# Rosalind: LIA — Independent Alleles
# https://rosalind.info/problems/lia/
#
# Given: Integers k <= 7 and N <= 2^k. Tom is AaBb; every organism mates with
# an AaBb partner and has two children.
# Return: The probability that at least N organisms in generation k are AaBb.

let k = 2
let n = 1

# Mendel's second law makes the two loci independent, so each child is AaBb
# with probability 1/4 regardless of generation. Generation k holds 2^k
# organisms, so the count is Binomial(2^k, 1/4).
let population = int(pow(2.0, float(k)))
let p = 0.25

fn factorial(x) { range(1, x + 1) |> reduce(|acc, i| acc * i, 1) }
fn choose(total, taken) { factorial(total) / (factorial(taken) * factorial(total - taken)) }

# P(at least N) = 1 - P(fewer than N).
let below = range(0, n)
    |> map(|i| float(choose(population, i)) * pow(p, float(i)) * pow(1.0 - p, float(population - i)))
    |> sum()

let result = 1.0 - below

println("Result:   " + str(round(result, 3)))
println("Expected: 0.684")

fn test_lia_independent_alleles() {
    assert round(result, 3) == 0.684, "LIA: got " + str(result)
}