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package factors
// Score returns a "factor score" equal to the sum of the reciprocoals
// of the number n's factors.
// Rationale:
// A number's factors are one of the most important things that determines
// how well it functions as a number base. An easy way to determine how
// good these factors are is to simply count them, but that comes with
// the problem that all factors are considered equal when they really aren't
// - divisibility by 2 (which ensures 1/2 is a terminating fraction and
// you can tell whether a number is even or odd by looking at the last digit)
// is more important than divisibility by 23. The most obvious way of
// accounting for this is by giving each factor a score and adding those
// scores to get the overall score. I chose score(f) = 1/f because it is
// the simplest function that captures the intuition that smaller factors
// are more valuable than larger ones. It also gives the score a meaning:
// a factor's score is the probability a random number is divisible by it.
func Score(n uint) float64 {
if n == 0 {
panic("Cannot get factor score of 0.")
}
factorSum := uint(0)
for _, f := range Factors(n) {
factorSum += f
}
return float64(factorSum) / float64(n)
}
// BasicRank returns a rank describing how well a base handles the simplest
// fractions (1/2, 1/3, 1/4 and 1/5)
// also known as 2345 Rank
func BasicRank(n uint) string {
var firstRank, secondRank string
if n%2 == 0 {
if n%3 == 0 {
if n%4 == 0 {
firstRank = "A"
} else {
firstRank = "B"
}
} else {
if n%4 == 0 {
firstRank = "C"
} else {
firstRank = "D"
}
}
} else {
if n%3 == 0 {
firstRank = "E"
} else {
firstRank = "F"
}
}
switch n % 5 {
case 0:
secondRank = "+"
case 1, 4:
secondRank = "~"
case 2, 3:
secondRank = "-"
}
return firstRank + secondRank
}
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