 # emengd's solution

## to Rectangles in the OCaml Track

Published at Feb 21 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)``````
``````open Base

let count_duplicates l1 l2 =
let rec loop n l1 l2 =
match l1, l2 with
| [], _ | _, [] -> n
| x :: xs, y :: ys ->
if x < y then
loop n l1 ys
else if x = y then
loop (n +  1) xs ys
else
loop n xs l2
in
loop 0 l1 l2

let merge l1 l2 =
let rec loop l l1 l2 =
match l1, l2 with
| [], l0 | l0, [] ->
List.rev_append l0 l
| x :: xs, y :: ys ->
if x < y then
loop (y :: l) l1 ys
else if x = y then (* shouldn't occur *)
loop (x :: l) xs ys
else
loop (x :: l) xs l2
in
List.rev (loop [] l1 l2)

let count_rectangles lines =
let h = Array.length lines in
if h = 0 then
0
else
let w = String.length lines.(0) in
if w = 0 then
0
else
let column_memo_1 = Array.create ~len:w [] in
let column_memo_2 = Array.create ~len:w [] in
let rec loop i j id total line_memo_1 line_memo_2 =
if j >= w then
loop (i + 1) 0 id total [] []
else if i >= h then
total
else
match lines.(i).[j] with
| ' ' -> begin
column_memo_1.(j) <- [];
column_memo_2.(j) <- [];
loop i (j + 1) id total [] []
end
| '|' ->
loop i (j + 1) id total [] []
| '-' -> begin
column_memo_1.(j) <- [];
column_memo_2.(j) <- [];
loop i (j + 1) id total line_memo_1 line_memo_2
end
| '+' -> begin
let n = count_duplicates column_memo_2.(j) line_memo_2 in
let new_line_memo_2 = merge line_memo_2 column_memo_1.(j) in
column_memo_1.(j) <- id :: column_memo_1.(j);
column_memo_2.(j) <- merge column_memo_2.(j) line_memo_1;
loop i (j + 1) (id + 1) (total + n) (id :: line_memo_1) new_line_memo_2
end
| _ ->
raise (Invalid_argument "invalid input")
in
loop 0 0 0 0 [] []``````