Published at May 28 2019
·
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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 `Base`

. 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 base:

```
opam install base
```

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.

```
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 point = {
x: int;
y: int;
}
type direction =
| Horizontal
| Vertical
type line = {
start: point;
length: int;
direction: direction;
}
type rectangle = {
a: point;
b: point;
}
let y_points (y: int) (l: char array): point array =
let is_point = Char.equal '+' in
Array.filter_mapi l ~f:(fun x s -> if is_point s then Some { x=x; y=y } else None)
let points (board: string array): point array =
board
|> Array.map ~f:(String.to_array)
|> Array.concat_mapi ~f:(y_points)
let connected_x (board: string array) (start: point) (b: point): line option =
let length = b.x - start.x in
if length <= 0 || b.y <> start.y then
None
else
let connection = String.sub (Array.get board start.y) ~pos:(start.x) ~len:(b.x - start.x) in
let empty = Char.equal ' ' in
if not (String.for_all connection ~f:(Fn.non empty)) then
None
else
Some { start; length; direction=Horizontal }
let connected_y (board: string array) (a: point) (b: point): bool =
Int.equal a.x b.x &&
Array.filteri board ~f:(fun i _ -> i >= a.y && i <= b.y)
|> Array.for_all ~f:(fun line ->
Char.equal line.[a.x] '|' || Char.equal line.[a.x] '+')
let sides (board: string array) (points: point array): line array =
let connected_points p = Array.filter_map points ~f:(connected_x board p) in
points |> Array.concat_map ~f:(connected_points)
let opposing (a: line) (b: line): bool = a.start.y < b.start.y && Int.equal a.start.x b.start.x && Int.equal a.length b.length
let candidates (sides: line array) =
let opposing' b a = if opposing a b then Some { a=a.start; b={ x=(b.start.x + b.length); y=b.start.y } } else None in
let candidates' b = Array.filter_map sides ~f:(opposing' b) in
Array.concat_map sides ~f:(candidates')
let closed (board: string array) (cs: rectangle array): rectangle array =
Array.filter cs ~f:(fun c -> connected_y board c.a { x=c.a.x; y=c.b.y } && connected_y board { x=c.b.x; y=c.a.y } c.b)
let count_rectangles (board: string array): int =
points board
|> sides board
|> candidates
|> closed board
|> Array.length
```

```
type point = {
x: int;
y: int;
}
type direction =
| Horizontal
| Vertical
type line = {
start: point;
length: int;
direction: direction;
}
val count_rectangles : string array -> int
val sides : string array -> point array -> line array
val points : string array -> point array
val opposing : line -> line -> bool
```

```
open OUnit2
open Rectangles
let ae exp got _test_ctxt = assert_equal exp got ~printer:string_of_int
let print_point p = Printf.sprintf "point { x=%i; y=%i }" p.x p.y
let print_direction = function | Horizontal -> "Horizontal" | Vertical -> "Vertical"
let print_line l = Printf.sprintf "line { start=%s; length=%i; direction=%s }" (print_point l.start) l.length (print_direction l.direction)
let print_array a ~item = Printf.sprintf "[| %s |]" ((Array.map item a) |> Array.to_list |> String.concat "; ")
let tests = [
"points - no rows" >::
(fun _ -> assert_equal [||] (points [||]));
"points - single" >::
(fun _ -> assert_equal [|{ x=0; y=0 }|] (points [|"+"|]) ~printer:(print_array ~item:print_point));
"points - multiple" >::
(fun _ -> assert_equal [|{ x=0; y=0 }; { x=3; y=0 }; { x=3; y=1 }|] (points [|"+--+"; " +"|]) ~printer:(print_array ~item:print_point));
"sides - single" >::
(fun _ -> assert_equal [|{ start={x=0; y=0}; length=3; direction=Horizontal }|] (sides [|"+--+"; " +"|] [|{ x=0; y=0 }; { x=3; y=0 }; { x=3; y=1 }|]) ~printer:(print_array ~item:print_line));
"sides - multiple" >::
(fun _ -> assert_equal [|{ start={x=0; y=0}; length=3; direction=Horizontal }; { start={x=0; y=1}; length=5; direction=Horizontal }|] (sides [|"+--+ "; "+----+"|] [|{ x=0; y=0 }; { x=3; y=0 }; { x=0; y=1 }; { x=5; y=1 }|]) ~printer:(print_array ~item:print_line));
"sides - nested" >::
(fun _ -> assert_equal [|
{ start={x=0; y=0}; length=3; direction=Horizontal }; { start={x=0; y=0}; length=7; direction=Horizontal }; { start={x=0; y=0}; length=12; direction=Horizontal };
{ start={x=3; y=0}; length=4; direction=Horizontal }; { start={x=3; y=0}; length=9; direction=Horizontal };
{ start={x=7; y=0}; length=5; direction=Horizontal };
|] (sides [|"+--+---+----+"|] [|{ x=0; y=0 }; { x=3; y=0 }; { x=7; y=0 }; { x=12; y=0 }|]) ~printer:(print_array ~item:print_line));
"opposing - equivalent" >::
(fun _ -> assert_equal false (opposing { start={x=0; y=0}; length=3; direction=Horizontal } { start={x=0; y=0}; length=3; direction=Horizontal }));
"opposing - simple" >::
(fun _ -> assert_equal true (opposing { start={x=0; y=0}; length=3; direction=Horizontal } { start={x=0; y=1}; length=3; direction=Horizontal }));
"opposing - inverted" >::
(fun _ -> assert_equal false (opposing { start={x=0; y=1}; length=3; direction=Horizontal } { start={x=0; y=0}; length=3; direction=Horizontal }));
"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)
```

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- What compromises have been made?
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