Euclidean Algorithm: GCD Calculation

This lecture introduces the Euclidean algorithm for calculating the greatest common divisor (GCD) of two positive integers. The algorithm is based on the property that the GCD of two numbers is also the GCD of the smaller number and the remainder of their division. Through a series of slides, the instructor explains the termination conditions of the algorithm, the importance of the loop invariant, and the constant nature of the returned GCD value. The lecture also covers the complexity analysis of algorithms, focusing on time measurements and the evaluation criteria based on the size of the input.