Data structures are fundamental components in data science, enabling efficient storage, organization, and manipulation of information. Mastery of advanced data structures is vital for programmers, as they underpin the design and implementation of effective algorithms and software systems. The efficiency of algorithms often hinges on the choice and implementation of data structures, influencing both time and space complexity. We’ll look at a few advanced data structures in this article.

## Classification of Advanced Data Structures

Advanced data structures have evolved significantly, branching into diverse categories to meet varied computational needs. These broad classifications includes:

- Primitive Data Structures
- Composite or Non-Primitive Data Structures
- Abstract Data Types
- Linear Data Structure
- Tree
- Hash
- Graphs

## Primitive Data Structures

Elementary data structures serve as the foundational components for representing data in programming languages. In general, there are eight data types, includes boolean, byte, char, short, long, int, float, and double data types, each tailored to store specific types of data efficiently.

### 1. Boolean

The boolean data type is a fundamental primitive used to represent logical values, typically true or false. It consumes minimal memory and plays a crucial role in decision-making and logical operations within programs. Let’s take a simple program and see how it works.

```
public class BooleanExample {
public static void main(String[] args) {
boolean isSunny = true;
boolean isRaining = false;
if (isSunny) {
System.out.println("It's sunny today.");
} else {
System.out.println("It's not sunny today.");
}
if (isRaining) {
System.out.println("It's raining today.");
} else {
System.out.println("It's not raining today.");
}
}
}
```

**Output:**

```
It's sunny today.
It's not raining today.
```

### 2. Byte

The byte data type is a fundamental component of primitive data structures, representing small integer values. It occupies 8 bits or 1 byte of memory and can store values from -128 to 127 (signed) or 0 to 255 (unsigned). They are crucial for memory optimization and constructing complex data structures like arrays and buffers. Let’s take a simple program and see how it works.

```
public class ByteExample {
public static void main(String[] args) {
byte positiveByte = 100; // Range: -128 to 127
byte negativeByte = -50;
System.out.println("Positive Byte: " + positiveByte);
System.out.println("Negative Byte: " + negativeByte);
System.out.println("Sum: " + (positiveByte + negativeByte));
System.out.println("Difference: " + (positiveByte - negativeByte));
System.out.println("Product: " + (positiveByte * negativeByte));
}
}
```

**Output:**

```
Positive Byte: 100
Negative Byte: -50
Sum: 50
Difference: 150
Product: -5000
```

### 3. Char

The char data type is a simple building block used in programming to represent single characters, like letters, numbers, and symbols. It’s typically stored as 1 byte of memory, allowing it to hold values from 0 to 255, or a single character. Let’s take a simple program and see how it works.

```
public class CharExample {
public static void main(String[] args) {
```*// Declare and initialize a char variable*
char myChar = 'A';
*// Print the value of myChar*
System.out.println("The value of myChar is: " + myChar);
*// Increment the ASCII value of myChar*
myChar++;
*// Print the updated value of myChar*
System.out.println("After incrementing, myChar is now: " + myChar);
}
}

**Output:**

```
The value of myChar is: A
After inc
```*rementing, myChar is now: B*

### 4. Short

The short data type is a primitive structure for storing integers within a limited range, typically occupying 16 bits of memory. It can represent values from -32,768 to 32,767. Let’s take a simple program and see how it works.

```
public class ShortExample {
public static void main(String[] args) {
```*// Declare a variable of type short*
short myShortNumber = 1000;
*// Print the value of the short variable*
System.out.println("Value of myShortNumber: " + myShortNumber);
*// Increment the value of the short variable*
myShortNumber++;
*// Print the updated value of the short variable*
System.out.println("Updated value of myShortNumber: " + myShortNumber);
}
}

**Output:**

```
Value of myShortNumber: 1000
Updated value of myShortNumber: 1001
```

### 5. Int

The int data type is a fundamental primitive structure used to represent integers in programming. It stores whole numbers ranging from -2147483648 to 2147483647 and supports basic arithmetic, bitwise, and comparison operations. Let’s take a simple program and see how it works.

```
public class SimpleSum {
public static void main(String[] args) {
int num1 = 7;
int num2 = 9;
int sum = num1 + num2;
System.out.println("The sum of " + num1 + " and " + num2 + " is: " + sum);
}
}
```

