Hi, all. I have an exceedingly simple problem to address, and am wondering if there are relatively straightforward ways to improve the efficiency of my solution. The task is simply to look at a lengthy list of stock keeping units (SKUs -- what retailers call individual items), stores, dates that a promotion started, dates the promotion ended, and something like sales amount; we want to pull out the records where promotions overlap. I will have dates in yyyymmdd format, so there's probably no harm in treating them as Ints. My suggestion went something like this (I'm not at my desk so I don't have exactly what I typed):
data PromotionRec = PR {sku :: String, store :: String, startDate :: Int, endDate :: Int, amount::Float}
match :: PromotionRec -> [PromotionRec] -> [PromotionRec] match _ [] = [] match x (x:xs) = filter (meet x) xs
nomatch :: PromoRec -> [PromotionRec] -> [PromotionRec] nomatch _ [] = [] nomatch x (x:xs) = filter (nomeet x) xs
meet :: PromoRec -> PromoRec -> Bool meet x y = and [startDate x <= endDate y, startDate y <= startDate x]
nomeet :: PromoRec -> PromoRec -> Bool nomeet x y = not (meet x y)
overlaps :: [PromoRec] -> [[PromoRec]] overlaps [] = [] overlaps (x:xs) = (x : match x xs) : (overlaps (nomatch x xs))
overlap :: [PromoRec] -> [[PromoRec]] overlap [] = [] overlap (x:xs) = filter g1 (overlaps (x:xs)) where g1 ys = (length ys) > 1
What I sent might have been slightly different, and I might have some typos in the above (as I'm composing from memory at the keyboard), but that's the rough idea: treat this like a quicksort, pulling out the records that overlap the first record, consing the first record onto the list, and then consing the resulting list onto the same function applied to the records that didn't overlap. As a last step, delete the records that were not on promotion while anything else was on promotion. I'm pretty confident that this will be more efficient than my colleague's SAS code, as he was comparing each record to every other record (giving n (n-1) comparisons). It seems like this, in the worst case where everything is on promotion at distinct times, will compare the first record to (n-1) records, the second to (n-2) records, etc., giving n (n-1)/2 comparisons. Thus, while this is worst-case O(n^2), it seems like it should have at most half as much work to do as the earlier approach in SAS. On the other hand, in the best case, when everything is on promotion at the same time, there should be something like n-1 comparisons made and then that should be it. So it seems like, depending on how frequently promotions co-occur for this retailer, the above should be somewhere between O(n) and O(n^2) time complexity. Since these people are always having some sale or other, I suspect this won't be much worse than O(n log n). Is there anything that is an obvious improvement in efficiency -- some clever tricks with the fold functions, some way of loading the data into some sort of convenient structure first, etc -- that I could easily implement? Please share your thoughts. Many thanks, Jack Stecher jack.stecher@retek.com