Amortized analysis
Often we are not so interested in the time complexity of individual operations, but rather the time averaged running time of sequences of operations. This is called amortized analysis. It is different from average case analysis, which we will discuss shortly, in that it makes no assumptions regarding the data distribution of input values. It does, however, take into account the state change of data structures. For example, if a list is sorted it should make any subsequent find operations quicker. Amortized analysis can take into account the state change of data structures because it analyzes sequences of operations, rather then simply aggregating single operations.
Amortized analysis finds an upper bound on runtime by imposing an artificial cost on each operation in a sequence of operations, and then combining each of these costs. The artificial cost of a sequence takes in to account that the initial expensive operations can make subsequent operations cheaper.
When we have...