**Output:**

```
The sum of num1 and num2 is: 16
```

### 6. Long

The long data type is a primitive structure for storing integral numbers with a wider range than int. It typically occupies 64 bits of memory, enabling storage of larger integer values. It’s useful for scenarios requiring numbers beyond the range of int, such as timestamps or large numerical computations. Let’s take a simple program and see how it works.

```
public class LongDataTypeExample {
public static void main(String[] args) {
```*// Define a long variable*
long bigNumber = 123456789012345L; *// Note the 'L' suffix to indicate it's a long value*
*// Print the value of the long variable*
System.out.println("The value of the bigNumber variable is: " + bigNumber);
*// Perform some arithmetic operations with long*
long result = bigNumber * 2;
*// Print the result*
System.out.println("Twice the value of bigNumber is: " + result);
}
}

**Output:**

```
The value of the bigNumber variable is: 123456789012345
Twice the value of bigNumber is: 246913578024690
```

### 7. Float

The float data type is a primitive structure used in programming languages for storing single-precision floating-point numbers. This data type supports fractional numbers ranging from 3.4e038 to 3.4e+038. It occupies 4 bytes of memory and is commonly employed in scenarios where approximate values suffice, such as scientific computing and graphics processing. Let’s take a simple program and see how it works.

```
public class Main {
public static void main(String[] args) {
// Declare and initialize a float variable
float floatValue = 3.14f; // Note the 'f' suffix to specify float literal
// Print the float value
System.out.println("The value of floatValue is: " + floatValue);
// Perform some arithmetic operations
float result = floatValue * 2;
System.out.println("Double of floatValue is: " + result);
// Update the float value
floatValue = 4.5f;
System.out.println("Updated value of floatValue is: " + floatValue);
}
}
```

**Output:**

```
The value of floatValue is: 3.14
Double of floatValue is: 6.28
Updated value of floatValue is: 4.5
```

### 8. Double

The double data type is a primitive data type used to store double-precision floating-point numbers. It offers a larger range and higher precision compared to single-precision floating-point numbers. In languages like Java, it’s represented as a 64-bit floating-point type, allowing values from approximately 4.9e-324 to 1.7976931348623157e+308 with a precision of about 15 decimal digits. Let’s take a simple program and see how it works.

```
public class CircleAreaCalculator {
public static void main(String[] args) {
```*// Define the radius of the circle*
double radius = 5.0;
*// Calculating the area of the circle using the formula: pi * radius^2*
double area = Math.PI * radius * radius;
*// Print the result*
System.out.println("The area of the circle with radius " + radius + " is: " + area);
}
}

**Output:**

```
The area of the circle with radius 5.0 is: 78.53981633974483
```

## Composite or Non-Primitive Data Structures

Composite or non-primitive data structures are formed by combining primitive data types. They provide a means to organize and manage more complex data arrangements, allowing for greater flexibility and efficiency in data manipulation. Here are some key examples:

- Array
- Record
- Union

### 1. Array

Arrays are one of the most fundamental composite data structures, capable of storing elements of the same data type in contiguous memory locations. They offer quick access to individual elements through indexing and are widely used in various algorithms and applications. Let’s take a simple program and see how it works.

```
public class ArrayExample {
public static void main(String[] args) {
// Declare and initialize an array of integers
int[] num = {1, 2, 3, 4, 5};
// Print out the elements of the array
System.out.println("Elements of the array:");
for (int i = 0; i < num.length; i++) {
System.out.println(num[i]);
}
}
}
```

**Output:**

```
Elements of the array:
1
2
3
4
5
```

### 2. Record

Also known as structures or tuples in some programming languages, records are composite data structures that allow for the grouping of different data types under a single entity. Each element within a record is typically referred to as a field or member, and records are useful for representing structured data, such as database records or complex objects. Let’s take a simple program and see how it works.

```
public class RecordExample {
public static void main(String[] args) {
// Create a new record instance
Person person = new Person("John", 30);
// Print out the record details
System.out.println("Name: " + person.name());
System.out.println("Age: " + person.age());
}
// Define a record named Person with two components: name and age
record Person(String name, int age) {
// Constructor, accessors, and other methods are automatically generated by the compiler
}
}
```

**Output:**

```
Name: John
Age: 30
```

### 3. Union

Unions are a special type of composite data structure that enables the storage of different data types in the same memory location. Unlike arrays or records, unions can only hold one value at a time, with the size of the union being determined by the largest member within it. They are often used in low-level programming for efficient memory utilization or in scenarios where multiple data representations are possible. Let’s take a simple program and see how it works.

```
public class UnionExample {
public static void main(String[] args) {
```*// Simulate a union-like behavior with two different types*
int intValue = 10;
String stringValue = "Hello";
*// Print out the values*
System.out.println("Value 1: " + intValue);
System.out.println("Value 2: " + stringValue);
}
}

