🚀 Zero to Master Data Structures & Algorithms Syllabus

A comprehensive, modular roadmap to master Data Structures and Algorithms from beginner to expert level

📋 Table of Contents

1. Prerequisites
2. Phase 1: Foundation
3. Phase 2: Core Data Structures
4. Phase 3: Advanced Data Structures
5. Phase 4: Core Algorithms
6. Phase 5: Advanced Algorithms
7. Phase 6: Specialized Topics
8. Phase 7: System Design & Optimization
9. Phase 8: Contest Programming & Advanced Topics

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📚 Prerequisites

Mathematical Foundation

• Basic Mathematics

  • Logarithms and Exponentials
  • Modular Arithmetic
  • Combinatorics (Permutations & Combinations)
  • Probability Theory Basics
  • Set Theory

• Discrete Mathematics

  • Logic and Proofs
  • Graph Theory Basics
  • Number Theory
  • Recurrence Relations

Programming Fundamentals

• Language Proficiency (Choose one: C++, Java, Python, JavaScript)
  • Variables, Data Types, Operators
  • Control Structures (if-else, loops)
  • Functions and Recursion
  • Arrays and Strings
  • Object-Oriented Programming Concepts

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🏗️ Phase 1: Foundation

1.1 Time & Space Complexity Analysis

• Big O Notation

  • Understanding O, Ω, Θ notations
  • Best, Average, Worst case analysis
  • Amortized Analysis
  • Space Complexity

• Common Complexity Classes

  • O(1), O(log n), O(n), O(n log n)
  • O(n²), O(n³), O(2ⁿ), O(n!)
  • Master Theorem for Divide & Conquer

1.2 Problem Solving Fundamentals

• Problem Analysis

  • Understanding problem statements
  • Identifying constraints
  • Input/Output analysis
  • Edge case identification

• Basic Debugging Techniques

  • Print debugging
  • Test case generation
  • Boundary testing

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🧱 Phase 2: Core Data Structures

2.1 Linear Data Structures

2.1.1 Arrays

• Static Arrays

  • Declaration and initialization
  • Indexing and traversal
  • Multi-dimensional arrays
  • Array rotation and reversal

• Dynamic Arrays

  • Resizing mechanisms
  • Amortized analysis
  • Implementation details

• Array Algorithms

  • Two pointers technique
  • Sliding window
  • Prefix sums
  • Kadane's algorithm (Maximum subarray)

2.1.2 Strings

• String Fundamentals

  • ASCII vs Unicode
  • String immutability
  • Common string operations

• String Algorithms

  • Pattern matching (Naive, KMP, Rabin-Karp)
  • String hashing
  • Palindrome detection
  • Anagram problems
  • Longest common substring/subsequence

2.1.3 Linked Lists

• Singly Linked Lists

  • Node structure
  • Insertion (head, tail, middle)
  • Deletion (by value, by position)
  • Traversal and searching

• Doubly Linked Lists

  • Bidirectional traversal
  • Efficient insertion/deletion
  • Memory overhead considerations

• Circular Linked Lists

  • Implementation variations
  • Use cases and applications

• Advanced Linked List Problems

  • Cycle detection (Floyd's algorithm)
  • Finding intersection point
  • Reversing linked lists
  • Merging sorted lists

2.1.4 Stacks

• Stack Implementation

  • Array-based implementation
  • Linked list-based implementation
  • Dynamic resizing

• Stack Applications

  • Expression evaluation (infix, postfix, prefix)
  • Parentheses matching
  • Function call management
  • Undo operations
  • Browser history

• Advanced Stack Problems

  • Next greater element
  • Largest rectangle in histogram
  • Valid parentheses variations
  • Stack sorting

2.1.5 Queues

• Basic Queue

  • FIFO principle
  • Array and linked list implementations
  • Circular queue implementation

• Priority Queues

  • Heap-based implementation
  • Array-based implementation
  • Applications in scheduling

• Deque (Double-ended Queue)

  • Implementation strategies
  • Applications and use cases

• Queue Applications

  • BFS traversal
  • Process scheduling
  • Buffer for data streams
  • Level order traversal

2.2 Hash-based Data Structures

2.2.1 Hash Tables/Hash Maps

• Hashing Fundamentals

  • Hash functions (division, multiplication, universal)
  • Collision resolution (chaining, open addressing)
  • Load factor and rehashing
  • Perfect hashing

• Hash Table Implementations

  • Separate chaining
  • Linear probing
  • Quadratic probing
  • Double hashing

• Applications

  • Dictionary implementation
  • Caching mechanisms
  • Database indexing
  • Compiler symbol tables

