9/1/2023 0 Comments Median formula![]() ![]() If you wanted instead average of lower and upper then you need to call above code twice. This question becomes particularly critical for set of 2 elements. Some textbooks use lower median as "standard" while others propose to use average of two. But when you even number of element (Count-1)/2 is not an integer anymore and you have two medians: Lower median Math.Floor((Count-1)/2) and Math.Ceiling((Count-1)/2). It's just the element with index (Count-1)/2 in sorted array. Definition of median is clear if you have odd number of elements.This is generally not necessary unless you know your data has certain patterns so that last element won't be random enough or if somehow your code is exposed outside for targeted exploitation. The NthOrderStatistics method allows to pass random number generator which would be then used to choose random pivot during partition.However if you would be calculating median mostly on very large data then its worth to look at. While this would improve worse case performance, it degrades average case because constant in O(n) is now larger. If you want O(n) worse case time then there is technique to use median-of-median. Above methods calculates median or any i-order statistics in O(n) expected time.If you use the version that accepts IList then keep in mind it modifies the order in list. I've provided two version of Median, one that accepts IEnumerable and then creates a list.It also eliminates unnecessary extra check from original version when start=end.This code replaces tail recursive code from the original version in book in to iterative loop.Var list = sequence.Select(getValue).ToList() Public static double Median(this IEnumerable sequence, Func getValue) Return list.NthOrderStatistic((list.Count - 1)/2) Public static T Median(this IList list) where T : IComparable If (i=j) //This check is not required but Partition function may make many calls so its for perf reason Var pivotIndex = list.Partition(start, end, rnd) Private static T NthOrderStatistic(this IList list, int n, int start, int end, Random rnd) where T : IComparable Return NthOrderStatistic(list, n, 0, list.Count - 1, rnd) Public static T NthOrderStatistic(this IList list, int n, Random rnd = null) where T : IComparable / Reference: Introduction to Algorithms 3rd Edition, Corman et al, pp 216 / Note: specified list would be mutated in the process. Here n starts from 0 so that n=0 returns minimum, n=1 returns 2nd smallest element etc. / Returns Nth smallest element from the list. Private static int Partition(this IList list, int start, int end, Random rnd = null) where T : IComparable / Reference: Introduction to Algorithms 3rd Edition, Corman et al, pp 171 / Pivot is selected ranodmly if random number generator is supplied else its selected as last element in the list. ![]() This method can be used for sorting, N-order statistics such as ![]() / Partitions the given list around a pivot element such that all elements on left of pivot are pivot. Median is simply (Count-1)/2-order statistic.īelow is the code adopted from Introduction to Algorithms by Cormen et al, 3rd Edition. So 0th order statistic would be minimal element in the set (Note: Some literature use index from 1 to N instead of 0 to N-1). ![]() The generalized version of this problem is known as "n-order statistics" which means finding an element K in a set such that we have n elements smaller or equal to K and rest are larger or equal K. It is possible to calculate median in O(n) time instead. That's not optimal from performance point of view because it takes O(n logn) time. Looks like other answers are using sorting. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |