Optimization Problems: Greedy Algorithms

This lecture covers optimization problems, which aim to minimize or maximize a parameter over all possible inputs, and how greedy algorithms can be used to solve them by making the 'best' choice at each step. The instructor explains the concept through examples like finding the shortest route between cities and encoding messages efficiently. The lecture also delves into the Cashier's Algorithm, demonstrating how to find the least total number of coins for a given amount using a greedy approach. The proof of optimality for the U.S. coin change-making algorithm is discussed, showing that the greedy algorithm indeed produces the fewest coins possible.