Algorithms for System Architects

Master the algorithms and data structures essential for designing large-scale, distributed systems. From consistent hashing to consensus algorithms, learn the algorithms that power modern system architecture.

What You'll Learn

• Distributed Systems Algorithms: Consensus, load balancing, sharding

• Data Structures for Scale: Hash tables, B-trees, bloom filters

• Caching Strategies: LRU, LFU, consistent hashing

• Graph Algorithms: Shortest path, minimum spanning trees

• Concurrency Patterns: Threading, locks, atomic operations

• Performance Optimization: Time complexity, space efficiency

📚 Complete Course Table of Contents

> 🔓 Preview Content (Free): You're currently viewing the preview version with sample algorithms and implementations. Subscribe to unlock the full course with 50+ advanced algorithms, detailed implementations, and exclusive system design patterns.

🎯 Part 1: Foundation (Beginner to Intermediate) - 15 Algorithms

1.1 Basic Data Structures for Scale (5 Algorithms)

Preview (Free):

• ✅ Hash Tables: Collision resolution, load factors

• ✅ Arrays and Strings: Memory optimization

• ✅ Stacks and Queues: Application in system design

Full Content (Subscribers Only):

• 🔒 Consistent Hashing: Complete implementation with virtual nodes

• 🔒 Distributed Hash Tables: Chord protocol implementation

• 🔒 Skip Lists: Probabilistic data structure for distributed systems

• 🔒 B-Trees: Database indexing with concurrent access

• 🔒 LSM Trees: Write-optimized storage for modern databases

1.2 Simple Algorithms (5 Algorithms)

Preview (Free):

• ✅ Sorting algorithms: Quick sort, merge sort

• ✅ Search algorithms: Binary search, linear search

• ✅ Basic graph traversal: BFS, DFS

Full Content (Subscribers Only):

• 🔒 External Sorting: Merge sort for large datasets

• 🔒 Distributed Sorting: MapReduce implementation

• 🔒 Parallel Graph Traversal: Multi-threaded BFS/DFS

• 🔒 Bloom Filters: Space-efficient membership testing

• 🔒 HyperLogLog: Cardinality estimation for big data

1.3 Caching Fundamentals (5 Algorithms)

Preview (Free):

• ✅ Cache basics: Hit rates, miss rates

• ✅ Simple replacement policies: FIFO, Random

• ✅ Cache consistency: Write-through, write-back

Full Content (Subscribers Only):

• 🔒 LRU Cache: Least Recently Used with O(1) operations

• 🔒 LFU Cache: Least Frequently Used with frequency tracking

• 🔒 ARC Cache: Adaptive Replacement Cache algorithm

• 🔒 Write-Behind Caching: Asynchronous write optimization

• 🔒 Cache Coherence: MESI protocol implementation

🚀 Part 2: Intermediate Level - 20 Algorithms

2.1 Advanced Data Structures (7 Algorithms)

Preview (Free):

• ✅ B-Trees and B+ Trees: Database indexing

• ✅ Bloom Filters: Space-efficient membership testing

• ✅ Skip Lists: Probabilistic data structures

Full Content (Subscribers Only):

• 🔒 B+ Trees: Optimized for database storage with range queries

• 🔒 LSM Trees: Log-Structured Merge trees for write-heavy workloads

• 🔒 R-Trees: Spatial indexing for geographic data

• 🔒 Quad Trees: 2D spatial partitioning for game engines

• 🔒 Suffix Trees: String matching for text search engines

• 🔒 Trie Data Structures: Prefix trees for autocomplete systems

• 🔒 Fenwick Trees: Binary indexed trees for range queries

2.2 Graph Algorithms (7 Algorithms)

Preview (Free):

• ✅ Shortest path: Dijkstra, Bellman-Ford

• ✅ Minimum spanning trees: Kruskal, Prim

• ✅ Network flow: Ford-Fulkerson

Full Content (Subscribers Only):

• 🔒 A* Search: Heuristic pathfinding for game AI

• 🔒 Floyd-Warshall: All-pairs shortest path for network routing

• 🔒 Johnson's Algorithm: All-pairs shortest path with negative weights

• 🔒 Tarjan's Algorithm: Strongly connected components

• 🔒 Kosaraju's Algorithm: Alternative SCC algorithm

• 🔒 Topological Sort: Kahn's algorithm for dependency resolution

• 🔒 Minimum Cut: Max-flow min-cut theorem applications

2.3 Concurrency Basics (6 Algorithms)

Preview (Free):

• ✅ Threading models: Thread pools, actors

• ✅ Synchronization: Mutexes, semaphores

• ✅ Lock-free programming: Atomic operations

Full Content (Subscribers Only):

• 🔒 Lock-Free Hash Tables: Concurrent data structures

• 🔒 Wait-Free Algorithms: Progress guarantees in concurrent systems

• 🔒 Compare-and-Swap: Atomic operations for lock-free programming

• 🔒 Memory Barriers: CPU memory ordering for concurrent algorithms

• 🔒 Actor Model: Message-passing concurrency patterns

• 🔒 CSP (Communicating Sequential Processes): Go-style concurrency

🎯 Part 3: Advanced Level - 15 Algorithms

3.1 Distributed Systems (8 Algorithms)

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• ✅ Consensus algorithms: Raft, Paxos

• ✅ Load balancing: Round robin, consistent hashing

• ✅ Sharding strategies: Range, hash, directory

Full Content (Subscribers Only):

• 🔒 Raft Algorithm: Leader election and log replication

• 🔒 Paxos Algorithm: Classic consensus protocol

• 🔒 PBFT: Practical Byzantine Fault Tolerance

• 🔒 Gossip Protocols: Epidemic algorithms for distributed systems

• 🔒 Vector Clocks: Causality tracking in distributed systems

• 🔒 CRDTs: Conflict-free Replicated Data Types

• 🔒 Two-Phase Commit: Distributed transaction protocol

• 🔒 Three-Phase Commit: Improved distributed transaction protocol

3.2 Performance Optimization (7 Algorithms)

Preview (Free):

• ✅ Algorithm complexity analysis

• ✅ Memory hierarchy optimization

• ✅ Parallel processing patterns

Full Content (Subscribers Only):

• 🔒 Cache-Oblivious Algorithms: Optimal cache performance

• 🔒 Parallel Prefix Sum: Scan algorithms for parallel computing

• 🔒 MapReduce: Distributed computing framework

• 🔒 Bulk Synchronous Parallel: BSP model for parallel algorithms

• 🔒 Work-Stealing: Load balancing for parallel tasks

• 🔒 NUMA-Aware Algorithms: Non-uniform memory access optimization

• 🔒 GPU Algorithms: CUDA and OpenCL implementations

🏗️ Part 4: Architect Level - 10 Algorithms

4.1 Large-Scale Systems (6 Algorithms)

Preview (Free):

• ✅ Distributed algorithms

• ✅ Scalability patterns

• ✅ Fault tolerance mechanisms

Full Content (Subscribers Only):

• 🔒 Chord Protocol: Distributed hash table implementation

• 🔒 Pastry: Structured peer-to-peer overlay network

• 🔒 Kademlia: Distributed hash table with XOR metric

• 🔒 Consistent Hashing: Load balancing for distributed systems

• 🔒 Rendezvous Hashing: Highest random weight hashing

• 🔒 Jump Consistent Hash: Fast, minimal memory consistent hashing

4.2 Real-World Applications (4 Algorithms)

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• ✅ Database systems: B+ trees, LSM trees

• ✅ Message queues: Priority queues, dead letter queues

• ✅ CDN optimization: Content delivery algorithms

Full Content (Subscribers Only):

