![]() this is inefficient because the lookup time increases (and efficiency decreases/converges to that of looking up an unsorted list) when the bins are filled larger. if the data is pathological (wrt key hashing algorithm), it all "piles up" in fewer bins, and some bins have far less. for nonpathological data each bin has/contains roughly the same amount of data. one would expect/hope that the data is evenly distributed between all the bins, "balanced". Pathological (implying bad but rare) cases.Īnother way to think about this: hash keys are like separate "bins" that contain the data. The fact that quicksort is as good on average may be attributed to theįact that the $O(n^2)$ time complexity actually occurs only on $O(n \lg n)$ on average, and the space complexity is $O(\lg n)$ for ![]() ![]() But people will often use quicksort, because they both are time Quicksort is time $O(n^2)$ while merge sort is $O(n \lg n)$ in the worstĬase. There are many algorithms that, while having a worst case complexityĪbove the optimal one, are on the average as good or better than worstĬase optimal algorithm. Tomatoes are very rare so that tomato dishes are considered excellent, Pathological people, meaning those people who are allergic to More precise (for example with probabilities), but the use of theįor example, tomato salad and ketchup are excellent food, except for This can sometimes be made mathematically Pathological when it is rare enough in actual uses, so that things Pathological data is supposed to be data that makes things go wrong in
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