Entropy and Algorithms: Applications in Sorting and Weighing

This lecture discusses the role of entropy in algorithms, particularly in sorting and decision-making processes. It begins with the 20 Questions Problem, exploring how to minimize the number of yes/no questions needed to identify a random variable. The instructor explains the optimal querying strategy using Huffman codes, demonstrating how to construct binary codes for efficient questioning. The lecture then transitions to sorting algorithms based on pairwise comparisons, detailing how to sort an unsorted list and the expected number of comparisons required. The concept of entropy is further applied to the Billiard Balls Puzzle, where the challenge is to identify a unique ball among several using a limited number of weighings. The instructor emphasizes that while entropy provides a lower bound for algorithmic performance, it does not guarantee the existence of an optimal strategy. The session concludes with a summary of key concepts, including the relationship between entropy, coding, and algorithm efficiency.