• 🔒 LSM Tree Compaction: LevelDB/RocksDB compaction strategies

• 🔒 B+ Tree Splitting: Database index maintenance

• 🔒 Priority Queue: Heap-based task scheduling

• 🔒 Dead Letter Queue: Message failure handling

🎯 System Design Patterns

🔓 Preview (Free):

• ✅ Circuit Breaker Pattern: Complete implementation

• ✅ Rate Limiting: Token bucket algorithm

• ✅ Load Balancing: Round robin and weighted round robin

🔒 Full Content (Subscribers Only):

• 🔒 Bulkhead Pattern: Fault isolation in microservices

• 🔒 Saga Pattern: Distributed transaction management

• 🔒 CQRS Pattern: Command Query Responsibility Segregation

• 🔒 Event Sourcing: Event-driven architecture patterns

• 🔒 CQRS with Event Sourcing: Complete implementation

• 🔒 Saga Orchestration: Centralized saga management

• 🔒 Saga Choreography: Decentralized saga management

• 🔒 Outbox Pattern: Reliable message publishing

• 🔒 Inbox Pattern: Reliable message processing

• 🔒 Idempotency Patterns: Safe retry mechanisms

🎯 Real-World System Implementations

🔓 Preview (Free):

• ✅ Database Systems: B+ trees, LSM trees

• ✅ Message Queues: Priority queues, dead letter queues

• ✅ CDN Optimization: Content delivery algorithms

🔒 Full Content (Subscribers Only):

• 🔒 Redis Implementation: In-memory data structures

• 🔒 Memcached Implementation: Distributed caching

• 🔒 Kafka Implementation: Distributed streaming platform

• 🔒 Cassandra Implementation: NoSQL database algorithms

• 🔒 MongoDB Implementation: Document database algorithms

• 🔒 Elasticsearch Implementation: Search engine algorithms

• 🔒 CDN Algorithms: Content delivery optimization

• 🔒 Load Balancer Algorithms: Traffic distribution

• 🔒 API Gateway Algorithms: Request routing and rate limiting

• 🔒 Service Mesh Algorithms: Microservices communication

🎯 Performance Metrics & Optimization

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• ✅ Latency Optimization: P50, P95, P99 analysis

• ✅ Scalability Patterns: Horizontal vs vertical scaling

• ✅ Throughput Optimization: Requests per second

🔒 Full Content (Subscribers Only):

• 🔒 Profiling Algorithms: CPU and memory profiling

• 🔒 Benchmarking Algorithms: Performance measurement

• 🔒 Load Testing Algorithms: Stress testing strategies

• 🔒 Capacity Planning: Resource estimation algorithms

• 🔒 Auto-scaling Algorithms: Dynamic resource allocation

• 🔒 Cost Optimization: Resource cost minimization

• 🔒 Energy Efficiency: Green computing algorithms

• 🔒 Carbon Footprint: Environmental impact optimization

🎯 What Subscribers Get

🔓 Free Preview Includes:

• ✅ 3 complete algorithm implementations with detailed explanations

• ✅ Basic system design patterns

• ✅ Performance optimization techniques

• ✅ Real-world application examples

🔒 Full Subscription Unlocks:

• 🔒 50+ Advanced Algorithm Implementations with production-ready code

• 🔒 System Design Patterns for large-scale applications

• 🔒 Distributed Systems Algorithms for microservices architecture

• 🔒 Performance Optimization techniques for high-traffic systems

• 🔒 Real-World Case Studies from top tech companies

• 🔒 Code Reviews and best practices

• 🔒 Architecture Decision Records (ADRs) templates

• 🔒 Exclusive Discord Community access

• 🔒 Priority Support and Q&A sessions

• 🔒 Certificate of Completion for LinkedIn

💰 Pricing & Subscription

Free Preview: Access to 3 algorithms and basic patterns

Pro Subscription: $5/month (Founding Cohort Pricing)

Full Access: All 50+ algorithms, system patterns, and exclusive content

> 🎯 Ready to become a system architect? Subscribe now and master the algorithms that power the world's largest systems!

