TREE -NON-LINEAR DATA STRUCTURE

Tree is a non-linear data structure that consists of nodes arranged in a hierarchical order. Each node in a tree has one or more child nodes, and each child node has one parent node. The topmost node in a tree is called the root node, and the nodes at the bottom of the tree are called leaf nodes.

In Java, trees are implemented using the Tree class. The Tree class provides methods for traversing the tree, as well as for accessing and modifying the nodes in the tree.

import java.util.Tree;   public class TreeExample {     public static void main(String[] args) {     Tree<Integer> tree = new Tree<>();       tree.add(10);     tree.add(5);     tree.add(15);     tree.add(2);     tree.add(7);     tree.add(12);     tree.add(17);       System.out.println("The root node is: " + tree.getRoot()); // 10     System.out.println("The children of the root node are: " + tree.getChildren(tree.getRoot())); // [5, 15]     System.out.println("The parent of the node with value 12 is: " + tree.getParent(12)); // 7   } }

This code creates a tree and adds seven nodes to the tree. The code then prints the root node, the children of the root node, and the parent of the node with value 12.

Here is an explanation of how the code works:

• The Tree class is imported from the java.util package.
• A new Tree object is created.
• Seven nodes are added to the tree.
• The root node, the children of the root node, and the parent of the node with value 12 are printed.

 

GRAPHS

graph is a non-linear data structure that consists of nodes and edges. The nodes represent the elements in the graph, and the edges represent the relationships between the elements.

In Java, graphs are implemented using the Graph class. The Graph class provides methods for traversing the graph, as well as for accessing and modifying the nodes and edges in the graph.

import java.util.Graph;   public class GraphExample {     public static void main(String[] args) {     Graph<String> graph = new Graph<>();       graph.addVertex("A");     graph.addVertex("B");     graph.addVertex("C");     graph.addVertex("D");       graph.addEdge("A", "B");     graph.addEdge("A", "C");     graph.addEdge("B", "C");     graph.addEdge("C", "D");       System.out.println("The neighbors of the node A are: " + graph.getNeighbors("A")); // ["B", "C"]     System.out.println("The distance between the nodes A and C is: " + graph.distance("A", "C")); // 1   } }

This code creates a graph and adds four nodes and four edges to the graph. The code then prints the neighbors of the node A and the distance between the nodes A and C.

Here is an explanation of how the code works:

• The Graph class is imported from the java.util package.
• A new Graph object is created.
• Four nodes and four edges are added to the graph.
• The neighbors of the node A and the distance between the nodes A and C are printed.

HASH TABLES (HASHING)

hash table is a data structure that maps keys to values. The keys are used to access the values, and the values can be anything. Hash tables are often used to store data in a way that allows for quick lookups.

In Java, hash tables are implemented using the HashMap class. The HashMap class provides methods for adding, removing, and accessing keys and values in the hash table.

import java.util.HashMap;   public class HashTableExample {     public static void main(String[] args) {     HashMap<String, Integer> hashTable = new HashMap<>();       hashTable.put("A", 1);     hashTable.put("B", 2);     hashTable.put("C", 3);       System.out.println(hashTable.get("A")); // 1     System.out.println(hashTable.get("B")); // 2     System.out.println(hashTable.get("C")); // 3   } }

This code creates a hash table and adds three key-value pairs to the hash table. The code then prints the values associated with the keys "A", "B", and "C".

Here is an explanation of how the code works:

• The HashMap class is imported from the java.util package.
• A new HashMap object is created.
• Three key-value pairs are added to the hash table.
• The values associated with the keys "A", "B", and "C" are printed.

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COMPARISON OF TREES, GRAPHS, AND HASH TABLES:

Data Structure	Description	Advantages	Disadvantages
Tree	A hierarchical data structure where each node has at most one parent node, except for the root node which has no parent node.	Easy to traverse and search.	Can be inefficient for storing large amounts of data.
Graph	A non-linear data structure where each node can have multiple parent nodes and multiple child nodes.	Flexible and can represent complex relationships.	Can be difficult to traverse and search.
Hash table	A data structure that maps keys to values.	Fast for searching and inserting data.	Can be inefficient for storing large amounts of data.

KEY DIFFERENCES BETWEEN TREES, GRAPHS, AND HASH TABLES

Property	Tree	Graph	Hash table
Data structure type	Hierarchical	Non-linear	Associative
Relationship between nodes	Parent-child	Adjacent	Key-value
Traversal	Depth-first or breadth-first	Breadth-first or depth-first	Not applicable
Searching	Efficient	Inefficient	Efficient
Inserting data	Efficient	Inefficient	Efficient
Deleting data	Efficient	Inefficient	Efficient

 

Examples of when to use each data structure:

• Trees: Trees are often used to represent hierarchical data, such as the file system on a computer.
• Graphs: Graphs are often used to represent relationships between entities, such as the social network of friends.
• Hash tables: Hash tables are often used to store data that is accessed frequently, such as the login credentials for a website.

RECURSION

 

RECURSION

RECURSION

Recursion is a programming technique where a function calls itself. This may sound confusing, but it can be used to solve some problems that would be difficult or impossible to solve with other techniques.

