Published at Jul 13 2018
·
2 comments

Instructions

Test suite

Solution

Correctly determine the fewest number of coins to be given to a customer such that the sum of the coins' value would equal the correct amount of change.

- An input of 15 with [1, 5, 10, 25, 100] should return one nickel (5) and one dime (10) or [0, 1, 1, 0, 0]
- An input of 40 with [1, 5, 10, 25, 100] should return one nickel (5) and one dime (10) and one quarter (25) or [0, 1, 1, 1, 0]

- Does your algorithm work for any given set of coins?
- Can you ask for negative change?
- Can you ask for a change value smaller than the smallest coin value?

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

To work on the exercises, you will need `Opam`

and `Core`

. 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 core:

```
opam install core
```

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!

Software Craftsmanship - Coin Change Kata https://web.archive.org/web/20130115115225/http://craftsmanship.sv.cmu.edu:80/exercises/coin-change-kata

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

```
(* Test/exercise version: "1.1.0" *)
open Base
open OUnit2
open Change
let printer = Option.value_map ~default:"None" ~f:(fun xs -> String.concat ~sep:";" (List.map ~f:Int.to_string xs))
let ae exp got _test_ctxt = assert_equal ~printer exp got
let tests = [
"single coin change" >::
ae (Some [25])
(make_change ~target:25 ~coins:[1; 5; 10; 25; 100]);
"multiple coin change" >::
ae (Some [5; 10])
(make_change ~target:15 ~coins:[1; 5; 10; 25; 100]);
"change with Lilliputian Coins" >::
ae (Some [4; 4; 15])
(make_change ~target:23 ~coins:[1; 4; 15; 20; 50]);
"change with Lower Elbonia Coins" >::
ae (Some [21; 21; 21])
(make_change ~target:63 ~coins:[1; 5; 10; 21; 25]);
"large target values" >::
ae (Some [2; 2; 5; 20; 20; 50; 100; 100; 100; 100; 100; 100; 100; 100; 100])
(make_change ~target:999 ~coins:[1; 2; 5; 10; 20; 50; 100]);
"possible change without unit coins available" >::
ae (Some [2; 2; 2; 5; 10])
(make_change ~target:21 ~coins:[2; 5; 10; 20; 50]);
"another possible change without unit coins available" >::
ae (Some [4; 4; 4; 5; 5; 5])
(make_change ~target:27 ~coins:[4; 5]);
"no coins make 0 change" >::
ae (Some [])
(make_change ~target:0 ~coins:[1; 5; 10; 21; 25]);
"error testing for change smaller than the smallest of coins" >::
ae None
(make_change ~target:3 ~coins:[5; 10]);
"error if no combination can add up to target" >::
ae None
(make_change ~target:94 ~coins:[5; 10]);
"cannot find negative change values" >::
ae None
(make_change ~target:(-5) ~coins:[1; 2; 5]);
]
let () =
run_test_tt_main ("change tests" >::: tests)
```

```
open Core
module Change = struct
module T = struct
type t =
{ length : int
; coins : int list
}
[@@deriving sexp]
;;
let compare a b = Int.compare a.length b.length
end
include T
include Comparable.Make(T)
let empty = { length = 0; coins = [] }
let add { length; coins } ~coin =
{ length = length + 1
; coins = coin :: coins
}
;;
let coins t = List.sort t.coins ~cmp:Int.ascending
end
let make_change ~target ~coins =
if target < 0
then None
else begin
let shortest = Array.create None ~len:(target + 1) in
let update_shortest target change =
let current = shortest.(target) in
let new_solution = Option.merge current change ~f:Change.min in
shortest.(target) <- new_solution
in
shortest.(0) <- Some Change.empty;
List.iter coins ~f:(fun coin ->
for i = 0 to target - coin do
let new_target = i + coin in
shortest.(i)
|> Option.map ~f:(Change.add ~coin)
|> update_shortest new_target
done);
shortest.(target)
|> Option.map ~f:Change.coins
end
;;
```

```
(* If it is impossible to make the target with the given coins, then return None *)
val make_change : target: int -> coins: int list -> int list option
```

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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## Community comments

Good optimization to avoid calls to List.length.

Thanks. It seemed possibly excessive but I felt that I might as well make a module, seeing as I could use Comparable as well.