Implement an inventory facility
Implement the following module:
module Inventory : sig type 'a inventory = ('a * int) list val valid : 'a inventory -> bool val sort : 'a inventory -> 'a inventory val union : 'a inventory -> 'a inventory -> 'a inventory val difference : 'a inventory -> 'a inventory -> 'a inventory * 'a inventory val intersects : 'a inventory -> 'a inventory -> bool val length : 'a inventory -> int val eval : 'a inventory -> 'a inventory -> int * int val discriminate : 'a inventory -> 'a inventory -> 'a inventory -> int type ('a, 'b) catalog = ('a * 'b inventory) list val place_order : ('a, 'b) catalog -> 'b inventory -> 'a inventory * 'b inventory end
inventory is an association list of item/counts.
sort just sorts an
inventory according to its items.
valid checks that an
1. is strictly sorted according to its items
2. has only stricly positive item counts
By "strictly" sorted we mean that each item must be strictly greater than its predecessor which verifies item unicity in linear time.
In the following module functions,
assert must be systematically used to ensure argument(s) validity where needed.
union sums two inventories into an augmented
difference subtracts one
inventory to another
inventory. There are two results:
b-a, respectively the items of the first minus the items of the second, and the items of the second minus the items of the first.
intersects checks if two inventories intersect.
length returns the sum of item counts.
eval returns two integers:
1. how many items of the first inventory are in the second inventory
2. how many items of the second inventory are not in the first inventory
eval to determine whether its second or its third argument is closer to its first argument and returns -1,0,1 accordingly.
i) The last function
place_order is the big one that justifies all the previous utilities.
A new type
catalog is defined that is an association list made available to you, the client, by your supplier. Each key in this list has an associated inventory. The first argument of
place_order is the available catalog. The second argument is the exact inventory wanted by the client. The challenge is to compute:
1. the cheapest order, that is the order inventory that includes the wanted inventory with as few extras as possible
2. the extra inventory that will be received and stocked while waiting an usage
The problem ressembles the "Backpack problem", here you can find hints for solving it: A solution to the Backpack Problem.
Otherwise here is the code:
type ('a, 'b) catalog = ('a * 'b inventory) list;;
let place_order cat wanted = let rec helper (cat: ('a,'b) catalog) (wanted: 'b inventory) keys extras = if wanted= then keys,extras else let passed = List.find_all (fun (_,inv) -> intersects wanted inv) cat in match passed with |  -> raise Not_found | (k,inv)::l -> let k_max = ref k and inv_max = ref inv in begin List.iter (fun (k,inv) -> if discriminate wanted inv !inv_max > 0 then begin k_max := k; inv_max := inv end) l; let rest,more = difference wanted !inv_max in helper passed rest (union keys [!k_max,1]) (union more extras) end in helper cat wanted  ;;