Preview Chapter: Consistent Hashing

Problem: How do you distribute data across multiple servers while minimizing data movement when servers are added or removed?

Traditional Hashing Problems

Server 1: hash(key) % 3 = 0
Server 2: hash(key) % 3 = 1  
Server 3: hash(key) % 3 = 2

Adding Server 4: hash(key) % 4 = ?
→ 75% of data needs to be moved!

Consistent Hashing Solution

import hashlib
import bisect

class ConsistentHash:
    def __init__(self, nodes=None, replicas=3):
        self.replicas = replicas
        self.ring = {}
        self.sorted_keys = []
        
        if nodes:
            for node in nodes:
                self.add_node(node)
    
    def _hash(self, key):
        return int(hashlib.md5(key.encode()).hexdigest(), 16)
    
    def add_node(self, node):
        for i in range(self.replicas):
            key = self._hash(f"{node}:{i}")
            self.ring[key] = node
            self.sorted_keys.append(key)
        
        self.sorted_keys.sort()
    
    def remove_node(self, node):
        for i in range(self.replicas):
            key = self._hash(f"{node}:{i}")
            if key in self.ring:
                del self.ring[key]
                self.sorted_keys.remove(key)
    
    def get_node(self, key):
        if not self.ring:
            return None
        
        hash_key = self._hash(key)
        idx = bisect.bisect_right(self.sorted_keys, hash_key)
        
        if idx == len(self.sorted_keys):
            idx = 0
        
        return self.ring[self.sorted_keys[idx]]

Benefits:

• Only 1/n of data moves when adding/removing nodes

• Load balancing across servers

• Fault tolerance

Course Structure

1. Distributed Systems Algorithms (2 hours)

Consensus Algorithms

• Raft Algorithm: Leader election, log replication

• Paxos: Distributed consensus protocol

• PBFT: Practical Byzantine Fault Tolerance

Load Balancing

• Round Robin: Simple distribution

• Weighted Round Robin: Server capacity consideration

• Least Connections: Dynamic load balancing

• Consistent Hashing: Minimal data movement

Sharding Strategies

• Range-based Sharding: Data partitioning by ranges

• Hash-based Sharding: Even distribution

• Directory-based Sharding: Flexible partitioning

2. Data Structures for Scale (1.5 hours)

Hash Tables

• Collision Resolution: Chaining vs Open Addressing

• Load Factor: Optimal performance tuning

• Rehashing: Dynamic resizing strategies

B-Trees and B+ Trees

• Database Indexing: Efficient range queries

• Disk I/O Optimization: Minimizing disk access

• Concurrent Access: Lock-free operations

Bloom Filters

• Space-efficient Probabilistic Data Structure

• Use Cases: Cache filtering, duplicate detection

• False Positive Rate: Tuning parameters

import hashlib
from bitarray import bitarray

class BloomFilter:
    def __init__(self, size, hash_count):
        self.size = size
        self.hash_count = hash_count
        self.bit_array = bitarray(size)
        self.bit_array.setall(0)
    
    def _hash(self, item, seed):
        return int(hashlib.md5(f"{item}{seed}".encode()).hexdigest(), 16) % self.size
    
    def add(self, item):
        for i in range(self.hash_count):
            index = self._hash(item, i)
            self.bit_array[index] = 1
    
    def contains(self, item):
        for i in range(self.hash_count):
            index = self._hash(item, i)
            if not self.bit_array[index]:
                return False
        return True