**Output:**

```
Value 1: 10
Value 2: Hello
```

## Abstract Data Types

Abstract Data Types (ADTs) provide a high-level view of data and operations, abstracting away implementation details. They define the behavior of a data type without specifying how it should be implemented. Here are some key examples:

- List
- Queue
- Stack

### 1. List

A list is a linear arrangement of elements in a data structure, where each element occupies a defined position or index. Lists can be dynamic in size, meaning elements can be added or removed at any position within the list. Let’s take a simple program and see how it works.

```
import java.util.ArrayList;
import java.util.List;
public class ListExample {
public static void main(String[] args) {
// Create a list of integers
List<Integer> numbers = new ArrayList<>();
// Add elements to the list
numbers.add(10);
numbers.add(20);
numbers.add(30);
// Access elements by index
System.out.println("Element at index 0: " + numbers.get(0));
System.out.println("Element at index 1: " + numbers.get(1));
System.out.println("Element at index 2: " + numbers.get(2));
//
```*Remove an element*
numbers.*remove(1);*
System.out.println("After removing element at index 1: " + numbers);
}
}

**Output:**

```
Element at index 0: 10
Element at index 1: 20
Element at index 2: 30
After
```*removing element at index 1: [10, 30]*

### 2. Queue

A queue adheres to the First-In-First-Out (FIFO) principle, wherein elements are inserted at one end (rear) and extracted from the opposite end (front) within the data structure. It maintains a linear order and supports operations like enqueue (adding elements) and dequeue (removing elements). Commonly used in scenarios requiring orderly processing, such as task scheduling and breadth-first search algorithms, queues efficiently manage elements in a sequential fashion, ensuring fairness and orderly execution of tasks. Let’s take a simple program and see how it works.

```
import java.util.LinkedList;
import java.util.Queue;
public class QueueExample {
public static void main(String[] args) {
```*// Create a queue*
Queue<Integer> queue = new LinkedList<>();
*// Enqueue elements*
queue.offer(10);
queue.offer(20);
queue.offer(30);
*// Dequeue elements*
System.out.println("Dequeued element: " + queue.poll());
System.out.println("Dequeued element: " + queue.poll());
*// Peek at the front element*
System.out.println("Front element: " + queue.peek());
}
}

**Output:**

```
Dequeued element: 10
Dequeued element: 20
Front element: 30
```

### 3. Stack

A stack is a fundamental abstract data type (ADT) characterized by its Last-In-First-Out (LIFO) principle, where the last element added is the first one to be removed. This linear structure organizes elements in a sequential manner, restricting access to only the topmost element for insertion, removal, or inspection. Typical actions performed on a stack involve push (placing an element atop), pop (eliminating the uppermost element), and peek (observing the uppermost element without eliminating it). Stacks find applications in various scenarios, such as expression evaluation, function call management, undo mechanisms, and backtracking algorithms, owing to their simplicity and efficiency in managing elements in a last-in-first-out fashion. Let’s take a simple program and see how it works.

```
import java.util.Stack;
public class StackExample {
public static void main(String[] args) {
```*// Create a stack*
Stack<Integer> stack = new Stack<>();
*// Push elements onto the stack*
stack.push(10);
stack.push(20);
stack.push(30);
*// Pop elements from the stack*
System.out.println("Popped element: " + stack.pop());
System.out.println("Popped element: " + stack.pop());
*// Peek at the top element*
System.out.println("Top element: " + stack.peek());
}
}

**Output:**

```
Popped element: 30
Popped element: 20
Top element: 10
```

## Linear Data Structure

Linear data structures arrange and store data elements sequentially, with each element having both a predecessor and a successor, except for the initial and final elements. Here’s a brief explanation of each linear data structure:

- Control tables
- Image
- Matrix
- Lists

**Control Tables:**Control tables are data structures used to manage and control the flow of operations or processes within a system. They typically consist of rows and columns, where each row represents an operation or process, and columns contain related data or attributes. Control tables are commonly used in computer systems for task scheduling, resource allocation, and configuration management.**Image:**In the context of linear data structures, an image is represented as a one-dimensional array of pixels arranged sequentially. Every pixel within the image is associated with a particular position within the array, allowing for efficient storage and manipulation of image data. Linear image representation facilitates operations such as image processing, compression, and transmission in computer graphics and digital imaging applications.**Matrix:**A matrix is a two-dimensional array of elements arranged in rows and columns. While matrices are often represented as rectangular grids, they can also be stored linearly in memory by flattening the rows or columns into a one-dimensional array. Linear storage of matrices simplifies memory management and enables efficient matrix operations such as addition, multiplication, and inversion, commonly used in mathematical computations, data analysis, and graphics rendering.**Lists:**Lists are dynamic data structures that store a collection of elements in a linear sequence. Each element in the list is linked to its successor, forming a chain of nodes. Lists may be either singly linked, where each node points to the next node, or doubly linked, where each node points to both the next and previous nodes. Lists offer flexibility in adding, removing, and accessing elements, making them suitable for various applications such as task management, data processing, and implementing other data structures like stacks and queues.

