• 🔗 **Use of Linked Lists in Hash Tables**: Linked lists are used in hash tables to resolve collisions, allowing for efficient storage even when multiple keys hash to the same index.

Q & A

What are the main topics covered in the upcoming videos on data structures?

The upcoming videos will cover hash tables, including their concept, uses, simple hashing algorithms, collision handling through rehashing, and a comparison with arrays and linked lists.

What is the primary advantage of using arrays as a data structure?

Arrays allow for quick and easy random access to all elements due to each element being associated with its own index.

What is a limitation of the array data structure mentioned in the script?

A limitation of arrays is that they are fixed in size, making them static data structures that cannot easily grow.

How does a linked list differ from an array in terms of memory storage?

In a linked list, each element is not stored continuously in memory; instead, each element contains data and a pointer to the next element's memory address.

What is the trade-off when using a linked list compared to an array?

While linked lists are dynamic and can grow during program use, they do not allow for random access to elements and require sequential searching, which can be inefficient for large lists.

How does a hash table combine the best features of arrays and linked lists?

A hash table combines the fast access of arrays with the dynamic nature of linked lists, making it ideal for scenarios where quick lookup, deletion, or insertion is a priority.

What is a hash function and how does it relate to a hash table?

A hash function is a piece of code that takes a key and produces a hash value, which maps the key to a fixed index in the hash table. It's used to determine the storage location for data associated with a given key.

What is a collision in the context of hash tables?

A collision occurs when two keys produce the same hash value, leading to a conflict over the same index in the hash table.

How is the collision handled in the example provided in the script?

In the example, when a collision occurs, the next available space in the hash table is checked, and if that is also occupied, the data is stored in a linked list at the overflow for that index.

What is clustering, and how can it be a problem in hash tables?

Clustering is the problem that arises when multiple items are stored in the same overflow list, increasing the likelihood of further collisions and slowing down the search process.

What is the solution proposed in the script to avoid clustering?

The script suggests using linked lists to handle overflow, which helps maintain fast access times and avoids clustering by distributing colliding items across different overflow lists.

Outlines

00:00

📚 Introduction to Data Structures: Hash Tables

The video script introduces the concept of hash tables, emphasizing their importance in data structure studies. It mentions a comparison with arrays and linked lists to highlight the unique advantages of hash tables. Arrays are praised for their ability to provide quick and easy random access to elements due to their fixed nature and continuous memory allocation. However, their limitation is the inability to grow dynamically. Linked lists, on the other hand, are dynamic structures that can grow during program execution but lack the ability for random access, requiring a sequential search which can be inefficient for large lists. The script then sets the stage for a detailed exploration of hash tables, which are described as combining the best features of both arrays and linked lists, prioritizing speed in lookup, deletion, and insertion of items. A hash table is depicted as an array paired with a hash function that maps data (keys) to a fixed index, ensuring quick data retrieval.

05:03

🔑 Understanding Hash Functions and Collisions

This section delves into the mechanics of hash functions and how they translate data into hash values that correspond to indices in a hash table. It uses a simplistic hash function to demonstrate the process of mapping keys to table indices. The script also addresses the issue of collisions, which occur when different keys generate the same hash value, leading to the same index. It explains how collisions are handled by rehashing, using the next available space in the hash table. The concept of clustering, where frequent collisions in the same index can slow down data retrieval, is introduced. The paragraph concludes by discussing the use of linked lists to manage collisions efficiently, allowing for fast access while avoiding clustering issues. The video script promises to cover basic pseudocode for hash table operations in the subsequent video, including adding, searching, and removing data.

Keywords

💡Hash Tables

Hash tables are a data structure that implements an associative array abstract data type, a structure that can map keys to values. In the video, hash tables are introduced as a way to combine the best features of arrays and linked lists, offering fast access times for lookups, insertions, and deletions. The concept is central to the video's theme as it sets the stage for discussing how data can be efficiently managed and accessed.

💡Hashing Algorithms

Hashing algorithms are functions that take an input (or 'key') and return a fixed-size string of bytes. In the context of the video, simple hashing algorithms are mentioned as a method to apply to keys to determine their position in the hash table. The script uses a basic example where the hash function is the key value modulo 50, illustrating how keys are mapped to indices in the hash table.

