Elixir Code

The following is a collection of problems and exercises solved in Elixir, demonstrating core concepts in concurrent programming.

Elixir 1.17.2 | Erlang/OTP 27

01: RSA Cryptography Fundamentals

Implementation of core mathematical functions used in RSA encryption/decryption:

• mod_inverse/2 - Extended Euclidean algorithm to find multiplicative inverse modulo n
• mod_pow/3 - Fast modular exponentiation using binary exponentiation to handle large numbers efficiently

These functions demonstrate foundational cryptographic operations and efficient algorithms for handling large integer arithmetic in Elixir.

02: Binary Manipulation & Taylor Series

• reverse_bytes/1 - Manual binary reversal without library functions
• sine_stream/1 - Lazy stream implementation of Taylor series for sine function
• sin/1 - Accurate sine calculation using series convergence with period reduction

Demonstrates binary pattern matching, mathematical series implementation, and stream processing in Elixir.

03: GenServer Applications

Two GenServer implementations demonstrating different OTP patterns:

Card.Server

• Unregistered GenServer - Card deck management with PID-based API
• State persistence - Tracks remaining cards across operations
• Mix project structure - Proper Elixir application organization

Arith.Server + Arith.Worker

• Worker pool pattern - Round-robin request dispatching
• Registered server - Single entry point managing multiple workers
• Concurrent processing - Non-blocking operations across worker processes

Demonstrates advanced GenServer patterns, process supervision, and concurrent system design.

04: Supervision & Fault Tolerance

Advanced OTP patterns with supervision trees and state persistence:

Card.Worker + Card.Store

• Supervised GenServer - Automatic restart with state recovery
• State persistence - File-based storage (cards.db) survives crashes
• Fault tolerance - Intentional crashes on invalid input for testing
• OTP Supervisor - Created with --sup flag

Enhanced Arith.Server

• Process monitoring - Server tracks worker health without polling
• Dynamic supervision - Automatic worker replacement on failure
• Fault injection - Crashes on non-numeric input for testing supervision

Demonstrates production-ready OTP applications with supervision, monitoring, and state recovery patterns.

05: Dynamic Supervision & Process Registry

Production-grade OTP application with dynamic worker management:

Card.WorkerSupervisor

• DynamicSupervisor - Runtime worker creation and management
• Process Registry - Named worker lookup via Card.Registry
• ETS state storage - Persistent state across worker restarts (Card.Store)

Enhanced Card.Worker

• Registry integration - Workers registered by name, not PID
• State recovery - Automatic state restoration from ETS on restart
• Fault injection - Crashes on invalid input for supervision testing

Application Supervision Tree

• Multi-tier supervision - Registry → DynamicSupervisor → Workers
• OTP Application - Proper startup sequence and dependency management

Demonstrates enterprise Elixir architecture with dynamic processes, state persistence, and fault-tolerant design patterns used in production systems.

06: TCP Echo Servers - Socket Mode Comparison

Three TCP server implementations demonstrating different socket handling strategies:

ActiveEchoServer

• Active mode (active: true) - Messages delivered automatically to process mailbox
• Message-driven - Uses receive pattern matching for incoming data
• High throughput - No blocking calls, but potential mailbox flooding

PassiveEchoServer

• Passive mode (active: false) - Explicit recv calls required
• Blocking I/O - Synchronous data reading with error handling
• Flow control - Prevents message queue overflow

HybridEchoServer

• Hybrid mode (active: :once) - Single message delivery, then switches to passive
• Balanced approach - Combines benefits of both modes
• Optimal control - Manual reactivation after processing each message

Demonstrates low-level network programming patterns and socket management strategies in Elixir/Erlang.