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Ingy döt Net
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set alist to {1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0}
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set med to medi(alist)
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on medi(alist)
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set temp to {}
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set lcount to count alist
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if lcount is equal to 2 then
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return ((item 1 of alist) + (item 2 of alist)) / 2
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else if lcount is less than 2 then
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return item 1 of alist
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else --if lcount is greater than 2
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set min to findmin(alist)
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set max to findmax(alist)
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repeat with x from 1 to lcount
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if x is not equal to min and x is not equal to max then set end of temp to item x of alist
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end repeat
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set med to medi(temp)
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end if
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return med
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end medi
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on findmin(alist)
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set min to 1
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set alength to count every item of alist
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repeat with x from 1 to alength
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if item x of alist is less than item min of alist then set min to x
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end repeat
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return min
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end findmin
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on findmax(alist)
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set max to 1
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set alength to count every item of alist
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repeat with x from 1 to alength
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if item x of alist is greater than item max of alist then set max to x
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end repeat
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return max
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end findmax
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@ -0,0 +1 @@
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4.5
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106
Task/Averages-Median/AppleScript/averages-median-3.applescript
Normal file
106
Task/Averages-Median/AppleScript/averages-median-3.applescript
Normal file
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-- MEDIAN ---------------------------------------------------------------------
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-- median :: [Num] -> Num
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on median(xs)
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-- nth :: [Num] -> Int -> Maybe Num
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script nth
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on |λ|(xxs, n)
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if length of xxs > 0 then
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set {x, xs} to uncons(xxs)
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script belowX
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on |λ|(y)
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y < x
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end |λ|
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end script
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set {ys, zs} to partition(belowX, xs)
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set k to length of ys
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if k = n then
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x
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else
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if k > n then
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|λ|(ys, n)
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else
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|λ|(zs, n - k - 1)
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end if
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end if
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else
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missing value
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end if
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end |λ|
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end script
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set n to length of xs
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if n > 0 then
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tell nth
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if n mod 2 = 0 then
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(|λ|(xs, n div 2) + |λ|(xs, (n div 2) - 1)) / 2
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else
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|λ|(xs, n div 2)
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end if
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end tell
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else
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missing value
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end if
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end median
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-- TEST -----------------------------------------------------------------------
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on run
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map(median, [¬
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[], ¬
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[5, 3, 4], ¬
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[5, 4, 2, 3], ¬
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[3, 4, 1, -8.4, 7.2, 4, 1, 1.2]])
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--> {missing value, 4, 3.5, 2.1}
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end run
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-- GENERIC FUNCTIONS ----------------------------------------------------------
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-- map :: (a -> b) -> [a] -> [b]
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on map(f, xs)
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tell mReturn(f)
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set lng to length of xs
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set lst to {}
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repeat with i from 1 to lng
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set end of lst to |λ|(item i of xs, i, xs)
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end repeat
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return lst
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end tell
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end map
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-- Lift 2nd class handler function into 1st class script wrapper
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-- mReturn :: Handler -> Script
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on mReturn(f)
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if class of f is script then
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f
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else
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script
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property |λ| : f
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end script
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end if
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end mReturn
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-- partition :: predicate -> List -> (Matches, nonMatches)
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-- partition :: (a -> Bool) -> [a] -> ([a], [a])
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on partition(f, xs)
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tell mReturn(f)
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set lst to {{}, {}}
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repeat with x in xs
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set v to contents of x
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set end of item ((|λ|(v) as integer) + 1) of lst to v
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end repeat
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end tell
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{item 2 of lst, item 1 of lst}
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end partition
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-- uncons :: [a] -> Maybe (a, [a])
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on uncons(xs)
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if length of xs > 0 then
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{item 1 of xs, rest of xs}
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else
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missing value
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end if
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end uncons
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@ -0,0 +1 @@
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{missing value, 4, 3.5, 2.1}
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-- Return the median value of items l thru r of a list of numbers.
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on getMedian(theList, l, r)
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if (theList is {}) then return theList
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script o
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property lst : theList's items l thru r -- Copy of the range to be searched.