💡Collision

A collision in hash tables occurs when two keys hash to the same index in the table. The video explains collisions as a common issue that arises when using hash tables, particularly with simplistic hash functions. An example given is when 'Dave' and 'Amy' both hash to index 1, causing a collision.

💡Rehashing

Rehashing is the process of resolving collisions in a hash table. The video mentions rehashing as a concept used to handle collisions. When a collision occurs, the script suggests checking the next available space in the hash table, which is a form of rehashing to find an alternative location for the colliding key.

💡Arrays

Arrays are a data structure that stores elements of the same type in contiguous memory locations, each indexed by integers. The video discusses arrays as a precursor to hash tables, highlighting their advantage of providing quick and easy random access to elements, which is beneficial for binary trees that require such access.

💡Linked Lists

Linked lists are a dynamic data structure consisting of a sequence of nodes, where each node contains data and a reference to the next node in the sequence. The video contrasts linked lists with arrays, noting that while they can grow dynamically, they do not allow for random access to elements, which can lead to slow search times.

💡Random Access

Random access in the context of data structures refers to the ability to access any element directly in constant time. The video emphasizes the random access feature of arrays, which allows for efficient retrieval of elements using their indices, as opposed to linked lists which require sequential access.

💡Static Data Structures

Static data structures, like arrays, have a fixed size and cannot grow beyond their initial allocation. The video points out that arrays are static, meaning they cannot easily expand once declared, which is a limitation when more data needs to be stored.

💡Dynamic Data Structures

Dynamic data structures, such as linked lists, can grow or shrink in size during the runtime of a program. The video contrasts dynamic structures with static ones, highlighting how linked lists can adapt to changing data requirements, but at the cost of not supporting random access.

💡Hash Function

A hash function is a critical component of a hash table that takes an input (or 'key') and computes a value (or 'hash value') which determines the index at which the data will be stored in the hash table. The video introduces the concept of a hash function and demonstrates how it is used to map keys to indices, using a simple hash function for illustrative purposes.

💡ASCII Character Codes

ASCII character codes are numerical representations of characters in the ASCII standard. The video script uses ASCII codes as an example to demonstrate how string data values can be converted into numerical values for the purpose of hashing, showing a practical application of character encoding in the context of hash table operations.

Highlights

Introduction to hash tables and their uses in data structures.

Explanation of simple hashing algorithms.

Definition and handling of collisions in hash tables.

Concept of rehashing to manage collisions.

Advantages and limitations of arrays as data structures.

Advantages and limitations of linked lists.

Arrays allow quick random access but are static.

Linked lists are dynamic but have slow search times.

Hash tables combine the best features of arrays and linked lists.

Hash tables are used for quick lookup, deletion, or insertion.

Hash table is an array coupled with a hash function.

Hash function maps a key to a fixed index in the hash table.

Example of a simple hash function using mod 50.

How hash functions convert string data into ASCII codes.

Collision occurs when two keys map to the same index.

Solution to collisions by checking the next available space.

Problem of clustering when using next available space.

Use of linked lists to avoid clustering in hash tables.

Benefits of fast random access and avoiding clustering.

Overview of the process for adding, searching, and removing data from a hash table.

