Stopping a Reduce() operation mid way. Functional way of doing partial running sum

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I have been doing some functional programming and had a question. Perhaps I might be missing something but is there any way to stop a "reduce()" function midway? Lets say when I reach a certain condition? The idea somehow seems anti functional. I haven't seen any such option in python or F#,

As an example, lets say I have a list such as [1,2,3,4,5]. I want to sum the elements in this list until the sum is not greater than some number (lets say 8), and return/mark/store/identify somehow, the number of elements I have actually added.

If we looked at python for example for I might try something like

reduce(lambda a,b : a if a + b > 8 else a + b, input)

This gives me the right answer 6, but how do I find that I had added 3 elements to get here. There is no counter as such. I can't do assignments inside lambdas. I think F# has the same situation.

I know I can use a for loop or use a function that can store state etc. But what would be the functional way of doing/thinking about this. Reduce() wants to run until the end, but somewhere along this line of processing, we either want to stop it (because we don't care about processing the rest of the elements) or at least make a note of the place where we stopped caring.

Reduce is often used in combination with map. Google for example has developed a map-reduce framework for querying their databases and this map-reduce pattern is now used in several other projects (e.g. CouchDB, Hadoop, etc).

First, you need to map the input variables [2, 1, 3, 4, 5] to something like:

[(1, 2), (1, 1), (1, 3), (1, 4), (1, 5)]

In that case, x[0] will represent the number of the elements to get the sum x[1]. Of course, the number of elements is 1 at the beginning for each single element.

The next thing then, is to operate on those tuples:

reduce(
    lambda a, b: a if a[1] + b[1] > 8 else (a[0] + b[0], a[1] + b[1]),
    map(lambda x: (1, x), input))

This will return (3, 6), meaning the partial sum is 6 using 3 elements.

I hope you got the idea behind map-reduce-algorithms.

Regards, Christoph

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I agree with JaredPar that writing your own recursive function that behaves similarly to fold, but allows you to stop the computation earlier is the best approach. The way I would write it is a bit more general (so that you can use the function for any situation where you need folding that can stop earlier):

// Generalized 'fold' function that allws you to stop the execution earlier
// The function 'f' has a type 'State -> 'T -> Option<'State>
// By returning 'None' we can stop the execution (and return the 
// current state), by returning Some(newState), we continue folding
let rec foldStop f state input = 
  match input with
  | x::xs -> 
      match f state x with
      | None -> state
      | Some(newState) -> foldStop f newState xs
  | [] -> state

// Example that stops folding after state is larger than 10
foldStop (fun st n -> if st > 10 then None else Some(st + n)) 0 [ 1 .. 10 ]

This is a very general function and you can use it for all similar scenarios. The nice thing about writing it is that you will never need to write similar explicit recursion again (because you can just use foldStop once you have it).

Note that you can use foldStop to implement fold by always wrapping the result of the accumulation function in 'Some' (so it is more general):

let fold f state input = 
  foldStop (fun st n -> Some(f st n)) state input

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Let's imagine Python had two functions, ireduce (similar to reduce but it would yield intermediate values; it's called scanl in some languages) and ilast (get last item of an iterable):

from itertools import takewhile
from operator import add
xs = [1, 2, 3, 4, 5]
pair = ilast(enumerate(takewhile(lambda x: x < 8, ireduce(add, xs, 0))))
# (3, 6)

In Haskell:

last $ zip [0..] (takeWhile (< 8) (scanl (+) 0 xs))

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I think that the 'most functional' way to do this is probably via lazy evaluation. If you're in a lazy language like Haskell, or in an eager language but using a lazy list data structure (like LazyList in the F# PowerPack), you can create e.g. a 'scan' of the running sums, and then leave it in the hands of the consumer of the list to decide how much she wants/needs to evaluate.

Or, you know, write a simple recursive function, like @JaredPar's answer. For some reason I often get a mental block on that, preventing me from noticing that "not everything has to be a fold, you can in fact write your own recursive functions" :)

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Try the following

let sumUntil list stopAfter = 
    let rec inner list sum = 
        if sum >= stopAfter then sum
        else 
            match list with
            | [] -> sum
            | h::t-> inner t (sum + h)
    inner list 0    

F# interactive result

> sumUntil [1;2;3;4;5] 8;;
val it : int = 10

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Comments
  • What's important to you, the 3 or the 6? Or both? How would you want to use this function? Return a tuple - (num_items, result)? It's a neat idea, but I think a loop is the most straightforward code.
  • They are both important. I want to know I can take 3 elements and that the closest I can get to my limit is 6. Yes, a loop would be pretty straight forward, but I wanted to see how a functional programmer would attack it / think about it. I can't return a tuple, because reduce needs another int from the function to add to the next element in the list.
  • Regarding Python, it could be possible to write a filtered_reduce function, but Python remains to be an imperative language whose functional-like features should not be overestimated. In Python the call to reduce is translated into a simple loop anyway, so you gain nothing from it.
  • Oooohhhh.... niiice. I had read about map reduce, but I guess I didn't fully grok it. Very nicely done.
  • Here are two links which might interest you: Google's Map-Reduce paper (labs.google.com/papers/mapreduce.html) and a course Map Reduce in a Week (code.google.com/edu/submissions/mapreduce/listing.html).
  • And a Python framework (based on Erlang) for doing efficient map-reduce computing is Disco. With that you can use multiple cores / computers and work with (nearly) unlimited data sets... discoproject.org
  • I'm not downvoting, but this can hardly be idiomatic FP..? Chaitanya has picked his golden hammer, and you're helping him/her use it to bash a square peg into a round hole.
  • Nice description of map/reduce, but if the input contained a million values and we hit the exit condition after three of them that's a lot of empty work being done. When you hit the exit condition use an exception to exit the loop.
  • But I want to return the final state when I stopped as well as place where I stopped as well. My F# isn't fluent enough, but this would require changing the state and the input function as follows : foldStop (fun (st,i) n -> if st > 10 then None else Some(st + n, i + 1)) (0,0) [ 1 .. 10 ]
  • @Chaitanya: Yes, that would require changing the code a little bit (or you would need to update the condition to stop on the next state). Alternatively, you could use Choice instead of Option (that allows you to return the state, but still break the computation by returning a speical case).
  • Hmmm ... Haskell one of those languages I keep wanting to learn but never get around to it