2.2.2 Hash Sets

• Set Operations
  • Union, intersection, difference
  • Membership testing
  • Set-based algorithms

2.2.3 Advanced Hashing Techniques

• Robin Hood Hashing

  • Variance reduction in probe distances
  • Implementation optimizations

• Cuckoo Hashing

  • Guaranteed O(1) lookup time
  • Two-table approach
  • Rehashing strategies

• Consistent Hashing

  • Distributed systems applications
  • Ring-based hashing
  • Virtual nodes concept

2.3 Specialized Linear Structures

2.3.1 Bit Manipulation Data Structures

• Bitset

  • Efficient boolean array representation
  • Bitwise operations optimization
  • Space-efficient set operations

• Bit Vector

  • Compressed data representation
  • Rank and select operations
  • Succinct data structures

2.3.2 Memory-Efficient Structures

• Packed Arrays

  • Variable-width integer storage
  • Memory alignment considerations
  • Cache-friendly layouts

• Rope Data Structure

  • Efficient string concatenation
  • Tree-based string representation
  • Applications in text editors

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🌳 Phase 3: Advanced Data Structures

3.1 Tree Data Structures

3.1.1 Binary Trees

• Tree Fundamentals

  • Terminology (root, leaf, height, depth)
  • Tree representations
  • Binary tree properties

• Tree Traversals

  • Inorder, Preorder, Postorder (recursive & iterative)
  • Level order traversal (BFS)
  • Morris traversal (space-optimized)

• Binary Tree Problems

  • Tree height and diameter
  • Lowest common ancestor
  • Path sum problems
  • Tree serialization/deserialization

3.1.2 Binary Search Trees (BST)

• BST Properties

  • Search, insertion, deletion
  • BST validation
  • Inorder successor/predecessor

• BST Variations

  • Self-balancing concepts
  • BST to sorted array conversion
  • Range sum queries

3.1.3 Balanced Trees

• AVL Trees

  • Rotation operations (LL, LR, RL, RR)
  • Balance factor maintenance
  • Insertion and deletion with rebalancing

• Red-Black Trees

  • Color properties and rules
  • Insertion and deletion algorithms
  • Comparison with AVL trees

• Splay Trees

  • Splaying operation
  • Amortized analysis
  • Applications

3.1.4 Specialized Trees

• Heap (Binary Heap)

  • Min-heap and max-heap properties
  • Heapify operations
  • Heap sort algorithm
  • Priority queue implementation

• Trie (Prefix Tree)

  • String storage and retrieval
  • Auto-complete functionality
  • Word search problems
  • Compressed tries

• Segment Trees

  • Range query problems
  • Lazy propagation
  • Update operations
  • Applications in competitive programming

• Fenwick Tree (Binary Indexed Tree)

  • Prefix sum queries
  • Point updates
  • Range updates and queries

• B-Trees and B+ Trees

  • Multi-way search trees
  • Database indexing applications
  • Insertion and deletion operations

3.2 Graph Data Structures

3.2.1 Graph Fundamentals

• Graph Representations

  • Adjacency matrix
  • Adjacency list
  • Edge list
  • Implicit graphs

• Graph Types

  • Directed vs Undirected
  • Weighted vs Unweighted
  • Cyclic vs Acyclic
  • Connected vs Disconnected

3.2.2 Graph Traversal

• Depth-First Search (DFS)

  • Recursive and iterative implementations
  • DFS tree and classification of edges
  • Applications (topological sort, cycle detection)

• Breadth-First Search (BFS)

  • Queue-based implementation
  • Shortest path in unweighted graphs
  • Level-wise processing

3.3 Advanced Data Structures

3.3.1 Disjoint Set Union (DSU)

• Union-Find Structure
  • Path compression
  • Union by rank/size
  • Applications in Kruskal's algorithm

3.3.2 Advanced Trees

• Suffix Trees and Arrays

  • String matching applications
  • Longest common substring
  • Pattern searching

• Heavy-Light Decomposition

  • Tree decomposition techniques
  • Path and subtree queries

• Link-Cut Trees

  • Dynamic tree connectivity
  • Path queries and updates
  • Splay tree based implementation

• Cartesian Trees

  • Range minimum query applications
  • Stack-based construction
  • Treap implementation

3.3.3 Probabilistic Data Structures

• Bloom Filters

  • Membership testing with false positives
  • Space-efficient set representation
  • Applications in databases and caching

• Count-Min Sketch

  • Frequency estimation
  • Stream processing applications
  • Hash-based approximate counting

• HyperLogLog

  • Cardinality estimation
  • Memory-efficient distinct counting
  • Distributed systems applications

• Skip Lists

  • Probabilistic balanced structure
  • Alternative to balanced trees
  • Expected O(log n) operations