Transcripts

over the next two videos we'll be taking

a look at the data structure hash tables

you'll become familiar with the concept

of a hash table and its uses we have to

apply simple hashing algorithms and know

what is meant by collision and how

collisions are handled by using a

concept known as rehashing before we

dive into looking at hash tables we're

first going to look at the advantages

and limitations of a couple of other

data structures these were arrays and

linked lists now array already be

familiar with and as you know we use

them to store a single data type

continuously in memory this is because

every element of an array is associated

with its own index this is a very

powerful feature of an array and it

means we have quick and easy random

access to all the elements of an array

with a single command here you can see

that we directly access a single element

of the array in this case element four

with just a single line of code this is

important you've already seen the binary

tree store their information in array

structures and require random access

directly into any element of an array a

limitation though of the array data

structure is that it's fixed inside this

is because the array stores items

continuously in memory so when you

declare it you have to fix it sighs your

on effect telling the operating system

when you declare the array to set aside

as much memory for use as you think

you're going to need there is no way to

guarantee that more memory adjacent to

your array will be available for use

later on this is why arrays can't easily

grow and they're known as static data

structures

now this next data structure is not

technically in the specification for a

QA level this called a linked list but

it's very useful data structure to know

about especially when trying to

understand hash tables a bit later a

linked list is a dynamic data structure

and as

such it could grow while a programs

being used this is because each item or

element in a linked list is not stored

continuously in memory each element in a

linked list contains the data we want

plus a pointer effectively a memory

address to the location of the next item

in the linked list in memory of course

there's price for this we now have a

dynamic data structure but we can't now

access is elements randomly if we want

to find an item in a linked list we have

to start at the beginning and we have to

follow the linked list checking each

element as we go until we find the item

we want this could make for a very

inefficient search especially if the

list is large and the item we're looking

for stored to the end so just a recap

quickly arrays allow random access to

any element but as static whereas lists

links are dynamic but clambake can be

slow to search hash tables combine the

best features of both data types and

they're most commonly used when speed of

lookup or deletion or insertion of items

is a priority so what exactly is a hash

table in effect it is simply an array

which we call a hash table which is

coupled together with a hash function

the hash function is a piece of code

which takes in some kind of data which

we call a key and then Chuck's out a

value which we call a hash value the

hash value Maps our initial key to a

fixed index in our hash table in the

first instance you use the hash function

to work out where in the hash table to

store the data for a given key the hash

function will always chuck out the same

value for any given key so later you can

use it to determine where in the hash

table a given item will be found

based on its key here we're using an

incredibly simple hash function for

demonstration purposes so the address is

going to equal value and then mod 50 in

other words it's going to take in a

numerical value or a key it's going to

perform mod 50 on it and then it's going

to spit out our key our value in this

example we have simply converted our

string data values into their

corresponding ASCII character codes and

code those values or hard-coded those

values here for simplicity of course

this would actually happen

programmatically so the numbers of our

keys here are passed one at a time into

a hash function Dave when thrown in

generates the hash value one Craig

generates the hash value three Sam nine

kerala eight and finally mark seven this

allows us to map these initial keys to

these locations in our hash table should

we ever wish to retrieve Dave from the

hash table we simply feed the key Dave

into the hash function and it will

return the position of where to find

Dave position 1 so far so good so let's

try adding another item to our hash

table this time Amy the key amy gets fed

into our hash function and it spits out

the value 1 again so what happens now

well if we go to index 1 in our hash

table we find that dave is already here

this is known as a collision one

solution is to check the next available

space index 2 we discover it's empty so

we could store Amy here instead simple

enough

okay so let's now try adding Jessie

well once again Jessie generates a hash

value of 1 and of course dave is already

in this position if we check the next

one

Amy's there Kraig them full we could now

put Jess in location for now in fact any

name which ends in letter e will

generate a hash value of 1 and this of

course is because we're using an

incredibly simplistic and inefficient

hash function a good hash function

should be designed so it tries to avoid

creating duplicate hash values however

they are unavoidable and here we have a

problem when a collision occurs we're

using the next available space and a

hash table however every time we do this

we increase the likelihood of further

collisions and this problem is known as

clustering if you've been paying

attention to the start video you

probably won't even know solution and

one of those is to use linked lists so

if we go back to our Amy example we feed

the key into the hash function and the

hash value 1 is generated we discover

Dave is already in index 1 so now we go

to our overflow for index 1 and restore

Amy here jess would end up in the linked

list

directly after amy and so on we've

gained all the benefits of fast random

access to an array type data structure

while avoiding clustering if the hat and

hash function is good we're not going to

use this over the loaf a much so it's

going to be short

we've massively sped up finding data we

simply feed a key into the hash function

go to the hash table in the location

given and if the item we want is not

there we search the overflow

sequentially okay that's a pretty

comprehensive overview of hash tables in

the next video we're going to look at

some basic pseudocode

for adding searching and removing data

from a hash table

you