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Breadth-First Search (BFS) Algorithm Explained with Examples and Applications

  What is Breadth-First Search (BFS)? Breadth-First Search (BFS) is a fundamental graph traversal algorithm that explores all nodes at the present depth level before moving on to nodes at the next depth level. It is widely used for solving shortest path problems in unweighted graphs, searching in trees, and analyzing connected components in graphs. BFS Algorithm Explanation BFS uses a  queue  data structure to keep track of the nodes to be explored next. The key idea is: Visit the starting node and enqueue it. While the queue is not empty: Dequeue a node from the front. Process the node (e.g., print or record). Enqueue all its adjacent unvisited neighbors. Algorithm Steps (for Binary Tree) Start with the root node and put it into the queue. While the queue is not empty: Remove the node from the queue. Process the current node. If the left child exists, enqueue it. If the right child exists, enqueue it. Algorithm Steps (for General Graph) Start with the given node and enqu...

Search Algorithms Explained with Python

Introduction to Search Algorithms Search algorithms are foundational tools in artificial intelligence (AI) and computer science. They enable problem-solving agents to explore complex environments, discover solutions, and make decisions. A search algorithm systematically examines possible paths in a problem space to find a solution, such as reaching a goal state from a given start state. Broadly, search algorithms are divided into two main categories: Uninformed Search Algorithms : These algorithms do not have any domain-specific knowledge beyond the problem definition. They explore the search space blindly, treating all nodes equally without estimating the direction of the goal. While often inefficient in large or complex environments, they are guaranteed to find a solution (if one exists) under certain conditions, and they form the conceptual foundation for more advanced techniques. Informed Search Algorithms : Also known as heuristic search algorithms, these methods use addit...

Understanding Queue and Stack in Data Structures

Data structures are fundamental concepts in computer science that help organize, manage, and store data efficiently. Two of the most basic and essential data structures are   Queue   and   Stack . This article provides an in-depth explanation of their characteristics, Python implementation from scratch, and examples using Python's built-in libraries. 1. Stack (LIFO - Last In, First Out) A  Stack  is a linear data structure that follows the  Last In, First Out (LIFO)  principle. This means the last element added to the stack is the first one to be removed. Characteristics of a Stack Insertion (push) and removal (pop) happen at the same end, called the  top  of the stack. Access to elements is restricted to the top of the stack only. Common operations: push(item) : Add an item to the top. pop() : Remove the top item. peek() : View the top item without removing it. is_empty() : Check if the stack is empty. Python Implementation (From Scratch) cl...

What is a Singleton Design Pattern?

In programming, a  Singleton  is a design pattern that ensures a class has  only one instance  during the entire lifetime of a program, and provides a global access point to that instance. Singleton is widely used when you want to control resource usage, like database connections, configurations, or loading a heavy machine learning model only once. Why Use Singleton? Efficient memory usage Controlled access to a resource Ensures consistency across your application Simple Singleton Implementation in Python class SingletonMeta(type): _instances = {} def __call__(cls, *a rgs, **kwargs): if cls not in cls._instances: instance = super().__call__( *a rgs, **kwargs) cls._instances[cls] = instance return cls._instances[cls] class SingletonExample( metaclass =SingletonMeta): def __init__(self): print ( "Initializing SingletonExample" ) # Usage a = SingletonExample() b = SingletonExample() print (a is b) # T...

Understanding KL Divergence: A Deep Yet Simple Guide for Machine Learning Engineers

  What is KL Divergence? Kullback–Leibler Divergence (KL Divergence)  is a fundamental concept in probability theory, information theory, and machine learning. It measures the difference between two probability distributions. In essence,  KL Divergence tells us how much information is lost  when we use one distribution ( Q ) to approximate another distribution ( P ). It’s often described as a measure of "distance" between distributions — but  important : it is  not a true distance  because it is  not symmetric . That means: $KL(P \parallel Q) \neq KL(Q \parallel P)$ Why is KL Divergence Important in Deep Learning? KL Divergence shows up in many core ML/DL areas: Variational Autoencoders (VAE) : Regularizes the latent space by minimizing KL divergence between the encoder's distribution and a prior (usually standard normal). Language Models : Loss functions like  cross-entropy  are tightly related to KL Divergence. Reinforcement Learning :...