## Tree

A tree structure comprises nodes interconnected through edges in a hierarchical arrangement. It consists of a root node, which has zero or more child nodes, and each child node may have its own children. Trees are commonly used to represent hierarchical relationships, such as organizational structures, file systems, and family trees. Examples of Tree are

- Binary Tree
- Decision Tree

### 1. Binary Tree

A binary tree is a hierarchical data structure made up of nodes, each of which can have a maximum of two children: a left child and a right child. The highest node in a binary tree is termed the root, from which each node can branch into zero, one, or two child nodes. Nodes without children are termed leaf nodes.

Binary trees are commonly used for efficient sorting, searching, and data retrieval algorithms. In a binary search tree (BST), for example, every node’s left child has a value smaller than the node’s value, and every right child has a value greater than the node’s value. This property allows for fast searching of elements within the tree.

Binary trees can be traversed in different ways, including in-order, pre-order, and post-order traversals, each providing a different sequence of node visitation. These traversals are used in various algorithms and operations on binary trees, such as searching for elements, inserting new elements, and deleting elements.

### 2. Decision Tree

A decision tree is an algorithm in machine learning that constructs a model resembling a tree, representing decisions and their possible results. It recursively splits the dataset based on feature attributes to minimize impurity or variance. At each node, it selects the best attribute for splitting, aiming to create homogeneous subsets. Once constructed, the tree can classify or predict new data by traversing from the root to a leaf node, where the majority class (for classification) or mean value (for regression) determines the outcome. Decision trees offer simplicity and interpretability but can overfit. Techniques like pruning and limiting tree depth help mitigate overfitting.

## Hash

Hashing is a technique used to map data of arbitrary size to fixed-size values, typically integers, known as hash codes. It’s commonly used for data indexing, retrieval, and storage efficiency. Hash functions are designed to quickly generate unique hash codes for different inputs.

**Hash List:**A hash list, alternatively recognized as a hash table, is a data structure employing hash functions to assign keys to values, facilitating effective storage and retrieval of data. It typically consists of an array where elements are stored based on their hash codes. Collisions, when two different keys produce the same hash code, are handled using techniques like chaining or open addressing.**Double Hashing:**Double hashing is a collision resolution technique used in hash tables to deal with collisions. When a collision occurs, instead of simply placing the colliding element in the next available slot (as in linear probing), double hashing calculates a second hash function of the key and uses it to determine the next available slot, providing better distribution of elements and reducing clustering.

## Graphs

Graphs are mathematical structures that consist of vertices (nodes) and edges (connections) between them. They’re used to model relationships between objects. Here’s a concise explanation of different types of graphs:

**Complete Graph:**A complete graph is a graph in which every distinct pair of vertices is linked by a single, unique edge. In other words, every vertex is directly connected to every other vertex in the graph. Complete graphs are denoted by the symbol K_n, where n represents the number of vertices. Complete graphs are commonly used in theoretical contexts and algorithm analysis.**Regular Graph:**A regular graph is characterized by each vertex having an equal number of neighbors or edges. In other words, the degree of every vertex in the graph is the same. Regular graphs can be of various degrees, such as a regular graph of degree 2 (each vertex has exactly 2 neighbors) or a regular graph of degree k (each vertex has exactly k neighbors). Regular graphs are used in various applications, including network design, social network analysis, and routing algorithms.

## Conclusion

- Advanced Data structures are essential for efficient storage, organization, and manipulation of information across various applications in programming.
- The classification of advanced data structures encompasses primitive, composite, abstract data types, linear structures, trees, hash tables, and graphs, each tailored to unique computational needs.
- Proficiency in advanced data structures is crucial for optimizing program efficiency and performance, enabling tasks ranging from data processing to machine learning algorithms.
- Exploring different types of advanced data structures provides valuable insights into their characteristics, applications, and implications, enabling informed decisions in algorithm design and implementation.