3.3.4 Advanced Tree Structures

• Scapegoat Trees

  • Weight-balanced trees
  • Partial rebuilding strategy
  • Amortized analysis

• Treaps (Randomized BST)

  • Priority-based balancing
  • Expected O(log n) operations
  • Merge and split operations

• Persistent Data Structures

  • Path copying technique
  • Functional data structures
  • Version control applications

• Van Emde Boas Trees

  • Integer universe optimization
  • O(log log u) operations
  • Predecessor/successor queries

3.3.5 Specialized Graph Structures

• Adjacency Matrix Variations

  • Sparse matrix representations
  • Compressed sparse row (CSR)
  • Block-based storage

• Graph Compression

  • WebGraph framework concepts
  • Reference-based compression
  • Locality exploitation

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⚡ Phase 4: Core Algorithms

4.1 Sorting Algorithms

4.1.1 Basic Sorting

• O(n²) Algorithms
  • Bubble sort
  • Selection sort
  • Insertion sort
  • Analysis and optimizations

4.1.2 Advanced Sorting

• Divide & Conquer Sorting

  • Merge sort (recursive and iterative)
  • Quick sort (with optimizations)
  • Heap sort

• Non-Comparison Sorting

  • Counting sort
  • Radix sort
  • Bucket sort
  • When to use each algorithm

4.1.3 Specialized Sorting

• External Sorting

  • Multi-way merge
  • Memory-efficient algorithms

• Stable vs Unstable Sorting

  • Stability requirements
  • Making unstable sorts stable

• Parallel Sorting

  • Bitonic sort
  • Sample sort
  • Multi-threaded quicksort

• String Sorting

  • MSD (Most Significant Digit) radix sort
  • LSD (Least Significant Digit) radix sort
  • Suffix sorting algorithms

4.1.4 Advanced Sorting Techniques

• Adaptive Sorting

  • Timsort (Python's sorting algorithm)
  • Introsort (introspective sort)
  • Patience sorting

• Approximate Sorting

  • Bucket sort variations
  • Histogram-based sorting
  • Sampling techniques

4.2 Searching Algorithms

4.2.1 Linear Search Variations

• Sequential Search
  • Optimizations (early termination, move-to-front)
  • Sentinel search

4.2.2 Binary Search and Variants

• Classic Binary Search

  • Implementation details
  • Boundary conditions
  • Integer overflow handling

• Binary Search Variations

  • Lower bound and upper bound
  • Search in rotated arrays
  • Peak finding
  • Square root and nth root
  • Ternary search

4.2.3 Search in Data Structures

• Tree Search Algorithms
  • BST search
  • Trie-based search
  • Range searching

4.2.4 Advanced Search Techniques

• Exponential Search

  • Unbounded binary search
  • Applications in infinite arrays

• Interpolation Search

  • Uniformly distributed data optimization
  • Better than binary search in some cases

• Jump Search

  • Block-based searching
  • Optimal block size determination

• Fibonacci Search

  • Golden ratio based searching
  • Division-free implementation

4.3 Recursion and Divide & Conquer

4.3.1 Recursion Fundamentals

• Recursive Thinking

  • Base cases and recursive cases
  • Tail recursion optimization
  • Memoization techniques

• Classic Recursive Problems

  • Factorial and Fibonacci
  • Tower of Hanoi
  • Generate all permutations/combinations
  • Backtracking fundamentals

4.3.2 Divide & Conquer Paradigm

• Algorithm Design

  • Problem decomposition
  • Combine step optimization
  • Recurrence relation analysis

• Classic D&C Algorithms

  • Merge sort and quick sort
  • Maximum subarray (Kadane's variant)
  • Closest pair of points
  • Strassen's matrix multiplication

4.3.3 Advanced Divide & Conquer

• Fast Fourier Transform (FFT)

  • Polynomial multiplication
  • Signal processing applications
  • Cooley-Tukey algorithm

• Karatsuba Multiplication

  • Large integer multiplication
  • Complexity analysis
  • Recursive implementation

• Advanced Matrix Operations

  • Coppersmith-Winograd algorithm
  • Block matrix multiplication
  • Parallel matrix algorithms

4.4 Backtracking Algorithms

4.4.1 Systematic Search

• N-Queens Problem

  • Constraint satisfaction
  • Pruning techniques
  • Optimization strategies

• Sudoku Solver

  • Constraint propagation
  • Arc consistency
  • Heuristic improvements

4.4.2 Combinatorial Problems

• Graph Coloring

  • Chromatic number determination
  • Backtracking with pruning
  • Greedy approximations

• Hamiltonian Path/Cycle

  • Exhaustive search optimization
  • Dynamic programming on subsets
  • Heuristic approaches

