The median is somewhat tricky to compute in the general case, because it involves sorting the whole data set, or using a recursion with a depth that is also proportional to the data set size. That’s maybe the reason why many databases don’t have a median operator out of the box (MySQL doesn’t have one, … Read more
I found this post interesting and as an exercise I created this which ONLY does 6 comparisons and NOTHING else: static double MedianOfFive(double a, double b, double c, double d, double e) { return b < a ? d < c ? b < d ? a < e ? a < d ? e … Read more
Let’s say that the median is the element in the middle of an ordered list. SQLite (4 or 3) does not have any built-in function for that, but it’s possible to do this by hand: SELECT x FROM MyTable ORDER BY x LIMIT 1 OFFSET (SELECT COUNT(*) FROM MyTable) / 2 When there is an … Read more
Immutable Algorithm The first algorithm indicated by Taylor Leese is quadratic, but has linear average. That, however, depends on the pivot selection. So I’m providing here a version which has a pluggable pivot selection, and both the random pivot and the median of medians pivot (which guarantees linear time). import scala.annotation.tailrec @tailrec def findKMedian(arr: Array[Double], … Read more
I think your example input/output does not correspond to typical ways of calculating percentile. If you calculate the percentile as “proportion of data points strictly less than this value”, then the top value should be 0.8 (since 4 of 5 values are less than the largest one). If you calculate it as “percent of data … Read more
The correct O(n) solution is quite complicated, and takes a significant amount of text, code and skill to explain and prove. More precisely, it takes 3 pages to do so convincingly, as can be seen in details here http://www.cse.yorku.ca/~andy/pubs/X+Y.pdf (found by simonzack in the comments). It is basically a clever divide-and-conquer algorithm that, among other … Read more
There are a number of possibilities. One I like is Hoare’s Select algorithm. The basic idea is similar to a Quicksort, except that when you recurse, you only recurse into the partition that will hold the number(s) you’re looking for. For example, if you want the median of 100 numbers, you’d start by partitioning the … Read more
There is no need to completely sort the vector: std::nth_element can do enough work to put the median in the correct position. See my answer to this question for an example. Of course, that doesn’t help if your teacher forbids using the right tool for the job.