<div dir="ltr">Hi Apoorv,<div><br></div><div>There is indeed a left fold:</div><div><br></div><div><div><font face="monospace">foldlpart :: [Int] -> [a] -> [[a]]<br></font></div><div><font face="monospace">foldlpart ds ps = result</font></div><div><font face="monospace"> where result | null remaining = initial</font></div><div><font face="monospace"> | otherwise = initial ++ [remaining]</font></div><div><font face="monospace"> (initial, remaining) = foldl aux ([], ps) ds</font></div><div><font face="monospace"> aux (l, xs) d = case xs of</font></div><div><font face="monospace"> [] -> (l, xs)</font></div><div><font face="monospace"> _ -> let (f,s) = splitAt d xs in (l ++ [f], s)</font></div><div><br></div><div>I'm sure someone else can put something better together though.</div><div><br></div><div>I much prefer this right fold, since it avoids quadratic behavior incurred with (++) above:</div><div><br></div><div><div><font face="monospace">foldrpart :: [Int] -> [a] -> [[a]]</font></div><div><font face="monospace">foldrpart ds ps = myFunc ps</font></div><div><font face="monospace"> where myFunc = foldr buildMyFunc (: []) ds</font></div><div><font face="monospace"> buildMyFunc digit func = \ps -></font></div><div><font face="monospace"> case ps of</font></div><div><font face="monospace"> [] -> []</font></div><div><font face="monospace"> _ -> let (first, last) = splitAt digit ps</font></div><div><font face="monospace"> in first : func last</font></div></div><div><br></div><div>If it's unclear, buildMyFunc is basically composing a bunch of functions which know (from the fold on the list of Ints) how many elements</div><div>to take from some list.</div><div><br></div><div>Hope this is useful.</div><div><br></div><div>- David</div><div><br><div class="gmail_quote"><div dir="ltr">On Tue, Jul 11, 2017 at 3:30 PM Apoorv Ingle <<a href="mailto:apoorv.ingle@gmail.com">apoorv.ingle@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word"><div>Hi,</div><div><br></div><div>I am trying to write a partition function where we pass group sizes and the list we want to partition into groups </div><div>as arguments and get back a list of groups (or list of lists in this case). My first attempt was by using an auxiliary inner function</div><div><br></div><blockquote style="margin:0px 0px 0px 40px;border:none;padding:0px"><div><div><font color="#0056d6">{-# LANGUAGE ScopedTypeVariables #-}</font></div></div><div><div><font color="#0056d6"><br></font></div></div><div><div><font color="#0056d6">module Partition where</font></div></div><div><font color="#0056d6"><br></font></div><div><div><div><font color="#0056d6">partition :: [Int] -> [a] -> [[a]]</font></div></div></div><div><div><div><font color="#0056d6">partition ds ps = reverse $ paux ds ps []</font></div></div></div><div><div><div><font color="#0056d6"> where</font></div></div></div><div><div><div><font color="#0056d6"> </font><span style="color:rgb(0,86,214)">paux</span><font color="#0056d6"> :: [Int] -> [a] -> [[a]] -> [[a]]</font></div></div></div><div><div><div><font color="#0056d6"> </font><span style="color:rgb(0,86,214)">paux</span><font color="#0056d6"> [] [] ps' = ps'</font></div></div></div><div><div><div><font color="#0056d6"> </font><span style="color:rgb(0,86,214)">paux</span><font color="#0056d6"> [] ps ps' = [ps] ++ ps’ </font></div></div></div><div><div><div><font color="#0056d6"> </font><span style="color:rgb(0,86,214)">paux</span><font color="#0056d6"> _ [] ps' = ps'</font></div></div></div><div><div><div><font color="#0056d6"> </font><span style="color:rgb(0,86,214)">paux</span><font color="#0056d6"> (d:ds') ps ps' = </font><span style="color:rgb(0,86,214)">paux</span><font color="#0056d6"> ds' (snd (splitAt d ps)) ([fst (split</font><span style="color:rgb(0,86,214)">At d ps)] ++ ps')</span></div></div></div><div><font color="#0056d6"><br></font></div></blockquote>——————<br><blockquote style="margin:0px 0px 0px 40px;border:none;padding:0px"><div><font color="#0056d6"><br></font></div><div><div><div><font color="#0056d6">*Partition> partition [2, 3] [1,2,3,4,5]</font></div></div></div><div><div><div><font color="#0056d6">[[1,2],[3,4,5]]</font></div></div></div><div><div><div><font color="#0056d6">*Partition> partition [1, 2] [1,2,3,4,5]</font></div></div></div><div><div><div><font color="#0056d6">[[1],[2,3],[4,5]]</font></div></div></div><div><div><div><font color="#0056d6">*Partition> partition [1, 2, 5] [1,2,3,4,5]</font></div></div></div><div><div><div><font color="#0056d6">[[1],[2,3],[4,5]]</font></div></div></div></blockquote><div><div><br></div><div><br></div><div>I was speculating if we could write the same function using foldl function but haven’t been able to figure it out.</div><div>I would really appreciate if you can give me pointers on how we can implement it.</div><div><br></div></div><blockquote style="margin:0px 0px 0px 40px;border:none;padding:0px"><div><div><font color="#0056d6">partition' :: [Int] -> [a] -> [[a]]</font></div></div><div><div><font color="#0056d6">partition' [] ds = [ds]</font></div></div><div><div><font color="#0056d6">partition' ps ds = foldl ??? ???' ???''</font></div></div></blockquote><div><br></div><div>contrary to my speculation is it even possible to write such a function using foldl if so why not?</div><div><br></div>Regards,<br><div><div style="word-wrap:break-word">Apoorv Ingle<br>Graduate Student, Computer Science<br><a href="mailto:apoorv.ingle@ku.edu" target="_blank">apoorv.ingle@ku.edu</a></div></div></div>_______________________________________________<br>
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