This is the idea that we need to be aware of the limitations and pitfalls of greedy algorithms, such as when they fail to find optimal solutions, or when they are not applicable at all. For example, in the coin change problem, where we want to find the minimum number of coins needed to make a given amount of money, a greedy algorithm that always picks the largest coin available may not work for some coin systems. For instance, if we have coins of 25, 10, and 4 cents, and we want to make 41 cents, the greedy algorithm would pick one 25-cent coin and four 4-cent coins, for a total of five coins. However, the optimal solution is to pick four 10-cent coins and one 1-cent coin, for a total of four coins.
Greedy algorithms are a useful tool for algorithm design, but they require careful analysis and justification. By understanding the essential algorithm design concepts for greedy algorithms, you can apply them effectively and confidently to a variety of problems.