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end script
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set rangeLength to (r - l + 1)
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set m to (rangeLength + 1) div 2 -- Central position in the range copy, or the leftmost of two.
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set {l, r} to {1, rangeLength} -- Outer partition indices.
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set previousR to r -- Reminder of previous r.
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repeat -- quickselect repeat
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set pivot to o's lst's item ((l + r) div 2)
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set i to l
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set j to r
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repeat until (i > j)
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set lv to o's lst's item i
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repeat while (lv < pivot)
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set i to i + 1
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set lv to o's lst's item i
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end repeat
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set rv to o's lst's item j
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repeat while (rv > pivot)
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set j to j - 1
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set rv to o's lst's item j
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end repeat
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if (i > j) then
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else
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set o's lst's item i to rv
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set o's lst's item j to lv
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set i to i + 1
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set j to j - 1
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end if
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end repeat
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-- If i and j have crossed at m, item m's the median value.
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-- Otherwise reset to partition the partition containing m.
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if (j < m) then
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if (i > m) then exit repeat
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set l to i
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else
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set previousR to r
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set r to j
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end if
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end repeat
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set median to item m of o's lst
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-- If the range has an even number of items, find the lowest value to the right of m and average it
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-- with the median just obtained. We only need to search to the end of the range just partitioned —
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-- unless that's where m is, in which case to end of the most recent extent beyond that (if any).
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if (rangeLength mod 2 is 0) then
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set median2 to item i of o's lst
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if (r = m) then set r to previousR
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repeat with i from (i + 1) to r
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set v to item i of o's lst
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if (v < median2) then set median2 to v
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end repeat
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set median to (median + median2) / 2
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end if
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return median
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end getMedian
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-- Demo:
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local testList
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set testList to {}
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repeat with i from 1 to 8
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set end of testList to (random number 500) / 5
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end repeat
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return {|numbers|:testList, median:getMedian(testList, 1, (count testList))}
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@ -0,0 +1,62 @@
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-- Based on the heap sort algorithm ny J.W.J. Williams.
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on getMedian(theList, l, r)
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script o
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property lst : theList's items l thru r -- Copy of the range to be searched.
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-- Sift a value down into the heap from a given root node.
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on siftDown(siftV, root, endOfHeap)
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set child to root * 2
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repeat until (child comes after endOfHeap)
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set childV to item child of my lst
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if (child comes before endOfHeap) then
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set child2 to child + 1
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set child2V to item child2 of my lst
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if (child2V > childV) then
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set child to child2
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set childV to child2V
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end if
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end if
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if (childV > siftV) then
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set item root of my lst to childV
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set root to child
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set child to root * 2
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else
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exit repeat
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end if
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end repeat
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set item root of my lst to siftV
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end siftDown
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end script
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set r to (r - l + 1)
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-- Arrange the sort range into a "heap" with its "top" at the leftmost position.
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repeat with i from (r + 1) div 2 to 1 by -1
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tell o to siftDown(item i of its lst, i, r)
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end repeat
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-- Work the heap as if extracting the values that would come after the median when sorted.
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repeat with endOfHeap from r to (r - (r + 1) div 2 + 2) by -1
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tell o to siftDown(item endOfHeap of its lst, 1, endOfHeap - 1)
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end repeat
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-- Extract the median itself, now at the top of the heap.
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set median to beginning of o's lst
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-- If the range has an even number of items, also get the value that would come before the median
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-- just obtained. By now it's either the second or third item in the heap, so no need to sift for it.
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-- Get the average if it and the median.
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if (r mod 2 is 0) then
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set median2 to item 2 of o's lst
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if ((r > 2) and (item 3 of o's lst > median2)) then set median2 to item 3 of o's lst
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set median to (median + median2) / 2
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end if
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return median
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end getMedian
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-- Demo:
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local testList
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set testList to {}
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repeat with i from 1 to 8
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set end of testList to (random number 500) / 5
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end repeat
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return {|numbers|:testList, median:getMedian(testList, 1, (count testList))}
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@ -0,0 +1 @@
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{|numbers|:{28.0, 75.6, 21.4, 51.8, 79.6, 25.0, 95.4, 31.2}, median:41.5}
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