Method
The method requires knowledge of which series of operations are possible. This is most commonly the case with data structures, which have state that persists between operations. The basic idea is that a worst case operation can alter the state in such a way that the worst case cannot occur again for a long time, thus "amortizing" its cost.
There are generally three methods for performing amortized analysis: the aggregate method, the accounting method, and the potential method. All of these give the same answers, and their usage difference is primarily circumstantial and due to individual preference.
- Aggregate analysis determines the upper bound T(n) on the total cost of a sequence of n operations, then calculates the amortized cost to be T(n) / n.
- The accounting method determines the individual cost of each operation, combining its immediate execution time and its influence on the running time of future operations. Usually, many short-running operations accumulate a "debt" of unfavorable state in small increments, while rare long-running operations decrease it drastically.
- The potential method is like the accounting method, but overcharges operations early to compensate for undercharges later.
Read more about this topic: Amortized Analysis
Famous quotes containing the word method:
“Women stand related to beautiful nature around us, and the enamoured youth mixes their form with moon and stars, with woods and waters, and the pomp of summer. They heal us of awkwardness by their words and looks. We observe their intellectual influence on the most serious student. They refine and clear his mind: teach him to put a pleasing method into what is dry and difficult.”
—Ralph Waldo Emerson (1803–1882)
“I know no method to secure the repeal of bad or obnoxious laws so effective as their stringent execution.”
—Ulysses S. Grant (1822–1885)
“Traditional scientific method has always been at the very best 20-20 hindsight. It’s good for seeing where you’ve been. It’s good for testing the truth of what you think you know, but it can’t tell you where you ought to go.”
—Robert M. Pirsig (b. 1928)