AQA A’Level Hash tables - Part 1
Summary
TLDRThis 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
📚 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.
🔑 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.
Mindmap
Keywords
💡Hash Tables
💡Hashing Algorithms
💡Collision
💡Rehashing
💡Arrays
💡Linked Lists
💡Random Access
💡Static Data Structures
💡Dynamic Data Structures
💡Hash Function
💡ASCII Character Codes
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
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