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🎯 Phase 5: Advanced Algorithms

5.1 Dynamic Programming

5.1.1 DP Fundamentals

• DP Concepts
  • Optimal substructure
  • Overlapping subproblems
  • Memoization vs Tabulation
  • Space optimization techniques

5.1.2 1D Dynamic Programming

• Linear DP Problems
  • Fibonacci variations
  • Climbing stairs
  • House robber
  • Maximum sum non-adjacent elements
  • Longest increasing subsequence

5.1.3 2D Dynamic Programming

• Grid-based DP
  • Unique paths
  • Minimum path sum
  • Edit distance
  • Longest common subsequence
  • 0/1 Knapsack problem

5.1.4 Advanced DP Patterns

• Interval DP

  • Matrix chain multiplication
  • Palindrome partitioning
  • Burst balloons

• Bitmask DP

  • Traveling salesman problem
  • Assignment problems
  • Subset enumeration

• Tree DP

  • Diameter of tree
  • Maximum path sum
  • Re-rooting technique

• Digit DP

  • Counting numbers with constraints
  • Sum of digits problems

5.2 Greedy Algorithms

5.2.1 Greedy Fundamentals

• Greedy Choice Property
  • When greedy works
  • Proof techniques
  • Exchange argument

5.2.2 Classic Greedy Problems

• Scheduling Problems

  • Activity selection
  • Job scheduling with deadlines
  • Fractional knapsack

• Graph Greedy Algorithms

  • Minimum spanning tree (Kruskal's, Prim's)
  • Shortest path (Dijkstra's)
  • Huffman coding

5.2.3 Advanced Greedy Techniques

• Interval Problems
  • Interval scheduling maximization
  • Minimum number of intervals
  • Gas station problem

5.3 Graph Algorithms

5.3.1 Shortest Path Algorithms

• Single Source Shortest Path

  • Dijkstra's algorithm (min-heap implementation)
  • Bellman-Ford algorithm
  • SPFA (Shortest Path Faster Algorithm)

• All Pairs Shortest Path

  • Floyd-Warshall algorithm
  • Johnson's algorithm
  • Applications and optimizations

5.3.2 Minimum Spanning Tree

• MST Algorithms
  • Kruskal's algorithm with DSU
  • Prim's algorithm with priority queue
  • Borůvka's algorithm

5.3.3 Advanced Graph Algorithms

• Topological Sorting

  • Kahn's algorithm (BFS-based)
  • DFS-based approach
  • Applications in scheduling

• Strongly Connected Components

  • Kosaraju's algorithm
  • Tarjan's algorithm
  • Applications

• Cycle Detection

  • Undirected graphs (DFS, DSU)
  • Directed graphs (DFS, topological sort)
  • Floyd's cycle detection

5.4 String Algorithms

5.4.1 Pattern Matching

• Advanced Pattern Matching
  • KMP (Knuth-Morris-Pratt) algorithm
  • Rabin-Karp algorithm
  • Boyer-Moore algorithm
  • Z-algorithm

5.4.2 String Processing

• Suffix Structures

  • Suffix array construction
  • Longest common prefix array
  • Applications in substring problems

• String Hashing

  • Polynomial rolling hash
  • Multiple hash functions
  • Hash collision handling

5.4.3 Advanced String Techniques

• Suffix Automaton

  • Linear time construction
  • All substring queries
  • Pattern matching applications

• Palindromic Tree (Eertree)

  • Palindrome detection
  • All palindromic substrings
  • Linear time construction

• Lyndon Words

  • String factorization
  • Lexicographically minimal rotations
  • Booth's algorithm

5.5 Approximation Algorithms

5.5.1 NP-Hard Problem Approximations

• Traveling Salesman Problem

  • 2-approximation algorithm
  • Christofides algorithm
  • Local search heuristics

• Vertex Cover

  • 2-approximation greedy algorithm
  • Linear programming relaxation
  • Primal-dual approach

• Set Cover

  • Greedy logarithmic approximation
  • Submodular optimization
  • Online algorithms

5.5.2 Advanced Approximation Techniques

• FPTAS (Fully Polynomial-Time Approximation Scheme)

  • Knapsack FPTAS
  • Scheduling problems
  • Dynamic programming scaling

• Randomized Approximation

  • MAX-3SAT approximation
  • Randomized rounding
  • Derandomization techniques

5.6 Online Algorithms

5.6.1 Competitive Analysis

• Ski Rental Problem

  • Rent vs buy decisions
  • Competitive ratio analysis
  • Online vs offline performance

• Paging Algorithms

  • LRU (Least Recently Used)
  • FIFO and optimal algorithms
  • Competitive analysis

