Lecture Note
University
University of California San DiegoCourse
CSE 100/101 | Data Structures and AlgorithmsPages
2
Academic year
2023
anon
Views
38
Recognizing the Physicist's Amortized Analysis Method A method for figuring out an algorithm's average-case time complexity is amortized analysis. It is a crucial tool in computer science and by givingprogrammers a clear idea of the cost of operations over time, it can aid in thecreation of algorithms that are more effective. This article's main method forundertaking amortized analysis is the physicist's method. According to the physicist's method, a data structure's state can be translated into an integer that represents its potential using a potential function.This idea is comparable to what you learnt about potential energy in high schoolphysics. For instance, a ball's potential energy rises as it is carried to the top of ahill; when the ball is let to roll down the hill, however, its prospective energyfalls while its kinetic energy rises. The data structure of the physicist's techniqueis used in the same way, with the potential function serving as a placeholder forpotential future work. The Potential Function's Definition Two requirements must be met by the potential function: first, the potential of the data structure's initial state (phi of h sub 0) must equal 0, andsecond, the potential can never be negative (phi of h sub t is greater than orequal to 0). The amortized cost of an operation can be determined when the possible function has been identified. The genuine cost (c sub t) plus the difference inpotential before and after the operation (phi(h sub t) - phi(h sub t-1)) equal theamortized cost. Selecting the Possible Function The correct potential function must be selected in order to employ the physicist's method for amortized analysis properly. The potential should rise if
the actual cost of an operation is low in order to accumulate funds forsubsequent activities. The potential should decrease to cover the cost of thework being done, however, if the genuine cost is high. True Cost to Amortized Cost Ratio The definition of amortized cost is (c sub I + phi(h sub I - phi(h sub i-1)), and it can be used to calculate the relationship between the total actual costs ofall operations and the total amortized costs. The potential function's positive andnegative values will cancel out, leaving only the beginning potential (phi of hsub 0) and the end potential. This is vital to keep in mind (phi of h sub n). The physicist's approach is an effective instrument for amortized analysis and figuring out an algorithm's average-case time complexity. The amortizedcost of operations can be determined and linked to the true cost by creating apossible function and selecting it wisely. Understanding this approach is crucialfor creating effective algorithms and enhancing computer systems' performance.
Amortized Analysis: Physicist's Method
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