Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Add a solution for "94. An arithmetic puzzle." in 99 Problems #1597

Open
wants to merge 2 commits into
base: master
Choose a base branch
from
Open

Add a solution for "94. An arithmetic puzzle." in 99 Problems #1597

Changes from all commits
Commits
Show all changes
2 commits
Select commit Hold shift + click to select a range
c06d64f
Add a solution for 94. An arithmetic puzzle.
dracconi Jul 25, 2021
f5366c8
Added the quote marks per request and an example of usage
dracconi Aug 7, 2021
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
92 changes: 90 additions & 2 deletions site/learn/tutorials/99problems.md
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -2784,8 +2784,96 @@ equations 2 - 3 + 5 + 7 = 11 or 2 = (3 * 5 + 7) / 11 (and ten others!).

<!-- SOLUTION -->

```ocaml
(* example pending *);;
> ```ocamltop
> (* Simple bruteforce algorithm *)
> (* Produces duplicates sometimes *)
> type operand = Plus | Minus | Mult | Div;;
> type rat = (int * int);;
> type btree = Leaf of rat | Node of operand * btree * btree | Root of btree * btree;;
>
> let rat_add (a, b) (c, d) = (a*d+c*b, b*d);;
> let rat_sub a (c, d) = rat_add a (-c, d);;
> let rat_mul (a, b) (c, d) = (a*c, b*d);;
> let rat_div a (c, d) = rat_mul a (d, c);;
> let rat_eql (a, b) (c, d) = (a*d) == (c*b);;
>
> let rec convert_leafs arr = match arr with
> | [] -> []
> | a :: [] -> Leaf (a, 1) :: []
> | a :: rest -> Leaf (a, 1) :: convert_leafs rest;;
>
> let rec windowing op pre arr = match arr with
> | [] -> []
> | a :: [] -> []
> | a :: b :: rest -> (List.append pre (Node(op, a, b) :: rest)) :: (windowing op (List.append pre [a]) (b :: rest));;
>
> let all_ops_window arr = List.concat
> [windowing Plus [] arr;
> windowing Minus [] arr;
> windowing Mult [] arr;
> windowing Div [] arr];;
>
> let rec make_trees arr = match arr with
> | [] -> []
> | [a; b] :: rest -> [Root(a, b)] :: (make_trees rest)
> | a :: rest -> List.append (all_ops_window a) (make_trees rest);;
>
> let rec exhaust_tree arr = match arr with
> | [Root(a, b)] :: rest -> [Root(a, b)] :: rest
> | a -> exhaust_tree (make_trees a);;
>
> let node_fun n = match n with
> | Plus -> rat_add
> | Minus -> rat_sub
> | Mult -> rat_mul
> | Div -> rat_div;;
>
> let rec calc_tree t = match t with
> | Node(op, a, b) ->
> Option.bind (calc_tree a) (fun ctaa ->
> let ctb = calc_tree b in
> (match ctb with
> | None -> None
> | Some (0, _) -> (match op with
> | Div -> None
> | _ -> Some ((node_fun op) ctaa (0, 1)))
> | Some ctba -> Some ((node_fun op) ctaa ctba)))
> | Leaf(a) -> Some a
> | _ -> None;;
>
> let check_tree t = match t with
> | Root(a, b) -> (match calc_tree a with
> | None -> false
> | Some x -> (match calc_tree b with
> | None -> false
> | Some y -> rat_eql x y))
> | _ -> false;;
>
> let unpack_and_check tar = match tar with
> | [t] -> check_tree t
> | _ -> false;;
>
> let get_correct input = List.filter unpack_and_check (exhaust_tree [(convert_leafs input)]);;
>
> (* Some utility functions *)
> let op_to_text op = match op with
> | Plus -> "+"
> | Minus -> "-"
> | Mult -> "*"
> | Div -> "/";;
>
> let rec tree_to_text t = match t with
> | Root(a, b) -> String.concat " " [tree_to_text a; "="; tree_to_text b]
> | Node(op, a, b) -> String.concat " " ["("; tree_to_text a; op_to_text op; tree_to_text b; ")"]
> | Leaf((a,b)) -> Float.to_string (Int.to_float a /. Int.to_float b);;
> ```

```ocamltop
(* Gives the list of correct solutions *)
get_correct [2; 4; 8];;

(* Converts the tree to a readable format *)
tree_to_text (List.hd (List.hd (get_correct [2; 4; 8])));;
```

#### 95. English number words. (*medium*)
Expand Down