Last Minute Lecture

Online Algorithms, Competitive Analysis & Caching Strategies | Chapter 27 in Introduction to Algorithms Chapter 27 of Introduction to Algorithms explores the fascinating world of online algorithms—those that operate without access to future input. Unlike offline algorithms, which can optimize decisions with full knowledge of the input sequence, online algorithms must make real-time choices. This chapter introduces competitive analysis as a framework for evaluating their effectiveness and walks through key applications like list maintenance, caching, and scheduling. From the Move-to-Front (MTF) heuristic to randomized caching strategies like RANDOMIZED-MARKING, this chapter offers foundational concepts critical to understanding real-world systems such as memory management and web caching. Watch the video above for a complete walkthrough of Chapter 27, and read on for a full breakdown of the core models, algorithms, and theorems that define online decision-making in algorithm...

Quicksort — Partitioning, Randomization, and Performance Analysis | Chapter 7 of Intro to Algorithms Quicksort stands as one of the fastest and most practical sorting algorithms in computer science. Chapter 7 of introduction to algorithms details how quicksort combines divide-and-conquer strategy with clever partitioning to achieve remarkable average-case performance. From basic in-place sorting to powerful randomized variants and real-world optimization techniques, this chapter delivers everything you need to understand why quicksort is a cornerstone of algorithmic problem-solving. Prefer a podcast-style explanation? Watch the chapter summary below, and subscribe to Last Minute Lecture for clear, in-depth guides to every chapter of introduction to algorithms . How Quicksort Works Quicksort sorts an array by partitioning it around a pivot element, recursively sorting the left and right subarrays. The basic version chooses the last element as the pivot. All elements l...

Probabilistic Analysis & Randomized Algorithms — Indicator Variables, Secretary Problem, and Randomized Sorting | Chapter 5 of Intro to Algorithms Randomness is a powerful tool in algorithm design. Chapter 5 of Introduction to Algorithms introduces probabilistic analysis and randomized algorithms—two approaches that help us analyze performance or even improve efficiency when input distributions are unknown. This chapter covers key ideas such as indicator variables, linearity of expectation, random permutations, and optimal strategies for classic problems like hiring and the secretary problem. Prefer to learn by listening? Watch the podcast summary below, and subscribe to Last Minute Lecture for in-depth textbook explanations and more algorithm breakdowns. The Hiring Problem and Probabilistic Analysis A classic illustration of probabilistic analysis is the hiring problem : a deterministic HIRE-ASSISTANT algorithm hires a candidate only if they’re better than the cur...