5.6.2 Load Balancing

• List Scheduling

  • Greedy assignment
  • Competitive ratio bounds
  • Makespan minimization

• Online Bipartite Matching

  • AdWords problem
  • RANKING algorithm
  • Vertex arrival model

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🔬 Phase 6: Specialized Topics

6.1 Mathematical Algorithms

6.1.1 Number Theory

• Prime Numbers

  • Sieve of Eratosthenes
  • Miller-Rabin primality test
  • Prime factorization

• GCD and LCM

  • Euclidean algorithm
  • Extended Euclidean algorithm
  • Applications in modular arithmetic

• Modular Arithmetic

  • Modular exponentiation
  • Modular inverse
  • Chinese remainder theorem

6.1.2 Combinatorics

• Counting Techniques
  • Permutations and combinations
  • Inclusion-exclusion principle
  • Catalan numbers
  • Stars and bars method

6.1.3 Matrix Operations

• Matrix Algorithms
  • Matrix multiplication optimizations
  • Matrix exponentiation
  • Gaussian elimination
  • Determinant calculation

6.2 Computational Geometry

6.2.1 Basic Geometry

• Point and Line Operations
  • Distance calculations
  • Point-line relationships
  • Line intersection
  • Convex hull (Graham scan, Jarvis march)

6.2.2 Advanced Geometry

• Polygon Operations
  • Point in polygon test
  • Polygon area calculation
  • Closest pair of points
  • Line sweep algorithms

6.3 Game Theory and Optimization

6.3.1 Game Theory Basics

• Nim Game and Variants
  • Grundy numbers
  • Sprague-Grundy theorem
  • Impartial games

6.3.2 Linear Programming

• Optimization Problems
  • Simplex method basics
  • Applications in competitive programming

6.4 Advanced Mathematical Concepts

6.4.1 Information Theory

• Entropy and Compression

  • Shannon entropy
  • Huffman coding optimality
  • Arithmetic coding

• Error Correction

  • Hamming codes
  • Reed-Solomon codes
  • BCH codes

6.4.2 Cryptographic Algorithms

• Hash Functions

  • SHA family
  • MD5 and collision attacks
  • Cryptographic vs non-cryptographic hashing

• Public Key Cryptography

  • RSA algorithm
  • Diffie-Hellman key exchange
  • Elliptic curve cryptography basics

6.4.3 Random Number Generation

• Pseudorandom Generators

  • Linear congruential generators
  • Mersenne Twister
  • Cryptographically secure PRNGs

• Randomized Algorithms

  • Monte Carlo methods
  • Las Vegas algorithms
  • Randomized quicksort analysis

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🏛️ Phase 7: System Design & Optimization

7.1 Big Tech System Design Algorithms

7.1.1 Distributed System Fundamentals

• Consistent Hashing

  • Ring-based distribution
  • Virtual nodes implementation
  • Applications: Amazon DynamoDB, Cassandra

• Distributed Consensus

  • Raft consensus algorithm
  • PBFT (Practical Byzantine Fault Tolerance)
  • Paxos algorithm basics

• Load Balancing Algorithms

  • Round-robin and weighted round-robin
  • Least connections
  • Consistent hashing load balancing
  • Rendezvous hashing

7.1.2 Caching Algorithms

• Cache Eviction Policies

  • LRU (Least Recently Used)
  • LFU (Least Frequently Used)
  • ARC (Adaptive Replacement Cache)
  • Clock algorithm (Second chance)

• Distributed Caching

  • Cache coherence protocols
  • Write-through vs write-back
  • Cache partitioning strategies
  • Memcached vs Redis architectures

7.1.3 Big Tech Probabilistic Data Structures

• Bloom Filters (Google, Facebook)

  • Standard Bloom filter
  • Counting Bloom filters
  • Scalable Bloom filters
  • Applications: BigTable, Chrome safe browsing

• Count-Min Sketch (Google, Twitter)

  • Stream processing at scale
  • Heavy hitters detection
  • Applications: Google's MapReduce, Twitter's trending

• HyperLogLog (Google, Facebook, Redis)

  • Cardinality estimation
  • LogLog and SuperLogLog
  • Applications: Google Analytics, Facebook insights

• Locality Sensitive Hashing (LSH)

  • MinHash for set similarity
  • SimHash for near-duplicate detection
  • Applications: Google's web crawling, Dropbox deduplication

7.1.4 Rate Limiting Algorithms

• Token Bucket Algorithm

  • Implementation details
  • Burst handling
  • Applications: AWS API Gateway

• Leaky Bucket Algorithm

  • Smooth rate limiting
  • Queue-based implementation
  • Traffic shaping applications