In Java, recursion is implemented using the return statement. The return statement can be used to return a value from a function, or it can be used to call the function recursively.

public class Factorial {   public static int factorial(int n) {     if (n == 0) {       return 1;     } else {       return n * factorial(n - 1);     }   }   public static void main(String[] args) {     System.out.println(factorial(5)); // 120   } }

This code defines a function called factorial() that calculates the factorial of a number. The factorial of a number is the product of all the positive integers less than or equal to that number. For example, the factorial of 5 is 120.

The factorial() function is recursive. It calls itself to calculate the factorial of the number minus 1. The base case of the recursion is when the number is 0. In this case, the function simply returns 1.

The main() method of the code calls the factorial() function with the number 5. The factorial() function then recursively calculates the factorial of 5 and returns the value 120.

comparison of recursive and iterative methods in Java:

Recursive Method	Iterative Method
A method that calls itself.	A method that uses a loop to repeat a block of code.
Can be used to solve problems that are naturally recursive.	Can be used to solve problems that are not naturally recursive.
Can be more concise and elegant than iterative methods.	Can be easier to understand and debug than recursive methods.
Can be slower than iterative methods.	Can be faster than recursive methods.
Uses more stack space than iterative methods.	Uses less stack space than recursive methods.

example of a recursive method in Java:

public static int factorial(int n) {

    if (n == 0) {
        return 1;
    } else {
        return n * factorial(n - 1);
    }
}
 example of an iterative method in Java:
public static int factorial(int n) {
    int factorial = 1;
    for (int i = 1; i <= n; i++) {
        factorial *= i;
    }
    return factorial;
}

 

 Circular linked Stack, QUEUE -Data structure

Circular linked

 

circular linked list is a linked list in which the last node points back to the first node, forming a circle. This means that there is no "end" to the list, and you can start traversing the list from any node and eventually end up back at the node you started from.

Circular linked lists are often used in applications where it is necessary to keep track of the current position in the list, such as in a game where players take turns. They can also be used to implement queues and other data structures.

Here are some of the advantages of using circular linked lists:

• They are easy to implement.
• They can be used to implement queues and other data structures.
• They are efficient for traversing the list from any node.

Here are some of the disadvantages of using circular linked lists:

• They can be more difficult to debug than other types of linked lists.
• They can be less efficient for inserting and deleting nodes in the middle of the list.

stack

stack is a linear data structure that follows the last-in, first-out (LIFO) principle. This means that the last element added to the stack is the first element that is removed. Stacks are often used in applications where it is necessary to keep track of the order in which things were added, such as in a call stack or a undo/redo stack.

In Java, stacks are implemented using the Stack class. The Stack class provides methods for pushing and popping elements from the stack, as well as for checking if the stack is empty or full.

import java.util.Stack;

 

public class StackExample {

 

  public static void main(String[] args) {

    Stack<Integer> stack = new Stack<>();

 

    stack.push(1);

    stack.push(2);

    stack.push(3);

 

    System.out.println(stack.pop()); // 3

    System.out.println(stack.pop()); // 2

    System.out.println(stack.pop()); // 1

  }

}

This code creates a stack and pushes three elements onto the stack. The code then pops two elements from the stack and prints them.

Here is an explanation of how the code works:

• The Stack class is imported from the java.util package.
• A new Stack object is created.
• Three elements are pushed onto the stack.
• Two elements are popped from the stack and printed.

 

QUEUE

 

queue is a linear data structure that follows the first-in, first-out (FIFO) principle

In Java, queues are implemented using the Queue interface. The Queue interface provides methods for adding and removing elements from the queue, as well as for checking if the queue is empty or full.

import java.util.Queue; import java.util.LinkedList;   public class QueueExample {     public static void main(String[] args) {     Queue<Integer> queue = new LinkedList<>();       queue.add(1);     queue.add(2);     queue.add(3);       System.out.println(queue.poll()); // 1     System.out.println(queue.poll()); // 2     System.out.println(queue.poll()); // 3   } }

 

 

COMPLEXITY ANALYSIS

 

• Complexity analysis is the process of determining how the time and space requirements of an algorithm change as the size of its input increases.
• Time complexity measures how long an algorithm takes to run, as a function of the size of its input.
• Space complexity measures how much memory an algorithm uses, as a function of the size of its input.
• There are several different ways to measure complexity, but the most common are Big-O notation, Theta notation, and Omega notation.
• Big-O notation is used to describe the asymptotic behavior of an algorithm. This means that it describes how the algorithm's time or space requirements change as the size of its input approaches infinity.
• Theta notation is used to describe the exact time or space requirements of an algorithm.
• Omega notation is used to describe the lower bound of an algorithm's time or space requirements.

examples of complexity analysis in Java:

• The time complexity of the for loop is O(n), where n is the number of iterations in the loop.
• The space complexity of the ArrayList class is O(n), where n is the number of elements in the list.
• The time complexity of the binary search algorithm is O(log n), where n is the number of elements in the array.

Complexity analysis is an important tool for software developers. It can help developers to choose the most efficient algorithms for their problems, and to ensure that their code is scalable.