This lecture covers the coin change problem, where given a certain amount of money and a set of available coins, the goal is to make the exact change with the fewest coins possible. The instructor explains the greedy algorithm, its limitations, and introduces dynamic programming as a more exploratory approach. Examples are provided to illustrate scenarios where the greedy algorithm fails to find the optimal solution. The lecture concludes with the formal description of the dynamic programming algorithm and the concept of memoization to systematically explore all possible paths to solve the problem.