Efficient Algorithms and Median Search

This lecture covers various algorithms, including calculating the square of a large integer more efficiently than the product of two large integers, an ancient Egyptian recursive algorithm for integer multiplication, and a median search algorithm. It also discusses the efficiency of these algorithms compared to Karatsuba multiplication and their temporal complexity. The instructor presents exercises on these topics, such as testing algorithm correctness, linking with binary decomposition, and analyzing temporal complexity. Additionally, an in-place median search algorithm is proposed, involving subdivision of a list into three sublists. The lecture concludes with unconventional sorting algorithms and their temporal complexity analysis.