m1kal's solution to Change on the Scala track

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)
  }
}

object Change {
  def simpleFind(amount: Int, coins: List[Int], soFar: List[Int]=List()) :Option[List[Int]] = {
    if (amount < 0)
      None
    else if (amount == 0)
      Some(soFar)
    else {
      val maxPossibleCoin = coins.sorted.reverse.find(_ <= amount)
      maxPossibleCoin match {
        case Some(maxCoin) => simpleFind(amount - maxCoin, coins, maxCoin::soFar)
        case None => None
      }
    }
  }

  def findCoins(amount: Int, coins: List[Int]) :List[List[Int]] = {
    if (amount < 0 || coins.isEmpty)
      List[List[Int]]()
    else if (amount == 0)
      List(List[Int]())
    else {
      val coin :: rest = coins
      findCoins(amount - coin, coins).map(coin :: _) ::: findCoins(amount,rest)
    }
  }
  def canBeSimplified(coins:List[Int]) = {
    coins.isEmpty ||
      coins.sliding(2, 1).filter{
        case first::second::Nil => 2*first > second
      }.isEmpty
  }
  def findFewestCoinsGeneral(amount:Int, coins:List[Int]) = {
    val partitions = findCoins(amount, coins)
    if (partitions.isEmpty)
      None
    else
      Some(partitions.sortBy(_.length).head)
  }

  def findFewestCoins(amount: Int, coins: List[Int]) :Option[List[Int]] = {
    if (canBeSimplified(coins))
      simpleFind(amount, coins) match {
        case a:Some[List[Int]] => a
        case None => findFewestCoinsGeneral(amount, coins)
     }
    else 
      findFewestCoinsGeneral(amount, coins)
  }
}

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m1kal's solution

to Change in the Scala Track