Algorithmic Analysis: instances and amortized cost

In this video the concept of instances in algorithms refers to when multiple algorithms or the same algorithm takes different amounts of time depending on specific input. There are three cases: best case (lower bound), worst case (upper bound), and average case, which represents all other cases. The concept of amortized cost is introduced, where an expensive operation may be necessary to reduce the overall cost of an algorithm. An example is given of appending elements to a list, where initially, no copying is necessary until the capacity is reached, and then the list needs to be copied and its capacity increased. This concept of amortization means that even though a costly operation occurs, it can be divided among multiple insertions, resulting in a constant real cost.