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marionebl's solution

to Rectangles in the OCaml Track

Published at May 28 2019 · 0 comments
Instructions
Test suite
Solution

Note:

This exercise has changed since this solution was written.

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).

Getting Started

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

Installation

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

Running Tests

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

make

Interactive Shell

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.

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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!

Submitting Incomplete Solutions

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

test.ml

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)

rectangles.ml

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

rectangles.mli

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

test.ml

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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