Published at Oct 03 2018
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Instructions

Test suite

Solution

Count the rectangles in an ASCII diagram like the one below.

```
+--+
++ |
+-++--+
| | |
+--+--+
```

The above diagram contains 6 rectangles:

```
+-----+
| |
+-----+
```

```
+--+
| |
| |
| |
+--+
```

```
+--+
| |
+--+
```

```
+--+
| |
+--+
```

```
+--+
| |
+--+
```

```
++
++
```

You may assume that the input is always a proper rectangle (i.e. the length of every line equals the length of the first line).

For installation and learning resources, refer to the exercism help page.

To work on the exercises, you will need `Opam`

and `Core`

. Consult opam website for instructions on how to install `opam`

for your OS. Once `opam`

is installed open a terminal window and run the following command to install core:

```
opam install core
```

To run the tests you will need `OUnit`

. Install it using `opam`

:

```
opam install ounit
```

A Makefile is provided with a default target to compile your solution and run the tests. At the command line, type:

```
make
```

`utop`

is a command line program which allows you to run Ocaml code interactively. The easiest way to install it is via opam:

```
opam install utop
```

Consult utop for more detail.

The exercism/ocaml repository on GitHub is the home for all of the Ocaml exercises.

If you have feedback about an exercise, or want to help implementing a new one, head over there and create an issue. We'll do our best to help you!

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

```
(* Test/exercise version: "1.0.0" *)
open OUnit2
open Rectangles
let ae exp got _test_ctxt = assert_equal exp got ~printer:string_of_int
let tests = [
"no rows" >::
ae 0 (count_rectangles [||]);
"no columns" >::
ae 0 (count_rectangles [|""|]);
"no rectangles" >::
ae 0 (count_rectangles [|" "|]);
"one rectangle" >::
ae 1 (count_rectangles [|"+-+";
"| |";
"+-+"|]);
"two rectangles without shared parts" >::
ae 2 (count_rectangles [|" +-+";
" | |";
"+-+-+";
"| | ";
"+-+ "|]);
"five rectangles with shared parts" >::
ae 5 (count_rectangles [|" +-+";
" | |";
"+-+-+";
"| | |";
"+-+-+"|]);
"rectangle of height 1 is counted" >::
ae 1 (count_rectangles [|"+--+";
"+--+"|]);
"rectangle of width 1 is counted" >::
ae 1 (count_rectangles [|"++";
"||";
"++"|]);
"1x1 square is counted" >::
ae 1 (count_rectangles [|"++";
"++"|]);
"only complete rectangles are counted" >::
ae 1 (count_rectangles [|" +-+";
" |";
"+-+-+";
"| | -";
"+-+-+"|]);
"rectangles can be of different sizes" >::
ae 3 (count_rectangles [|"+------+----+";
"| | |";
"+---+--+ |";
"| | |";
"+---+-------+"|]);
"corner is required for a rectangle to be complete" >::
ae 2 (count_rectangles [|"+------+----+";
"| | |";
"+------+ |";
"| | |";
"+---+-------+"|]);
"large input with many rectangles" >::
ae 60 (count_rectangles [|"+---+--+----+";
"| +--+----+";
"+---+--+ |";
"| +--+----+";
"+---+--+--+-+";
"+---+--+--+-+";
"+------+ | |";
" +-+"|]);
]
let () =
run_test_tt_main ("rectangles tests" >::: tests)
```

```
open Base
type coords = int * int
type diagram = string array
let iter_diagram (diagram: diagram) : (coords * char) list =
diagram
|> Array.to_list
|> List.concat_mapi ~f: (fun y row ->
String.to_list row
|> List.mapi ~f: (fun x c ->
((x, y), c)
)
)
let positions_with_char (diagram: diagram) (c: char) : coords list =
iter_diagram diagram
|> List.filter_map ~f: (fun (coord, v) ->
if Char.equal c v then
Some coord
else
None
)
let unique_ints (l: int list) : int list =
List.dedup_and_sort l ~compare: Int.compare
let get_xs (positions: coords list) : int list =
List.map positions ~f: (fun (x, _) -> x)
|> unique_ints
let get_ys (positions: coords list) : int list =
List.map positions ~f: (fun (_, y) -> y)
|> unique_ints
let check_positions (positions: coords list) : bool =
List.length positions = 4 &&
List.length (get_xs positions) = 2 &&
List.length (get_ys positions) = 2
let take_two (l: int list) : (int * int) option =
match l with
| n1 :: n2 :: _ -> Some (n1, n2)
| _ -> None
let normalize_positions (positions: coords list) : (coords * coords) option =
match (take_two (get_xs positions), take_two (get_ys positions)) with
| (Some (x1, x2), Some (y1, y2)) -> Some ((x1, y1), (x2, y2))
| _ -> None
let at (diagram: diagram) (x: int) (y: int) : char =
let row = Array.get diagram y in
String.get row x
let contains (l: char list) (c: char) : bool =
List.exists l ~f: (fun v -> Char.equal c v)
let check_lines_for_coordinates (diagram: diagram) ((top_left): coords) (bottom_right: coords) : bool =
let (x1, y1) = top_left in
let (x2, y2) = bottom_right in
let xs = List.range x1 x2 ~stop: `inclusive in
let ys = List.range y1 y2 ~stop: `inclusive in
List.for_all xs ~f: (fun x -> contains ['+';'-'] (at diagram x y1)) &&
List.for_all xs ~f: (fun x -> contains ['+';'-'] (at diagram x y2)) &&
List.for_all ys ~f: (fun y -> contains ['+';'|'] (at diagram x1 y)) &&
List.for_all ys ~f: (fun y -> contains ['+';'|'] (at diagram x2 y))
let check_lines (diagram: diagram) (positions: coords list) : bool =
match normalize_positions positions with
| Some (top_left, bottom_right) -> check_lines_for_coordinates diagram top_left bottom_right
| _ -> false
let is_rectangle (diagram: diagram) (positions: coords list) : bool =
(check_positions positions) && (check_lines diagram positions)
let rec combinations (n: int) (l: coords list): (coords list) list =
if n <= 0 then [ [] ]
else match l with
| [] -> []
| h :: tl ->
let with_h = List.map ~f: (fun l -> h :: l) (combinations (n - 1) tl) in
let without_h = combinations n tl in
with_h @ without_h
let count_rectangles (diagram: diagram) : int =
combinations 4 (positions_with_char diagram '+')
|> List.count ~f: (fun (positions: coords list) ->
is_rectangle diagram positions
)
```

A huge amount can be learned from reading other people’s code. This is why we wanted to give exercism users the option of making their solutions public.

Here are some questions to help you reflect on this solution and learn the most from it.

- What compromises have been made?
- Are there new concepts here that you could read more about to improve your understanding?

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