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to Two Bucket in the F# Track

Published at Jul 13 2018 · 0 comments
Instructions
Test suite
Solution

Note:

This solution was written on an old version of Exercism. The tests below might not correspond to the solution code, and the exercise may have changed since this code was written.

Given two buckets of different size, demonstrate how to measure an exact number of liters by strategically transferring liters of fluid between the buckets.

Since this mathematical problem is fairly subject to interpretation / individual approach, the tests have been written specifically to expect one overarching solution.

To help, the tests provide you with which bucket to fill first. That means, when starting with the larger bucket full, you are NOT allowed at any point to have the smaller bucket full and the larger bucket empty (aka, the opposite starting point); that would defeat the purpose of comparing both approaches!

Your program will take as input:

  • the size of bucket one, passed as a numeric value
  • the size of bucket two, passed as a numeric value
  • the desired number of liters to reach, passed as a numeric value
  • which bucket to fill first, passed as a String (either 'one' or 'two')

Your program should determine:

  • the total number of "moves" it should take to reach the desired number of liters, including the first fill - expects a numeric value
  • which bucket should end up with the desired number of liters (let's say this is bucket A) - expects a String (either 'one' or 'two')
  • how many liters are left in the other bucket (bucket B) - expects a numeric value

Note: any time a change is made to either or both buckets counts as one (1) move.

Example: Bucket one can hold up to 7 liters, and bucket two can hold up to 11 liters. Let's say bucket one, at a given step, is holding 7 liters, and bucket two is holding 8 liters (7,8). If you empty bucket one and make no change to bucket two, leaving you with 0 liters and 8 liters respectively (0,8), that counts as one "move". Instead, if you had poured from bucket one into bucket two until bucket two was full, leaving you with 4 liters in bucket one and 11 liters in bucket two (4,11), that would count as only one "move" as well.

To conclude, the only valid moves are:

  • pouring from one bucket to another
  • emptying one bucket and doing nothing to the other
  • filling one bucket and doing nothing to the other

Written with <3 at Fullstack Academy by Lindsay.

Source

Water Pouring Problem http://demonstrations.wolfram.com/WaterPouringProblem/

Submitting Incomplete Solutions

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

TwoBucketTest.fs

// This file was auto-generated based on version 1.4.0 of the canonical data.

module TwoBucketTest

open FsUnit.Xunit
open Xunit

open TwoBucket

[<Fact>]
let ``Measure using bucket one of size 3 and bucket two of size 5 - start with bucket one`` () =
    let bucketOne = 3
    let bucketTwo = 5
    let goal = 1
    let startBucket = Bucket.One
    let expected = { Moves = 4; GoalBucket = Bucket.One; OtherBucket = 5 }
    measure bucketOne bucketTwo goal startBucket |> should equal expected

[<Fact(Skip = "Remove to run test")>]
let ``Measure using bucket one of size 3 and bucket two of size 5 - start with bucket two`` () =
    let bucketOne = 3
    let bucketTwo = 5
    let goal = 1
    let startBucket = Bucket.Two
    let expected = { Moves = 8; GoalBucket = Bucket.Two; OtherBucket = 3 }
    measure bucketOne bucketTwo goal startBucket |> should equal expected

[<Fact(Skip = "Remove to run test")>]
let ``Measure using bucket one of size 7 and bucket two of size 11 - start with bucket one`` () =
    let bucketOne = 7
    let bucketTwo = 11
    let goal = 2
    let startBucket = Bucket.One
    let expected = { Moves = 14; GoalBucket = Bucket.One; OtherBucket = 11 }
    measure bucketOne bucketTwo goal startBucket |> should equal expected

[<Fact(Skip = "Remove to run test")>]
let ``Measure using bucket one of size 7 and bucket two of size 11 - start with bucket two`` () =
    let bucketOne = 7
    let bucketTwo = 11
    let goal = 2
    let startBucket = Bucket.Two
    let expected = { Moves = 18; GoalBucket = Bucket.Two; OtherBucket = 7 }
    measure bucketOne bucketTwo goal startBucket |> should equal expected

