In algorithm analysis, what does "amortized analysis" refer to?

Amortized analysis is a technique used in algorithm analysis to determine the average time complexity of an operation over a worst-case sequence of operations. This approach provides a more realistic understanding of the performance of an algorithm by balancing expensive operations with cheaper ones over time. In scenarios where certain operations may be costly but occur infrequently, amortized analysis allows you to average the total cost across all operations, thus providing insight into the long-term performance of an algorithm rather than focusing solely on the worst-case time of individual operations.

Using this technique, you can demonstrate that although some operations can be costly, their impact on overall performance can be mitigated when distributed over multiple operations. This makes it particularly useful for data structures like dynamic arrays or splay trees, where resizing or restructuring events can temporarily increase the time of individual operations. Amortized analysis offers a comprehensive perspective that supports understanding the efficiency of an algorithm in practical applications, rather than just in theoretical scenarios.