Published at Jul 13 2018
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Instructions

Test suite

Solution

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
- the size of bucket two
- the desired number of liters to reach
- which bucket to fill first, either bucket one or bucket two

Your program should determine:

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

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.

Go through the setup instructions for TypeScript to install the necessary dependencies:

http://exercism.io/languages/typescript

Install assignment dependencies:

```
$ yarn install
```

Execute the tests with:

```
$ yarn test
```

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

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

```
import {TwoBucket, Bucket} from './two-bucket'
describe('TwoBucket', () => {
describe('works for input of 3, 5, 1', () => {
const buckOne = 3
const buckTwo = 5
const goal = 1
test('starting with bucket one', () => {
const starterBuck = Bucket.One // indicates which bucket to fill first
const twoBucket = new TwoBucket(buckOne, buckTwo, goal, starterBuck)
expect(twoBucket.moves()).toEqual(4) // includes the first fill
expect(twoBucket.goalBucket).toEqual('one') // which bucket should end up with the desired # of liters
expect(twoBucket.otherBucket).toEqual(5) // leftover value in the "other" bucket once the goal has been reached
})
xtest('starting with bucket two', () => {
const starterBuck = Bucket.Two
const twoBucket = new TwoBucket(buckOne, buckTwo, goal, starterBuck)
expect(twoBucket.moves()).toEqual(8)
expect(twoBucket.goalBucket).toEqual('two')
expect(twoBucket.otherBucket).toEqual(3)
})
})
describe('works for input of 7, 11, 2', () => {
const buckOne = 7
const buckTwo = 11
const goal = 2
xtest('starting with bucket one', () => {
const starterBuck = Bucket.One
const twoBucket = new TwoBucket(buckOne, buckTwo, goal, starterBuck)
expect(twoBucket.moves()).toEqual(14)
expect(twoBucket.goalBucket).toEqual('one')
expect(twoBucket.otherBucket).toEqual(11)
})
xtest('starting with bucket two', () => {
const starterBuck = Bucket.Two
const twoBucket = new TwoBucket(buckOne, buckTwo, goal, starterBuck)
expect(twoBucket.moves()).toEqual(18)
expect(twoBucket.goalBucket).toEqual('two')
expect(twoBucket.otherBucket).toEqual(7)
})
})
})
```

```
export enum Bucket {
One = "one",
Two = "two"
}
type State = [number, number]
const isSameState = (state1: State, state2: State) =>
state1[0] === state2[0] && state1[1] === state2[1]
interface Result {
moves: () => number
goalBucket: Bucket
otherBucket: number
}
export class TwoBucket implements Result {
moves: () => number
goalBucket: Bucket
otherBucket: number
constructor(buckOneSize: number, buckTwoSize: number, goal: number, starterBuck: Bucket) {
const initialState: State = starterBuck === Bucket.One ? [buckOneSize, 0] : [0, buckTwoSize]
const forbiddenState: State = starterBuck === Bucket.One ? [0, buckTwoSize] : [buckOneSize, 0]
const pourOneIntoTwo = (state: State): State => [
Math.max(state[0] - (buckTwoSize - state[1]), 0),
Math.min(state[1] + state[0], buckTwoSize)
]
const pourTwoIntoOne = (state: State): State => {
return [
Math.min(state[0] + state[1], buckOneSize),
Math.max(state[1] - (buckOneSize - state[0]), 0)
]
}
// Returns also forbidden states, that needs to get filtered later.
const findNextStates = (state: State): State[] => [
[buckOneSize, state[1]], // filling bucket one
[state[0], buckTwoSize], // filling bucket two
[0, state[1]], // empty bucket one
[state[0], 0], // empty bucket two
pourOneIntoTwo(state),
pourTwoIntoOne(state)
]
function searchMoves(statesStack: State[]): Result | undefined {
const state = statesStack[statesStack.length - 1]
if (state[0] === goal) {
return {
moves: () => statesStack.length,
goalBucket: Bucket.One,
otherBucket: state[1]
}
} else if (state[1] === goal) {
return {
moves: () => statesStack.length,
goalBucket: Bucket.Two,
otherBucket: state[0]
}
}
const newLegalStates = findNextStates(state)
.filter((newState) => !isSameState(newState, forbiddenState))
.filter((newState) => !statesStack.some((prevState) => isSameState(prevState, newState)))
for (const newState of newLegalStates) {
const result = searchMoves(statesStack.concat([newState]))
if (result) {
return result
}
}
return undefined
}
const result = searchMoves([initialState])!
this.moves = result.moves
this.goalBucket = result.goalBucket
this.otherBucket = result.otherBucket
}
}
```

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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