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1.) What is computational complexity theory, and why is it important? It studies how efficiently problems can be solved using algorithms. 2.) Explain the difference between time complexity and space complexity. Time complexity measures how the runtime of an algorithm grows with input size, while space complexity measures how much memory an algorithm uses as input size grows. 3.) What are P and NP classes in complexity theory? P contains problems that can be solved quickly (in polynomial time), while NP contains problems whose solutions can be verified quickly. 4.) What does it mean when a problem is NP-complete? It means the problem is one of the hardest in NP; solving one NP-complete problem quickly means all NP problems can be solved quickly.... Continue reading "Core Principles of Computation: Complexity, Automata, and Algorithms" »

AI Search Problem Fundamentals

Understanding different types of search problems is crucial in Artificial Intelligence.

• Deterministic, fully observable: Classical search problem.
• Non-deterministic and/or partially observable: Requires different approaches beyond classical search.
• Non-observable: Sensorless problems.
• Unknown state space: Exploration problem.

Basic Search Concepts

• State Space: The set of all possible states reachable from the initial state.
• Initial State: The starting state.
• Actions: Possible operations available in a state.
• State Transition Function: Determines the resulting state after performing an action.
• Goal State: A desired state to be reached.
• Step Cost: The cost associated with performing an action.
• Solution: A sequence of actions

Python Regular Expressions: Pattern Matching Power

Regular expressions (regex) are a powerful tool for pattern matching and text manipulation. They allow you to search for patterns within strings, extract specific information, and perform text transformations. Python provides the re module for working with regular expressions.

Basic Regular Expression Components

1. Literals: Characters that match themselves.
2. Metacharacters: Special characters with special meanings, such as . (matches any character) and * (matches zero or more occurrences).
3. Character Classes: [...] matches any single character within the brackets.
4. Anchors: ^ matches the start of a string, $ matches the end of a string.
5. Quantifiers: * matches zero or more occurrences, + matches one or

• Graph (G): A pair (V, E) where V is a set of vertices and E is a set of edges connecting pairs of vertices.
• Types of Graphs:
  • Simple Graph: No loops or multiple edges.
  • Multigraph: Multiple edges allowed.
  • Directed Graph (Digraph): Edges have directions.
  • Weighted Graph: Edges have weights.

Understanding Subgraphs

• Subgraph: A graph H is a subgraph of G if V(H) ⊆ V(G) and E(H) ⊆ E(G).
• Induced Subgraph: Formed by a subset of vertices and all edges between them in G.

Fundamental Graph Properties

• Order: Number of vertices (|V|).
• Size: Number of edges (|E|).
• Degree: Number of edges incident to a vertex.

Common Graph Examples

• Complete Graph (K_n): Every pair of vertices is connected.
• Cycle Graph (C_n): Forms a closed loop.
• Path Graph (P_n): A sequence of vertices connected

💾 Data Representation Fundamentals

Binary Coded Decimal (BCD) Benefits

BCD is a method to represent decimal numbers in binary form, where each decimal digit is represented by a fixed number of bits, usually four.

Benefits of BCD include:

• Straightforward conversion between BCD and **decimal (base 10)**.
• Less complex to encode and decode for programmers.
• Easier for digital equipment to use BCD to display information.
• Can represent monetary values exactly.

Applications of BCD:

• Electronic displays (e.g., calculators, digital clocks) - easier conversion between decimal and BCD when only individual digits need to be shown.
• Storage of date and time in PC BIOS - easier conversion with decimal values.

Hexadecimal Applications

Hexadecimal is used in:

1. MAC addresses.

CISC: Complex Instruction Set Computer

The Complex Instruction Set Computer (CISC) architecture packs more complex instructions into the processor. Some instructions might perform several tasks in one go. This design reduces the number of instructions a programmer needs to write but makes the CPU's internal logic more complicated and potentially slower for some tasks.

• Think: “Do more, but it might take longer.”

CISC is commonly found in x86 architectures (e.g., typical laptops or desktops), where compatibility and code density often matter more than raw efficiency.

RISC vs. CISC: Architectural Approaches

Both RISC (Reduced Instruction Set Computer) and CISC architectures aim to solve the same problem—efficient program execution—but they... Continue reading "Processor Architectures: RISC, CISC, and Micro-operations Demystified" »

1. Basics of Software Testing

• Definition of Software Testing: The process of verifying and validating that a software application or product meets specified requirements.
• Key Objectives: Ensure quality, detect errors, and assess functionality.

2. Differences Between:

• Errors: Mistakes made by developers during coding or design.
• Faults (Defects): Errors in the code that can cause failures when executed.
• Failures: The manifestation of a fault during program execution.
• Bugs: Common term for faults/defects found in the software.

3. Debugging

• Definition: The process of identifying, analyzing, and fixing bugs in software.
• Key Difference: Debugging fixes the bugs detected during testing.

4 & 5. Static Techniques and Testing Methods

Static Techniques:

• Benefits:

Packet Switching Fundamentals

Packet switching is a method used in computer networks to transmit data efficiently by breaking it into smaller units called packets. Each packet travels independently across the network and may take different routes to reach the destination. Once all packets arrive, they’re reassembled into the original message.

How Packet Switching Works

1. Segmentation: The original message is divided into packets.
2. Header Information: Each packet receives a header with source, destination, and sequencing information.
3. Independent Routing: Packets are sent through the network, possibly via different paths.
4. Reassembly: At the destination, packets are reordered and combined to form the original message.

Advantages of Packet Switching

• Efficient

Support Vector Machines (SVM)

Support Vector Machines (SVM) are powerful supervised machine learning algorithms used for classification and regression tasks. They work by finding the optimal boundary (or hyperplane) that separates different classes in the data.

Imagine you have a dataset with two classes of points belonging to different categories, such as cats and dogs. SVM aims to draw a straight line (or hyperplane) that best separates these two classes while maximizing the margin. The margin is the distance between the hyperplane and the nearest points from each class, known as support vectors.

SVM Example: Classifying Cats and Dogs

Let's illustrate SVM with a dataset of cats and dogs, aiming to classify them based on their weights (in kilograms)... Continue reading "SVM and Naive Bayes: Machine Learning Classification Fundamentals" »