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# Sendell's solution

## to Rectangles in the OCaml Track

Published at Jun 01 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.

## Feedback, Issues, Pull Requests

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!

## 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.mli

``val count_rectangles : string array -> int``

### rectangles.ml

``````open Base

let ( >> ) f g x = g (f x)

let to_coordinates =
Array.foldi ~init:[] ~f:(fun i ys line ->
let xs =
String.foldi line ~init:[] ~f:(fun j xs c ->
match c with '+' -> j :: xs | _ -> xs )
in
(i, xs) :: ys )
>> List.filter ~f:(snd >> List.is_empty >> not)
>> List.rev

let generates_candidates xs =
List.cartesian_product xs xs |> List.filter ~f:(fun (l, r) -> l < r)

let is_corner = Char.equal '+'

let is_vertical c = Char.equal '|' c || is_corner c

let is_horizontal c = Char.equal '-' c || is_corner c

let check_horizontal line x0 x1 =
(* A valid line contains either '+' or '-' in the middle *)
let inner =
let len = x1 - x0 + 1 in
if len > 2 then
String.sub line ~pos:x0 ~len
|> String.fold ~init:true ~f:(fun is_valid c ->
is_valid && is_horizontal c )
else true
in
(* And then a valid line starts and ends with '+' *)
inner && Char.equal line.[x0] '+' && Char.equal line.[x1] '+'

let check_vertical drawing x y0 y1 =
(* A valid line contains either '+' or '|' in the middle *)
let inner =
let len = y1 - y0 + 1 in
if len > 2 then
Array.sub drawing ~pos:y0 ~len
|> Array.fold ~init:true ~f:(fun is_valid l ->
let c = l.[x] in
is_valid && is_vertical c )
else true
in
(* And then a valid line starts and ends with '+' *)
inner && Char.equal drawing.(y0).[x] '+' && Char.equal drawing.(y1).[x] '+'

let is_valid_rectangle drawing x0 x1 y0 y1 =
check_horizontal drawing.(y0) x0 x1
&& check_horizontal drawing.(y1) x0 x1
&& check_vertical drawing x0 y0 y1
&& check_vertical drawing x1 y0 y1

let count_equal_pairs drawing ycs ypss =
let y0, cs = ycs in
List.fold cs ~init:0 ~f:(fun acc (c0, c1) ->
List.fold ypss ~init:0 ~f:(fun acc_inner yps ->
let y1, ps = yps in
List.count ps ~f:(fun (x0, x1) ->
c0 = x0 && c1 = x1 && is_valid_rectangle drawing x0 x1 y0 y1 )
+ acc_inner )
+ acc )

let count_rectangles drawing =
let rec aux total_count = function
| [] | [_] -> total_count
| ycs :: ypss ->
let sub_count = count_equal_pairs drawing ycs ypss in
aux (total_count + sub_count) ypss
in
to_coordinates drawing
|> List.map ~f:(fun (i, x) -> (i, generates_candidates x))
|> aux 0``````

### What can you learn from this solution?

A huge amount can be learned from reading other peopleâ€™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?