Published at Feb 21 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
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 [] []
```

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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