1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
|
module Lib
( partition
, partitionDays
) where
import Data.List (group, sortOn, span)
import Data.Ord (Down(Down))
import Data.Time.Calendar (Day, addDays, diffDays)
{- | Split a strictly increasing list of integer numbers into intervals
such that the width of each interval is defined by a positive, weakly increasing
function of the interval's serial number (1, 2, 3, ...).
Some of the intervals may be empty.
>>> partition (const 1) [1,2,3,4,5,6,7,8,9]
[[1],[2],[3],[4],[5],[6],[7],[8],[9]]
>>> partition (const 1) [1,3,5,7,9,11,13,15,17,19]
[[1],[],[3],[],[5],[],[7],[],[9],[],[11],[],[13],[],[15],[],[17],[],[19]]
>>> partition (const 2) $ take 10 [1,3 ..]
[[1],[3],[5],[7],[9],[11],[13],[15],[17],[19]]
>>> partition (\n -> floor (2^n)) $ take 20 [1, 2 ..]
[[1,2],[3,4,5,6],[7,8,9,10,11,12,13,14],[15,16,17,18,19,20]]
>>> partition (\n -> floor (2^n)) [2,5,14,20]
[[2],[5],[14],[20]]
>>> partition (\n -> floor (2^n)) $ take 20 [10,20 ..]
[[10],[],[20],[30],[40,50,60,70],[80,90,100,110,120,130],[140,150,160,170,180,190,200]]
-}
partition ::
(Ord t, Num t)
=> (Int -> t) -- ^ positive, weakly increasing function of a natural number
-> [t] -- ^ strictly increasing, non-empty list
-> [[t]]
partition f l = go 1 (head l) l
where
go _ _ [] = []
go n a aa =
let a' = a + f n
n' = n + 1
(slot, rest) = span (< a') aa
in slot : go n' a' rest
{- | Split days into intervals, backwards from the most recent day.
This function uses the 'partition' function after calculating differences
between the days.
>>> let days = map read ["2019-08-30", "2019-08-31", "2019-09-02"]
>>> partitionDays (const 1) days
[[2019-09-02],[],[2019-08-31],[2019-08-30]]
>>> let days = map read ["2019-08-30", "2019-08-31", "2019-09-01", "2019-09-02", "2019-09-03", "2019-09-04"]
>>> partitionDays (\n -> floor (2^(n-1))) days
[[2019-09-04],[2019-09-03,2019-09-02],[2019-09-01,2019-08-31,2019-08-30]]
-}
partitionDays ::
(Int -> Integer) -- ^ positive, weakly increasing function of a natural number
-> [Day] -- ^ non-empty list of days, with no other restrictions
-> [[Day]]
partitionDays f days = map (map int2day) (partition f ints)
where
sorted = map head . group . sortOn Down $ days
day1 = head sorted
ints = map (diffDays day1) sorted
int2day i = addDays (-i) day1
|
