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gstro's solution

to Change in the Scala Track

Published at Oct 06 2019 · 0 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.

For example

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

Edge cases

  • 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?

The Scala exercises assume an SBT project scheme. The exercise solution source should be placed within the exercise directory/src/main/scala. The exercise unit tests can be found within the exercise directory/src/test/scala.

To run the tests simply run the command sbt test in the exercise directory.

Please see the learning and installation pages if you need any help.

Source

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

Submitting Incomplete Solutions

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

ChangeTest.scala

import org.scalatest.{Matchers, FunSuite}

/** @version 1.2.0 */
class ChangeTest extends FunSuite with Matchers {
  
  test("single coin change") {
    Change.findFewestCoins(25, List(1, 5, 10, 25, 100)) should be (Some(List(25)))
  }

  test("multiple coin change") {
    pending
    Change.findFewestCoins(15, List(1, 5, 10, 25, 100)) should be (Some(List(5, 10)))
  }

  test("change with Lilliputian Coins") {
    pending
    Change.findFewestCoins(23, List(1, 4, 15, 20, 50)) should be (Some(List(4, 4, 15)))
  }

  test("change with Lower Elbonia Coins") {
    pending
    Change.findFewestCoins(63, List(1, 5, 10, 21, 25)) should be (Some(List(21, 21, 21)))
  }

  test("large target values") {
    pending
    Change.findFewestCoins(999, List(1, 2, 5, 10, 20, 50, 100)) should be (Some(List(2, 2, 5, 20, 20, 50, 100, 100, 100, 100, 100, 100, 100, 100, 100)))
  }

  test("possible change without unit coins available") {
    pending
    Change.findFewestCoins(21, List(2, 5, 10, 20, 50)) should be (Some(List(2, 2, 2, 5, 10)))
  }

  test("another possible change without unit coins available") {
    pending
    Change.findFewestCoins(27, List(4, 5)) should be (Some(List(4, 4, 4, 5, 5, 5)))
  }

  test("no coins make 0 change") {
    pending
    Change.findFewestCoins(0, List(1, 5, 10, 21, 25)) should be (Some(List()))
  }

  test("error testing for change smaller than the smallest of coins") {
    pending
    Change.findFewestCoins(3, List(5, 10)) should be (None)
  }

  test("error if no combination can add up to target") {
    pending
    Change.findFewestCoins(94, List(5, 10)) should be (None)
  }

  test("cannot find negative change values") {
    pending
    Change.findFewestCoins(-5, List(1, 2, 5)) should be (None)
  }
}
import scala.annotation.tailrec

object Change {
  import Tree._

  private sealed trait CoinTree {
    def path: List[Int] = Nil
    def depth: Int = path.length
  }
  private object Tree {
    case object Leaf extends CoinTree
    case class Node(value: Int, siblings: List[Int], branch: CoinTree) extends CoinTree {
      override def path: List[Int] = value :: branch.path
    }
  }

  def findFewestCoins(change: Int, coins: List[Int]): Option[List[Int]] =
    if (change == 0) Some(Nil)
    else checkCoins(change, coins.reverse, Leaf) match {
      case Leaf => None
      case tree => Some(tree.path)
    }

  @tailrec
  private def checkCoins(target: Int, coinsList: List[Int], minValid: CoinTree): CoinTree = coinsList match {
    case _ :: tail => checkCoins(target, tail, iterate(target, coinsList, Leaf, minValid))
    case Nil       => minValid
  }

  @tailrec
  private def iterate(remaining: Int, currentCoins: List[Int], acc: CoinTree, minValid: CoinTree): CoinTree = currentCoins match {
    case _ if remaining == 0       => List(acc, minValid).sortBy(_.depth).find(_.path.nonEmpty).getOrElse(Leaf)
    case c :: cs if c <= remaining => iterate(remaining - c, currentCoins, Node(c, cs, acc), minValid)
    case _ :: cs                   => iterate(remaining, cs, acc, minValid)
    case _                         => prune(remaining, acc, minValid)
  }

  private def prune(remaining: Int, acc: CoinTree, minValid: CoinTree): CoinTree = acc match {
    case a if a.depth < minValid.depth => minValid
    case Leaf                          => minValid
    case Node(v, sibs, branch)         => iterate(remaining + v, sibs, branch, minValid)
  }
}

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