Advanced Number Theory Interview Patterns: Chinese Remainder Theorem, Euler Totient, and Digit DP (2025)
Chinese Remainder Theorem (CRT) CRT solves systems of congruences: given x ≡ ai (mod mi) where mi are pairwise coprime, […]
Algorithms
System Design
System Design: Maps and Navigation Platform — Routing, ETA, and Real-Time Traffic (2025)
Requirements and Scale Functional: turn-by-turn navigation, ETA estimation, real-time traffic updates, points of interest search, route alternatives. Non-functional: 1B daily
System Design
Low-Level Design: Social Feed System — Fan-Out, Ranking, and Personalization
Core Entities and Fan-Out Strategies Post: post_id, author_id, content, media_urls (array), created_at, like_count, comment_count, share_count. Follow: follower_id, followee_id, created_at. FeedItem:
System Design
Low-Level Design: Ride-Sharing Dispatch System — Matching, Routing, and Surge Pricing
Core Entities Driver: driver_id, name, vehicle_type (ECONOMY/COMFORT/XL), status (OFFLINE, AVAILABLE, ON_TRIP), current_location (POINT: lat/lng), last_location_update, rating, acceptance_rate. Rider: rider_id, name,
System Design
System Design: Collaborative Document Editing — Operational Transformation and CRDT (2025)
Requirements and Core Challenge Functional: multiple users edit the same document simultaneously, changes from all users are reflected in real
System Design
Low-Level Design: Flash Sale System — Inventory Lock, Queue Fairness, and Oversell Prevention
Core Challenge and Entities A flash sale creates a sudden traffic spike (100x-1000x normal load) competing for limited inventory. The
Algorithms
Backtracking Interview Patterns: Subsets, Permutations, N-Queens, and Constraint Satisfaction (2025)
Backtracking Template Backtracking = DFS + undo. The universal template: choose (add to path), recurse (explore), unchoose (remove from path).
System Design
Low-Level Design: Content Moderation System – Rules Engine, ML Scoring, and Appeals (2025)
Problem Statement Design a content moderation system for a social platform. User-generated content (text, images, video) must be screened before
System Design
System Design: Payment Processing Platform – Authorization, Settlement, and Fraud Detection (2025)
Scope and Requirements A payment processing platform handles money movement between buyers and sellers through external payment processors (Stripe, Adyen,
Algorithms
Sorting Algorithm Deep Dive: Quicksort, Mergesort, Heapsort, and Counting Sort (2025)
Why Sorting Algorithms Still Matter in Interviews Interviewers at top tech companies still ask about sorting not to test memorization,
System Design
Low-Level Design: Appointment Scheduling System — Availability, Booking, and Conflict Prevention
Core Entities Provider: provider_id, name, email, type (DOCTOR, THERAPIST, CONSULTANT, TUTOR), timezone, settings (JSONB: buffer_minutes_between_appointments, max_advance_days, min_notice_hours, auto_confirm). Schedule: schedule_id,
Algorithms
Matrix and 2D Grid Interview Patterns: BFS, DFS, Rotation, and Search (2025)
2D Grid BFS and DFS Fundamentals from collections import deque DIRS = [(0,1),(0,-1),(1,0),(-1,0)] # right, left, down, up def bfs_grid(grid,
Algorithms
Graph Cycle Detection Interview Patterns: Directed, Undirected, and Floyd’s Algorithm (2025)
Cycle Detection in Undirected Graphs from collections import deque # DFS approach: track parent to distinguish back edge from tree
System Design
Low-Level Design: Warehouse Inventory Management — Stock Tracking, Reservations, and Replenishment
Core Entities Product: product_id, sku, name, category_id, unit_cost, unit_weight_grams, dimensions (JSONB: length, width, height in mm), reorder_point, reorder_quantity, lead_time_days, is_active.
System Design
System Design: Video Processing Platform — Upload, Transcoding, Storage, and Streaming (2025)
Requirements and Scale Functional: upload raw video, transcode to multiple resolutions (240p/480p/720p/1080p/4K), store and serve video streams, support adaptive bitrate