3. Caching Strategies (1 hour)

Cache Replacement Policies

• LRU (Least Recently Used): Time-based eviction

• LFU (Least Frequently Used): Frequency-based eviction

• FIFO (First In, First Out): Queue-based eviction

• Random: Simple probabilistic eviction

Cache Consistency

• Write-through: Immediate database updates

• Write-behind: Batched database updates

• Cache-aside: Application-managed cache

• Read-through: Cache-managed loading

4. Graph Algorithms (1.5 hours)

Shortest Path Algorithms

• Dijkstra's Algorithm: Single-source shortest path

• Bellman-Ford: Negative edge weights

• Floyd-Warshall: All-pairs shortest path

• A* Search: Heuristic-based pathfinding

Minimum Spanning Trees

• Kruskal's Algorithm: Edge-based MST

• Prim's Algorithm: Vertex-based MST

• Applications: Network design, clustering

Network Flow

• Max Flow Min Cut: Network optimization

• Ford-Fulkerson: Maximum flow algorithm

• Applications: Load balancing, resource allocation

5. Concurrency and Threading (1 hour)

Threading Models

• Thread Pool: Managed thread execution

• Actor Model: Message-passing concurrency

• Fork-Join: Parallel task execution

• Lock-free Programming: Atomic operations

Synchronization Primitives

• Mutexes: Mutual exclusion locks

• Semaphores: Resource counting

• Condition Variables: Thread coordination

• Atomic Operations: Lock-free synchronization

6. Performance Optimization (1 hour)

Algorithm Complexity Analysis

• Time Complexity: Big O notation

• Space Complexity: Memory usage analysis

• Amortized Analysis: Average-case performance

• Cache Complexity: Memory hierarchy considerations

Profiling and Optimization

• CPU Profiling: Hotspot identification

• Memory Profiling: Memory leak detection

• I/O Optimization: Disk and network efficiency

• Parallelization: Multi-core utilization

Real-World Applications

Database Systems

• B+ Trees: Database indexing

• LSM Trees: Write-optimized storage

• Consistent Hashing: Database sharding

• Bloom Filters: Query optimization

Distributed Systems

• Gossip Protocols: Eventual consistency

• Vector Clocks: Causality tracking

• CRDTs: Conflict-free replicated data types

• Consensus: Distributed agreement

Caching Systems

• Redis: In-memory data structures

• Memcached: Distributed caching

• CDN: Content delivery optimization

• Application Caching: Local optimization

Message Queues

• Round Robin: Simple distribution

• Priority Queues: Task prioritization

• Dead Letter Queues: Error handling

• Message Ordering: Sequence guarantees

System Design Patterns

Circuit Breaker Pattern

class CircuitBreaker:
    def __init__(self, failure_threshold=5, timeout=60):
        self.failure_threshold = failure_threshold
        self.timeout = timeout
        self.failure_count = 0
        self.last_failure_time = None
        self.state = 'CLOSED'  # CLOSED, OPEN, HALF_OPEN
    
    def call(self, func, *args, **kwargs):
        if self.state == 'OPEN':
            if time.time() - self.last_failure_time > self.timeout:
                self.state = 'HALF_OPEN'
            else:
                raise Exception("Circuit breaker is OPEN")
        
        try:
            result = func(*args, **kwargs)
            self.on_success()
            return result
        except Exception as e:
            self.on_failure()
            raise e
    
    def on_success(self):
        self.failure_count = 0
        self.state = 'CLOSED'
    
    def on_failure(self):
        self.failure_count += 1
        self.last_failure_time = time.time()
        if self.failure_count >= self.failure_threshold:
            self.state = 'OPEN'

Rate Limiting Algorithms

• Token Bucket: Burst handling

• Leaky Bucket: Smooth rate limiting

• Sliding Window: Time-based limiting

• Fixed Window: Simple rate limiting

Performance Metrics

Latency Optimization

• P50, P95, P99: Percentile analysis

• Tail Latency: Worst-case performance

• Jitter: Latency variance

• Throughput: Requests per second

Scalability Patterns

• Horizontal Scaling: Adding more servers

• Vertical Scaling: Increasing server capacity

• Auto-scaling: Dynamic resource allocation

• Load Balancing: Traffic distribution

What's Next

After mastering these algorithms, you'll be equipped to design and implement large-scale distributed systems. You'll understand not just how algorithms work, but how to apply them in real-world scenarios to build robust, scalable, and efficient systems.