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Here methods like random self-reducibility can be used for some specific problems to show that the worst case is no harder than the average case, or, equivalently, that the average case is no easier than the worst case. On the other hand, some data structures like hash tables have very poor worst-case behaviors, but a well written hash table of ...
The best case is (() + ) for already sorted data. The worst-case is () for reverse sorted data. In average cases, there are likely to be few heap updates and most input elements are processed with only a single comparison. For example, extracting the 100 largest or smallest values out of 10,000,000 random inputs makes 10,009,401 ...
One can combine basic quickselect with median of medians as fallback to get both fast average case performance and linear worst-case performance; this is done in introselect. Finer computations of the average time complexity yield a worst case of n ( 2 + 2 log 2 + o ( 1 ) ) ≤ 3.4 n + o ( n ) {\displaystyle n(2+2\log 2+o(1))\leq 3.4n+o(n ...
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To obtain the average-case complexity, given an input distribution, the expected time of an algorithm is evaluated, whereas for the almost-always complexity estimate, it is evaluated that the algorithm admits a given complexity estimate that almost surely holds.
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Jason Fitz and Frank Schwab pick 6 NFL teams and play a game of “Angels & Devils” to predict the best case and worst case scenarios for each team.
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