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cmbntr's solution

to Sum Of Multiples in the Elm Track

Published at May 31 2020 · 0 comments
Instructions
Test suite
Solution

Given a number, find the sum of all the unique multiples of particular numbers up to but not including that number.

If we list all the natural numbers below 20 that are multiples of 3 or 5, we get 3, 5, 6, 9, 10, 12, 15, and 18.

The sum of these multiples is 78.

Elm Installation

Refer to the Installing Elm page for information about installing elm.

Writing the Code

The code you have to write is located inside the src/ directory of the exercise. Elm automatically installs packages dependencies the first time you run the tests so we can start by running the tests from the exercise directory with:

$ elm-test

To automatically run tests again when you save changes:

$ elm-test --watch

As you work your way through the tests suite in the file tests/Tests.elm, be sure to remove the skip <| calls from each test until you get them all passing!

Source

A variation on Problem 1 at Project Euler http://projecteuler.net/problem=1

Submitting Incomplete Solutions

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

Tests.elm

module Tests exposing (tests)

import Expect
import SumOfMultiples exposing (sumOfMultiples)
import Test exposing (..)


tests : Test
tests =
    describe "Sum Of Multiples"
        [ test "[3, 5] 15" <|
            \() -> Expect.equal 45 (sumOfMultiples [ 3, 5 ] 15)
        , skip <|
            test "[7, 13, 17] 20" <|
                \() -> Expect.equal 51 (sumOfMultiples [ 7, 13, 17 ] 20)
        , skip <|
            test "[4, 6] 15" <|
                \() -> Expect.equal 30 (sumOfMultiples [ 4, 6 ] 15)
        , skip <|
            test "[5, 6, 8] 150" <|
                \() -> Expect.equal 4419 (sumOfMultiples [ 5, 6, 8 ] 150)
        , skip <|
            test "[43, 47] 10000" <|
                \() -> Expect.equal 2203160 (sumOfMultiples [ 43, 47 ] 10000)
        , skip <|
            test "[5, 25] 51" <|
                \() -> Expect.equal 275 (sumOfMultiples [ 5, 25 ] 51)
        ]
module SumOfMultiples exposing (sumOfMultiples)


sumOfMultiples : List Int -> Int -> Int
sumOfMultiples divisors limit =
    case divisors of
        [] ->
            0

        [ d ] ->
            singletonSumOfMultiples d limit

        _ ->
            genericSumOfMultiples divisors limit


dividesWithoutRemainder : Int -> Int -> Bool
dividesWithoutRemainder n d =
    modBy d n == 0


singletonSumOfMultiples : Int -> Int -> Int
singletonSumOfMultiples d limit =
    -- 1*d + 2*d + 3*d + 4*d == d * (1+2+3+4) == d * (4* (4+1)) / 2
    let
        n =
            (limit - 1) // d
    in
    d * (n * (n + 1)) // 2


genericSumOfMultiples : List Int -> Int -> Int
genericSumOfMultiples divisors limit =
    let
        isMultiple : Int -> Bool
        isMultiple =
            \x -> divisors |> List.any (dividesWithoutRemainder x)
    in
    List.range 1 (limit - 1) |> List.filter isMultiple |> List.sum

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