Algorithms

Probabilistic data structures offer approximate answers to complex queries on massive datasets, trading perfect accuracy for dramatic gains in memory efficiency and speed.[3][1] This tutorial progresses from foundational concepts and the simplest structure (Bloom Filter) to advanced ones like HyperLogLog and Count-Min Sketch, complete with math, code examples, and real-world applications. What Are Probabilistic Data Structures? Probabilistic data structures handle big data and streaming applications by using hash functions to randomize and compactly represent sets of items, ignoring collisions while controlling errors within thresholds.[1] Unlike deterministic structures that guarantee exact results, these provide approximations, enabling constant query times and far less memory usage.[1][3] ...

Introduction This comprehensive guide contains 500 curated LeetCode problems organized for efficient interview preparation. Each problem includes: ✅ Interactive checkboxes for progress tracking 🔥 Priority markers for must-solve problems 🟢🟡🔴 Difficulty indicators (Easy/Medium/Hard) Pattern tags for systematic learning Study Recommendations Beginner Path (3-4 months): Start with Easy problems in Array & Hash Table Master Two Pointers and Sliding Window patterns Build foundation with Trees and Linked Lists Practice 2-3 problems daily Intermediate Path (2-3 months): ...

The Union-Find data structure (also known as Disjoint Set Union or DSU) is a powerful tool for managing dynamic connectivity in sets of elements. It efficiently handles two core operations: union (merging sets) and find (determining if elements belong to the same set). This article dives deep into multiple Union-Find implementations in Python, their optimizations, performance characteristics, and critical applications in system design.[1][2][4] Whether you’re preparing for coding interviews, competitive programming, or designing scalable distributed systems, understanding Union-Find variants will give you a significant edge. ...

Demystifying Google Analytics Algorithms: How They Process and Analyze Your Data Google Analytics is a powerhouse tool for website owners, marketers, and businesses tracking user behavior online. At its core, its algorithms crunch vast amounts of data to deliver actionable insights, from session attribution to conversion tracking. Unlike the opaque Google Search algorithms—which crawl, index, and rank web pages[1][2][4]—Google Analytics algorithms focus on processing user interactions within your site or app, applying statistical models to filter noise, attribute credit, and predict trends. ...

Introduction Solving a Rubik’s Cube is far less about memorizing dozens of algorithms and far more about understanding how pieces move and how to control those movements. This guide gives you a mental model first—so every algorithm makes sense—and then a clear, beginner-friendly path from zero to hero. You’ll start with the simplest Layer‑by‑Layer method, learn the fewest essential algorithms to finish reliably, and see exactly how to upgrade your skills toward faster methods without feeling overwhelmed. ...