Created
November 20, 2012 19:38
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fib sums slightly improved (coding dojo)
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import org.scalatest.matchers.ShouldMatchers | |
import org.junit.Test | |
//object Sums { | |
// def main(args: Array[String]) { | |
// for(i <- 1 to 20) { println(i + " is " + new Sums().zeckendorfRepresentationOf(i).mkString(" or "))} | |
// } | |
//} | |
class Sums extends ShouldMatchers { | |
@Test def givenANumber_shouldFindItFibonacciRepresentations() { | |
fibonacciRepresentationsOf(1) should equal(Seq("1")) | |
fibonacciRepresentationsOf(2) should equal(Seq("10")) | |
fibonacciRepresentationsOf(3) should equal(Seq("100", "11")) | |
fibonacciRepresentationsOf(4) should equal(Seq("101")) | |
fibonacciRepresentationsOf(5) should equal(Seq("1000", "110")) | |
fibonacciRepresentationsOf(6) should equal(Seq("1001", "111")) | |
fibonacciRepresentationsOf(7) should equal(Seq("1010")) | |
fibonacciRepresentationsOf(8) should equal(Seq("10000", "1100", "1011")) | |
fibonacciRepresentationsOf(9) should equal(Seq("10001", "1101")) | |
fibonacciRepresentationsOf(10) should equal(Seq("10010", "1110")) | |
fibonacciRepresentationsOf(11) should equal(Seq("10100", "10011", "1111")) | |
fibonacciRepresentationsOf(12) should equal(Seq("10101")) | |
fibonacciRepresentationsOf(13) should equal(Seq("100000", "11000", "10110")) | |
} | |
@Test def givenANumber_shouldFindItZeckendorfRepresentation() { | |
zeckendorfRepresentationOf(1) should equal("1") | |
zeckendorfRepresentationOf(2) should equal("10") | |
zeckendorfRepresentationOf(3) should equal("100") | |
zeckendorfRepresentationOf(4) should equal("101") | |
zeckendorfRepresentationOf(5) should equal("1000") | |
zeckendorfRepresentationOf(6) should equal("1001") | |
zeckendorfRepresentationOf(7) should equal("1010") | |
zeckendorfRepresentationOf(8) should equal("10000") | |
zeckendorfRepresentationOf(9) should equal("10001") | |
zeckendorfRepresentationOf(10) should equal("10010") | |
zeckendorfRepresentationOf(11) should equal("10100") | |
zeckendorfRepresentationOf(12) should equal("10101") | |
zeckendorfRepresentationOf(13) should equal("100000") | |
} | |
@Test def givenANumber_shouldFindFibonacciNumbersWithSumEqualToIt() { | |
findFibonacciRepresentationsOf(0) should equal(Seq()) | |
findFibonacciRepresentationsOf(1) should equal(Seq(Seq(1))) | |
findFibonacciRepresentationsOf(5) should equal(Seq(Seq(5), Seq(2,3))) | |
} | |
@Test def givenFibonacciRepresentationOfANumeber_shouldConvertItToString() { | |
asString(Seq()) should equal("") | |
asString(Seq(1)) should equal("1") | |
asString(Seq(5)) should equal("1000") | |
asString(Seq(2, 3)) should equal("110") | |
} | |
@Test def shouldCalculateSequenceOfFibonacciNumbers_SkippingFirstZero() { | |
calculateFibonacciSequence(0) should equal(Seq()) | |
calculateFibonacciSequence(1) should equal(Seq(1)) | |
calculateFibonacciSequence(2) should equal(Seq(1, 2)) | |
calculateFibonacciSequence(6) should equal(Seq(1, 2, 3, 5, 8, 13)) | |
} | |
lazy val fibonacciSize = 6 | |
lazy val fibonacci = calculateFibonacciSequence(fibonacciSize) | |
type NumberAsFibs = Seq[Int] | |
def zeckendorfRepresentationOf(n: Int): String = { | |
fibonacciRepresentationsOf(n).filterNot{ _.contains("11") }.head | |
} | |
def fibonacciRepresentationsOf(n: Int): Seq[String] = { | |
findFibonacciRepresentationsOf(n) map asString | |
} | |
private def findFibonacciRepresentationsOf(n: Int): Seq[NumberAsFibs] = { | |
for ( | |
length <- 1 to fibonacciSize; | |
combination <- fibonacci.combinations(length) if (combination.sum == n) | |
) yield combination | |
} | |
private def asString(numberAsFibs: NumberAsFibs) = { | |
val chars = for (i <- fibonacci) yield if (numberAsFibs.contains(i)) '1' else '0' | |
chars.reverse.dropWhile(_ == '0').mkString | |
} | |
private def calculateFibonacciSequence(count: Int): Seq[Int] = { | |
def f(count: Int, current: Int, previous: Int): List[Int] = count match { | |
case 0 => List() | |
case _ => { | |
val newCurrent = current + previous | |
val newLast = current | |
current :: f(count - 1, newCurrent, newLast) | |
} | |
} | |
f(count, 1, 1) | |
} | |
private def calculateFibonacciStream: Stream[Int] = { | |
def f(current: Int, previous: Int): Stream[Int] = | |
current #:: f(current + previous, current) | |
f(1, 1) | |
} | |
} |
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