[<Fact(Skip = "Remove to run test")>]
let ``Measure one step using bucket one of size 1 and bucket two of size 3 - start with bucket two`` () =
    let bucketOne = 1
    let bucketTwo = 3
    let goal = 3
    let startBucket = Bucket.Two
    let expected = { Moves = 1; GoalBucket = Bucket.Two; OtherBucket = 0 }
    measure bucketOne bucketTwo goal startBucket |> should equal expected

[<Fact(Skip = "Remove to run test")>]
let ``Measure using bucket one of size 2 and bucket two of size 3 - start with bucket one and end with bucket two`` () =
    let bucketOne = 2
    let bucketTwo = 3
    let goal = 3
    let startBucket = Bucket.One
    let expected = { Moves = 2; GoalBucket = Bucket.Two; OtherBucket = 2 }
    measure bucketOne bucketTwo goal startBucket |> should equal expected
module TwoBucket

type Bucket = One | Two
type Moves = EmptyOne | EmptyTwo | OneIntoTwo | TwoIntoOne | FillOne | FillTwo
let movesList = [OneIntoTwo; TwoIntoOne; FillOne; FillTwo; EmptyOne; EmptyTwo]

let doMove bucketOneSize bucketTwoSize state move =
    let (one, two, count) = state
    let newCount = count + 1
    match move with
    | EmptyOne -> (0, two, newCount)
    | EmptyTwo -> (one, 0, newCount)
    | FillOne -> (bucketOneSize, two, newCount)
    | FillTwo -> (one, bucketTwoSize, newCount)
    | OneIntoTwo -> 
        match one + two <= bucketTwoSize with 
        | true -> (0, one + two, newCount)
        | false -> ((one + two) - bucketTwoSize, bucketTwoSize, newCount)
    | TwoIntoOne -> 
        match one + two <= bucketOneSize with 
        | true  -> (one + two, 0, newCount)
        | false -> (bucketOneSize, (one + two) - bucketOneSize, newCount)
let assess goal = function
    | (one,two,count) when one = goal -> Some (count, Bucket.One, two)
    | (one,two,count) when two = goal -> Some (count, Bucket.Two, one)
    | _ -> None
let removeTriedStates tried xs =
    List.filter (fun (one, two, _) -> Set.exists (fun (triedOne, triedTwo, _) -> one = triedOne && two = triedTwo )  tried |> not) xs
    

let moves bucketOneSize bucketTwoSize goal startBucket = 
    let oneBiggest = bucketOneSize > bucketTwoSize
    let twoBiggest = bucketTwoSize > bucketOneSize 
    let startedBiggestFull =
       match startBucket with
       | One when oneBiggest -> true
       | Two when twoBiggest -> true
       | _ -> false
    let move = doMove bucketOneSize bucketTwoSize
    let removeIllegalStates xs =
        match startedBiggestFull with 
                | false -> xs
                | true -> xs |> List.filter (fun (one, two, _) -> 
                    match startBucket with
                    | One when oneBiggest && one = 0 && two = bucketTwoSize -> false
                    | Two when twoBiggest && two = 0 && one = bucketOneSize -> false
                    | _ -> true
                )
    let rec calculateRoute states tried =
        let soultions = List.choose (assess goal) states
        match soultions with
        | s::_ -> Some s
        | [] -> 
            let potentialStates = states |> List.collect (fun state -> List.map (fun a -> move state a) movesList)
            let allowedStates = 
               removeIllegalStates potentialStates |> removeTriedStates tried
            match allowedStates with
            | [] -> None
            | _ -> calculateRoute allowedStates (Set.union tried <| Set.ofList states)
    match startBucket with
    | One -> calculateRoute [(bucketOneSize, 0, 1)] Set.empty
    | Two -> calculateRoute [(0, bucketTwoSize, 1)] Set.empty

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