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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 ...
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.
Average-case computational hardness assumptions are useful for proving average-case hardness in applications like statistics, where there is a natural distribution over inputs. [22] Additionally, the planted clique hardness assumption has also been used to distinguish between polynomial and quasi-polynomial worst-case time complexity of other ...
[1]: 306 As a conclusion: "Amortized analysis is a useful tool that complements other techniques such as worst-case and average-case analysis." [ 2 ] : 14 [ 3 ] For a given operation of an algorithm, certain situations (e.g., input parametrizations or data structure contents) may imply a significant cost in resources, whereas other situations ...
A skip list does not provide the same absolute worst-case performance guarantees as more traditional balanced tree data structures, because it is always possible (though with very low probability [5]) that the coin-flips used to build the skip list will produce a badly balanced structure. However, they work well in practice, and the randomized ...
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Binary search Visualization of the binary search algorithm where 7 is the target value Class Search algorithm Data structure Array Worst-case performance O (log n) Best-case performance O (1) Average performance O (log n) Worst-case space complexity O (1) Optimal Yes In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search ...