Elementary Data Structures
A data structure is a particular way of organising data in a computer so that it can
be used effectively. The idea is to reduce the space and time complexities of
different tasks.
Need Of Data Structure:
The structure of the data and the synthesis of the algorithm are
relative to each other. Data presentation must be easy to
understand so the developer, as well as the user, can make an
efficient implementation of the operation.
Data structures provide an easy way of organising, retrieving,
managing, and storing data.
Here is a list of the needs for data.
Data structure modification is easy.
It requires less time.
Save storage memory space.
Data representation is easy.
Easy access to the large database
Classification/Types of Data Structures:
1. Linear Data Structure
2. Non-Linear Data Structure.
Linear Data Structure:
Elements are arranged in one dimension ,also known as linear dimension.
Example: lists, stack, queue, etc.
Non-Linear Data Structure
Elements are arranged in one-many, many-one and many-many dimensions.
Example: tree, graph, table, etc.
1. Array:
An array is a collection of data items stored at contiguous memory locations.
The idea is to store multiple items of the same type together. This makes it
easier to calculate the position of each element by simply adding an offset to
a base value, i.e., the memory location of the first element of the array
(generally denoted by the name of the array).
2. Linked Lists:
Like arrays, Linked List is a linear data structure. Unlike arrays, linked list
elements are not stored at a contiguous location; the elements are linked
using pointers.
3. Stack:
Stack is a linear data structure which follows a particular order in which the
operations are performed. The order may be LIFO(Last In First Out) or
FILO(First In Last Out). In stack, all insertion and deletion are permitted at
only one end of the list.
Stack Operations:
push(): When this operation is performed, an element is inserted into the
stack.
pop(): When this operation is performed, an element is removed from the
top of the stack and is returned.
top(): This operation will return the last inserted element that is at the top
without removing it.
size(): This operation will return the size of the stack i.e. the total number of
elements present in the stack.
isEmpty(): This operation indicates whether the stack is empty or not.
4. Queue:
Like Stack, Queue is a linear structure which follows a particular order in
which the operations are performed. The order is First In First Out (FIFO).
In the queue, items are inserted at one end and deleted from the other end. A
good example of the queue is any queue of consumers for a resource where
the consumer that came first is served first. The difference between stacks
and queues is in removing. In a stack we remove the item the most recently
added; in a queue, we remove the item the least recently added.
Queue Operations:
Enqueue(): Adds (or stores) an element to the end of the queue..
Dequeue(): Removal of elements from the queue.
Peek() or front(): Acquires the data element available at the front node of
the queue without deleting it.
rear(): This operation returns the element at the rear end without removing
it.
isFull(): Validates if the queue is full.
isNull(): Checks if the queue is empty.
5. Binary Tree:
Unlike Arrays, Linked Lists, Stack and queues, which are linear data
structures, trees are hierarchical data structures. A binary tree is a tree data
structure in which each node has at most two children, which are referred to
as the left child and the right child. It is implemented mainly using Links.
A Binary Tree is represented by a pointer to the topmost node in the tree. If
the tree is empty, then the value of root is NULL. A Binary Tree node
contains the following parts.
1. Data
2. Pointer to left child
3. Pointer to the right child
6. Binary Search Tree:
A Binary Search Tree is a Binary Tree following the additional properties:
The left part of the root node contains keys less than the root node key.
The right part of the root node contains keys greater than the root node key.
There is no duplicate key present in the binary tree.
A Binary tree having the following properties is known as Binary search tree
(BST).
7. Heap:
A Heap is a special Tree-based data structure in which the tree is a complete binary tree.
Generally, Heaps can be of two types:
Max-Heap: In a Max-Heap the key present at the root node must be greatest among the keys
present at all of its children. The same property must be recursively true for all sub-trees in that
Binary Tree.
Min-Heap: In a Min-Heap the key present at the root node must be minimum among the keys
present at all of its children. The same property must be recursively true for all sub-trees in that
Binary Tree.
8. Hashing Data Structure:
Hashing is an important Data Structure which is designed to use a special
function called the Hash function which is used to map a given value with a
particular key for faster access of elements. The efficiency of mapping
depends on the efficiency of the hash function used.
Let a hash function H(x) maps the value x at the index x%10 in an Array.
For example, if the list of values is [11, 12, 13, 14, 15] it will be stored at
positions {1, 2, 3, 4, 5} in the array or Hash table respectively.
9. Matrix:
A matrix represents a collection of numbers arranged in an order of rows and
columns. It is necessary to enclose the elements of a matrix in parentheses or
brackets.
A matrix with 9 elements is shown below.
10. Trie:
Trie is an efficient information retrieval data structure. Using Trie, search
complexities can be brought to an optimal limit (key length). If we store
keys in the binary search tree, a well-balanced BST will need time
proportional to M * log N, where M is maximum string length and N is the
number of keys in the tree. Using Trie, we can search the key in O(M) time.
However, the penalty is on Trie storage requirements.
11. Graph:
Graph is a data structure that consists of a collection of nodes (vertices)
connected by edges. Graphs are used to represent relationships between
objects and are widely used in computer science, mathematics, and other
fields. Graphs can be used to model a wide variety of real-world systems,
such as social networks, transportation networks, and computer networks.
Applications of Data Structures:
Data structures are used in various fields such as:
Operating system
Graphics
Computer Design
Blockchain
Genetics
Image Processing
Simulation,
etc.
Algorithms and its complexity(Time and Space)
Analysing Algorithms, Asymptotic Notations, Priority Queue, Quick Sort.
