Definition of Amortized Time
In the potential method, a function Φ is chosen that maps states of the data structure to non-negative numbers. If S is a state of the data structure, Φ(S) may be thought of intuitively as an amount of potential energy stored in that state; alternatively, Φ(S) may be thought of as representing the amount of disorder in state S or its distance from an ideal state. The potential value prior to the operation of initializing a data structure is defined to be zero.
Let o be any individual operation within a sequence of operations on some data structure, with Sbefore denoting the state of the data structure prior to operation o and Safter denoting its state after operation o has completed. Then, once Φ has been chosen, the amortized time for operation o is defined to be
where C is a non-negative constant of proportionality (in units of time) that must remain fixed throughout the analysis. That is, the amortized time is defined to be the actual time taken by the operation plus C times the difference in potential caused by the operation.
Read more about this topic: Potential Method
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