# Rosalind: RSTR — Matching Random Motifs
# https://rosalind.info/problems/rstr/
#
# Given: A positive integer N, a number x between 0 and 1, and a DNA string s.
# Return: The probability that at least one of N random strings constructed
# with GC content x matches s exactly.

let n = 90
let gc_fraction = 0.6
let s = "ATAGCCGA"

# At GC content x each of G and C appears with probability x/2, and each of A
# and T with (1-x)/2.
let single = range(0, len(s)) |> reduce(|acc, i| {
    let base = substr(s, i, 1)
    let is_gc = base == "G" or base == "C"
    acc * (if is_gc then gc_fraction / 2.0 else (1.0 - gc_fraction) / 2.0)
}, 1.0)

# The N strings are independent, so the complement is the clean way in: the
# chance that none of them matches is (1-p)^N.
let result = 1.0 - pow(1.0 - single, float(n))

println("P(one string matches): " + str(single))
println("Result:   " + str(round(result, 5)))
println("Expected: 0.00117 — s has 4 weak bases and 4 strong ones, so")
println("          p = 0.2^4 x 0.3^4 = 1.296e-05, and 1-(1-p)^90 = 0.001166")

fn test_rstr_random_motif_match() {
    # p is the product of four A/T probabilities and four G/C ones.
    assert abs(single - 0.00001296) < 0.0000001, "RSTR: p = " + str(single)
    assert round(result, 5) == 0.00117, "RSTR: got " + str(result)
    # More strings can only raise the chance of a match.
    let fewer = 1.0 - pow(1.0 - single, 10.0)
    assert fewer < result, "RSTR: fewer trials did not lower the probability"
}