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Complexity Analysis

Title text: PERPETUALLY OPTIMISTIC CASE: Early in the execution, our research group makes a breakthrough on proving P=NP.

Explanation

This explanation may be incomplete or incorrect: Created by a PERPETUALLY OPTIMISTIC BOT - Please change this comment when editing this page. Do NOT delete this tag too soon.

Cueball is teaching about an algorithm's complexity. The average-case runtime of the algorithm, O(n log n), is written in Big O notation, expressing the asymptotic runtime of the algorithm as the number of inputs to it grows larger and larger. The "best case" for an algorithm is typically its runtime when its inputs have optimal values and it runs in as little time as possible. The joke here is that not only does it run this quickly, but that its runtime is actually an hour shorter because of an act of Congress changing daylight saving time, potentially giving it negative 'runtime'. The "worst case" refers to the movie Groundhog Day, in which the same events occur over and over in a sort of time loop. This may be an indirect reference to the halting problem, a famous problem in computer science of determining whether a given algorithm will ever halt. The halting problem is undecidable, meaning that there is no general algorithm that can tell whether a given algorithm will halt.

The title text refers to perhaps an even more famous problem in computer science, P versus NP. This asks whether every problem whose solution can be quickly verified (in nondeterministic polynomial time, NP) can also be quickly solved (in polynomial time, P). The P-versus-NP problem is one of the seven Millennium Prize Problems, and as such has a $1 million prize for its solution.

Transcript

This transcript is incomplete. Please help editing it! Thanks.

[Cueball is holding a presentation pointer stick, pointing to a table behind him]

[Title above the table:]

Results of algorithm complexity analysis:

[Table content:]

Average case | O(n log n)

Best case | Algorithm turns out to be unnecessary and is halted, then congress enacts surprise daylight saving time and we gain an hour

Worst case | Town in which hardware is located enters a groundhog day scenario, algorithm never terminates

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