CS310 Algorithms Lesson 3 | Randomized Algorithms скачать в хорошем качестве

CS310 Algorithms Lesson 3 | Randomized Algorithms

This lecture, part of the CS310 Algorithms series at LUMS, transitions from deterministic strategies to randomized approaches for solving complex algorithmic problems. Key highlights include: Course Logistics: Updates on Homework 1 grading and upcoming midterm schedules [00:55]. Recap of Prune and Search: A review of the Median of Medians algorithm used to solve the Selection Problem (finding the k-th smallest element). The instructor explains how dividing the array into groups of five and finding the median of medians results in a linear time complexity O(n) through recursive analysis and convexity [03:11]. Introduction to Randomized Selection: Shifting from the deterministic ‘Median of Medians’ pivot to a randomized approach, where a pivot is selected uniformly at random [24:24]. Probability Foundations: To analyze randomized algorithms, the lecture covers essential probability concepts: Random Experiments & Sample Spaces: Defining outcomes and events [33:04]. Probability Distributions: Rules for assigning values to outcomes [34:55]. Random Variables & Expected Value: Mathematical definitions and calculating the weighted average of outcomes [37:38]. Linearity of Expectation: A crucial property for analyzing the sum of random variables [43:07]. Practical Lab - Asymptotic Notation with Z3: An in-class activity using the Z3 Solver library in Python to programmatically verify Big O, Big Omega, and Little o notations by encoding mathematical constraints into code [57:16].