• Fixed Window Counter

  • Simple implementation
  • Edge case handling
  • Memory efficiency

• Sliding Window Log

  • Precise rate limiting
  • Log-based tracking
  • Space vs accuracy tradeoffs

• Sliding Window Counter

  • Hybrid approach
  • Approximate counting
  • Redis implementation patterns

7.2 Database & Storage Algorithms

7.2.1 Database Indexing (Used by MySQL, PostgreSQL, MongoDB)

• B+ Tree Indexing

  • Range queries optimization
  • Sequential access patterns
  • InnoDB storage engine

• LSM Trees (Log-Structured Merge Trees)

  • Write-optimized storage
  • Compaction strategies
  • Applications: Cassandra, LevelDB, RocksDB

• Fractal Trees

  • Cache-oblivious algorithms
  • TokuDB implementation
  • Write amplification reduction

7.2.2 Distributed Storage Algorithms

• Consistent Hashing for Storage

  • Data partitioning
  • Replication strategies
  • Amazon DynamoDB architecture

• Vector Clocks

  • Causality tracking
  • Conflict resolution
  • Amazon DynamoDB, Riak usage

• Merkle Trees

  • Data integrity verification
  • Efficient synchronization
  • Amazon DynamoDB, Cassandra anti-entropy

7.2.3 ACID and BASE Systems

• Two-Phase Commit (2PC)

  • Distributed transaction coordination
  • Coordinator-participant model
  • Failure handling mechanisms

• Saga Pattern

  • Long-running transactions
  • Compensating actions
  • Microservices architectures

7.3 Search & Retrieval Algorithms

7.3.1 Search Engine Algorithms (Google, Elasticsearch)

• PageRank Algorithm

  • Link analysis
  • Random walk interpretation
  • Power iteration method

• TF-IDF (Term Frequency-Inverse Document Frequency)

  • Document relevance scoring
  • Search ranking applications
  • Elasticsearch implementation

• BM25 (Best Matching 25)

  • Improved relevance function
  • Parameter tuning
  • Elasticsearch default scoring

7.3.2 Recommendation Algorithms (Netflix, Amazon, YouTube)

• Collaborative Filtering

  • User-based collaborative filtering
  • Item-based collaborative filtering
  • Matrix factorization (SVD, NMF)

• Content-Based Filtering

  • Feature extraction
  • Similarity measures
  • Hybrid approaches

• Association Rule Mining

  • Apriori algorithm
  • FP-Growth algorithm
  • Market basket analysis

7.4 Stream Processing Algorithms

7.4.1 Real-time Analytics (Kafka, Storm, Flink)

• Sliding Window Algorithms

  • Time-based windows
  • Count-based windows
  • Session windows

• Approximate Algorithms for Streams

  • Reservoir sampling
  • Count-distinct estimation
  • Heavy hitters detection

7.4.2 Event Processing

• Complex Event Processing (CEP)

  • Pattern detection
  • Temporal relationships
  • Rule-based systems

• Watermarking

  • Late data handling
  • Event time vs processing time
  • Out-of-order event processing

7.5 Machine Learning Infrastructure Algorithms

7.5.1 Large-Scale ML (Google, Facebook, Netflix)

• Gradient Descent Variants

  • Stochastic gradient descent
  • Mini-batch gradient descent
  • Adam optimizer

• Distributed Training

  • Parameter server architecture
  • All-reduce algorithms
  • Synchronous vs asynchronous training

7.5.2 Feature Engineering at Scale

• Dimensionality Reduction

  • Principal Component Analysis (PCA)
  • t-SNE for visualization
  • Random projections

• Locality Sensitive Hashing for ML

  • Nearest neighbor search
  • Similarity learning
  • Clustering acceleration

7.6 Algorithm Optimization Techniques

7.1.1 Space-Time Tradeoffs

• Memory Optimization
  • Cache-friendly algorithms
  • Memory hierarchy awareness
  • Space-efficient data structures

7.6 Algorithm Optimization Techniques

7.6.1 Space-Time Tradeoffs

• Memory Optimization

  • Cache-friendly algorithms
  • Memory hierarchy awareness
  • Space-efficient data structures

• CPU Optimization

  • Branch prediction optimization
  • SIMD (Single Instruction, Multiple Data)
  • Cache line optimization

7.6.2 Parallel and Concurrent Algorithms

• Parallel Computing Concepts

  • Parallel sorting algorithms
  • Map-reduce paradigm
  • Thread-safe data structures

• Lock-Free Data Structures

  • Compare-and-swap operations
  • ABA problem solutions
  • Memory ordering models

