Problem Statement

Write a program to find the   median   value of a vector of floating-point numbers. The program need not handle the case where the vector is empty, but must handle the case where there are an even number of elements.   In that case, return the average of the two middle values. There are several approaches to this.   One is to sort the elements, and then pick the element(s) in the middle. Sorting would take at least   O(n logn).   Another approach would be to build a priority queue from the elements, and then extract half of the elements to get to the middle element(s).   This would also take   O(n logn).   The best solution is to use the   selection algorithm   to find the median in   O(n)   time. Quickselect_algorithm

Let's start with the solution:

USING: arrays kernel locals math math.functions random sequences ;
IN: median

: pivot ( seq -- pivot ) random ;

: split ( seq pivot -- {lt,eq,gt} )
  [ [ < ] curry partition ] keep
  [ = ] curry partition
  3array ;

DEFER: nth-in-order
:: nth-in-order-recur ( seq ind -- elt )
  seq dup pivot split
  dup [ length ] map  0 [ + ] accumulate nip
  dup [ ind <= [ 1 ] [ 0 ] if ] map sum 1 -
  [ swap nth ] curry bi@
  ind swap -
  nth-in-order ;

: nth-in-order ( seq ind -- elt )
  dup 0 =
  [ drop first ]
  [ nth-in-order-recur ]
  if ;

: median ( seq -- median )
  dup length 1 - 2 / floor nth-in-order ;


( scratchpad ) 11 iota median .
5
( scratchpad ) 10 iota median .
4