7.7 Real-world Applications

7.7.1 Database Algorithms

• Indexing Strategies

  • B-tree and B+ tree indexing
  • Hash indexing
  • Query optimization

• Transaction Processing

  • MVCC (Multi-Version Concurrency Control)
  • Deadlock detection algorithms
  • Recovery algorithms (ARIES)

7.7.2 Distributed Systems

• Distributed Algorithms

  • Consistent hashing
  • Distributed consensus
  • Load balancing algorithms

• Fault Tolerance

  • Byzantine fault tolerance
  • Epidemic algorithms
  • Gossip protocols

7.8 Performance Monitoring & Observability

7.8.1 Metrics Collection (Prometheus, DataDog)

• Time Series Data Structures

  • Compressed time series
  • Downsampling algorithms
  • Anomaly detection

• Sampling Algorithms

  • Reservoir sampling
  • Stratified sampling
  • Importance sampling

7.8.2 Log Processing (ELK Stack, Splunk)

• Log Aggregation
  • Merge algorithms for sorted logs
  • Distributed log collection
  • Real-time log processing

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🏆 Phase 8: Contest Programming & Advanced Topics

8.1 Advanced Problem Solving

8.1.1 Problem Categories

• Ad-hoc Problems

  • Implementation challenges
  • Simulation problems
  • Constructive algorithms

• Interactive Problems

  • Binary search on answer
  • Query-based problems

8.1.2 Advanced Data Structures

• Persistent Data Structures

  • Persistent segment trees
  • Version control in data structures

• Probabilistic Data Structures

  • Bloom filters
  • Skip lists
  • Count-min sketch

• Advanced Tree Decompositions

  • Centroid decomposition
  • Heavy-light decomposition advanced
  • Link-cut trees

• String Data Structures

  • Suffix arrays with LCP
  • Suffix automaton
  • Palindromic trees

8.1.3 Advanced Number Theory

• Multiplicative Functions

  • Mobius function and inversion
  • Euler's totient function
  • Dirichlet convolution

• Advanced Primality

  • Pollard's rho algorithm
  • Quadratic sieve basics
  • Primality certificates

• Algebraic Structures

  • Group theory basics
  • Finite fields
  • Discrete logarithm

8.2 Competitive Programming Techniques

8.2.1 Contest Strategies

• Time Management
  • Problem prioritization
  • Implementation speed
  • Debugging techniques

8.2.2 Advanced Algorithms

• Flow Networks

  • Maximum flow (Ford-Fulkerson, Edmonds-Karp)
  • Minimum cut
  • Bipartite matching

• String Matching Advanced

  • Aho-Corasick algorithm
  • Suffix automaton
  • Manacher's algorithm

• Advanced Graph Algorithms

  • Bridges and articulation points
  • 2-SAT problem solving
  • Strongly connected components applications

• Network Flow Applications

  • Min-cost max-flow
  • Multi-commodity flow
  • Circulation with demands

8.2.3 Optimization Techniques

• Branch and Bound

  • Integer programming
  • Traveling salesman optimization
  • Pruning strategies

• Simulated Annealing

  • Cooling schedules
  • Local search improvement
  • Applications in optimization

• Genetic Algorithms

  • Selection strategies
  • Crossover and mutation
  • Population-based search

8.3 Modern Algorithm Paradigms

8.3.1 Quantum-Inspired Algorithms

• Quantum Computing Basics
  • Grover's search algorithm
  • Shor's factoring algorithm
  • Quantum parallelism concepts

8.3.2 Bio-Inspired Algorithms

• Ant Colony Optimization

  • Pheromone-based search
  • Traveling salesman applications
  • Graph shortest paths

• Particle Swarm Optimization

  • Swarm intelligence
  • Continuous optimization
  • Multi-objective optimization

8.3.3 Machine Learning Algorithms

• Supervised Learning

  • Decision trees (ID3, C4.5, CART)
  • Support vector machines
  • Neural network basics

• Unsupervised Learning

  • K-means clustering
  • Hierarchical clustering
  • DBSCAN density-based clustering

• Reinforcement Learning

  • Q-learning algorithm
  • Policy gradient methods
  • Multi-armed bandit problems

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📈 Learning Path Recommendations

Beginner (0-3 months)

• Focus on Phase 1-2: Foundation and Core Data Structures
• Practice 2-3 problems daily
• Master time complexity analysis

Intermediate (3-8 months)

• Complete Phase 3-4: Advanced Data Structures and Core Algorithms
• Participate in online contests
• Solve 300+ problems across different topics

Advanced (8-15 months)

• Master Phase 5-6: Advanced Algorithms and Specialized Topics
• Focus on optimization techniques
• Solve harder contest problems

Expert (15+ months)

• Complete Phase 7-8: System Design and Contest Programming
• Contribute to open source projects
• Mentor others in the community

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🛠️ Recommended Resources

Online Platforms

• LeetCode - Interview preparation and coding practice
• Codeforces - Competitive programming contests
• AtCoder - High-quality algorithmic problems
• CSES Problem Set - Comprehensive topic-wise practice
• GeeksforGeeks - Comprehensive tutorials and explanations
• TopCoder - Algorithm tutorials and competitions
• HackerRank - Skill-based challenges
• CodeChef - Monthly programming contests
• SPOJ - Classical programming problems
• Kattis - Problem archive for competitive programming

Books

• "Introduction to Algorithms" by CLRS - Comprehensive reference bible
• "Algorithm Design" by Kleinberg & Tardos - Problem-solving approach
• "Competitive Programming" by Steven Halim - Contest strategies and techniques
• "The Algorithm Design Manual" by Skiena - Practical algorithms with real applications
• "Algorithms" by Sedgewick & Wayne - Java-based algorithm implementations
• "Programming Pearls" by Jon Bentley - Elegant problem-solving techniques
• "Cracking the Coding Interview" by Gayle McDowell - Interview preparation
• "Elements of Programming Interviews" by Aziz, Lee & Prakash - Technical interviews
• "Designing Data-Intensive Applications" by Martin Kleppmann - System design
• "High Performance Computing" by Sterling, Anderson & Brodowicz - Parallel algorithms

Video Courses & Channels

• MIT 6.006 Introduction to Algorithms - Fundamental algorithms course
• MIT 6.046J Design and Analysis of Algorithms - Advanced algorithms
• Stanford CS161 Design and Analysis of Algorithms - Algorithm design techniques
• Stanford CS166 Data Structures - Advanced data structures
• Princeton Algorithms Course (Coursera) - Robert Sedgewick's course
• YouTube Channels:
  • Abdul Bari - Clear algorithm explanations
  • William Fiset - Graph theory and algorithms
  • Tushar Roy - Dynamic programming and coding interviews
  • Back To Back SWE - Interview-focused explanations
  • Tech With Tim - Practical programming tutorials
  • 3Blue1Brown - Mathematical intuition behind algorithms

System Design Resources

• "Designing Data-Intensive Applications" by Martin Kleppmann
• High Scalability Blog - Real-world system design case studies
• AWS Architecture Center - Cloud system design patterns
• Google Research Publications - Latest algorithmic research
• Facebook Engineering Blog - Large-scale system insights
• Netflix Tech Blog - Streaming system architectures
• Uber Engineering - Real-time system design
• System Design Interview by Alex Xu - Interview preparation

Research Papers & Advanced Topics

• ACM Digital Library - Latest research in algorithms
• arXiv.org - Preprints in computer science
• Google Scholar - Academic paper search
• SIAM Journal on Computing - Theoretical computer science
• Journal of the ACM - Foundational algorithms research

Coding Practice Platforms

• Pramp - Peer-to-peer mock interviews
• InterviewBit - Structured interview preparation
• Codility - Assessment-style problems
• LintCode - Algorithm practice with hints
• AlgoExpert - Curated interview problems with explanations

Competitive Programming Communities

• Codeforces Blogs - Community discussions and tutorials
• CP-Algorithms - Comprehensive algorithm implementations
• USACO Guide - Structured competitive programming learning
• IOI Syllabus - International Olympiad in Informatics topics
• Reddit r/algorithms - Algorithm discussions and help

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🎯 Assessment Milestones

Phase Completion Criteria

• Foundation: Solve 50+ basic problems, understand Big O
• Core DS: Implement all data structures from scratch
• Advanced DS: Solve 100+ tree/graph problems
• Core Algorithms: Master sorting, searching, basic DP
• Advanced Algorithms: Solve 200+ DP/graph problems
• Specialized: Complete geometry, number theory modules
• System Design: Design and implement efficient systems
• Expert Level: Consistently solve contest problems

Practice Targets

• Total Problems: 1000+ across all difficulty levels
• Contest Participation: 50+ contests
• Implementation: Build 20+ projects using learned concepts

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🤝 Contributing

This syllabus is designed to be comprehensive yet flexible. As you progress through your journey:

1. Track Progress: Check off completed topics
2. Add Notes: Include personal insights and tips
3. Share Resources: Contribute additional learning materials
4. Update Content: Suggest improvements and additions

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📞 Community & Support

Join algorithm study groups, participate in coding communities, and don't hesitate to ask questions. The journey from zero to mastery requires consistency, practice, and continuous learning.

Remember: The goal is not just to learn algorithms, but to develop algorithmic thinking that will serve you throughout your career in computer science.

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Happy Coding! 🚀