jdh30

let g = 0.02 and k = 500 and t = 1500

let evolve(r, f) =
  let dtrf = 0.0001 * r * f in
  Some((r, f), (r + (1.0 - r/k)*r*g - dtrf, dtrf + (1.0 - g)*f))

let () =
  Seq.unfold evolve (50, 10)
  @ Seq.truncate 1500
  @ Array.ofSeq

jdh30

let search p =
  let m = # p in
  let next = Array.init m [_ -> 0] in
  let rec init(i, j) =
    if i >= m-1 then () else
      if Array.get p i = Array.get p j then
        let () = Array.Unsafe.set next (i+1) (j+1) in
        init(i+1, j+1)
      else
        if j=0 then init(i+1, j) else init(i, Array.get next j) in

jdh30

type State =
  | S0
  | S1 Number
  | S2 Number

let charOfNumber n =
  if n<26 then Char.ofNumber(n+65)
  else if n<52 then Char.ofNumber(n-26+97)
  else if n<62 then Char.ofNumber(n-52+48)
  else if n=62 then '+' else '/'

jdh30

let suffixArray str =
  let g = Array.get in
  let n = # str in
  let sa = Array.init n id in
  let pos = Array.copy str in
  let tmp = Array.init n [_ -> 0] in
  let sufCmp gap (i, j) =
    compare (g pos i, g pos j) @
    [ Equal ->
        if i+gap >= n || j+gap >= n then compare(j, i) else

jdh30

let maxSumSubseq a =
  let maxm = Array.fold [a, b -> max a b] 0 a in
  let rec loop sum i =
    if i = # a then sum else
      let ai = Array.get a i in
      if ai > 0 then loop (sum + ai) (i+1) else loop sum (i+1) in
  loop 0 0

jdh30

let branches m =
  { { Vec2.rotate(π/2 - asin(4/5));
      Vec2.scale(4/5, 4/5);
      Vec2.translate(0, -1) };
    { Vec2.translate(1, -1);
      Vec2.rotate(-π/2 + asin(3/5));
      Vec2.scale(3/5, 3/5);
      Vec2.translate(1/3, 0) } }
  @ Array.map [m2 → Array.concat{m; m2}]

jdh30

let toHtml f =
  let x = Html "𝑥" in
  let pow = (* xⁿ *)
    [ 0 → {Html "1"}
    | 1 → {x}
    | n → {x; Html.tag "sup" {"style", "font-size:70%"} (Html.ofNumber n)} ] in
  let append(xs, x) = Array.Unsafe.append xs x in
  let appends(xs, xss) = Array.fold append xs xss in
  let minus = Html.of " - " in
  let ellipses = Html " + …" in

jdh30

let safe (x1, y1) (x2, y2) =
  x1 <> x2 && y1 <> y2 && x2 - x1 <> y2 - y1 && x1 - y2 <> x2 - y1

let rec next n s =
  Stack.pop s @
  [ None -> None
  | Some((qs, ps), s) ->
      Stack.pop ps @
      [ None -> if Stack.length qs = n then Some(qs, s) else next n s
      | Some(q, ps) ->

jdh30

let pearsonsCorrelationCoefficient xys =
  let n = Array.length xys in
  let ∑xy, ∑x, ∑y, ∑x2, ∑y2 =
    Array.fold [(∑xy, ∑x, ∑y, ∑x2, ∑y2), (x, y) →
      ∑xy+x*y, ∑x+x, ∑y+y, ∑x2+x*x, ∑y2+y*y]
      (0, 0, 0, 0, 0) xys in
  (n*∑xy-∑x*∑y)/(√(n*∑x2-∑x*∑x)*√(n*∑y2-∑y*∑y))

jdh30

let primes =
  let a = {2} in
  let grow() =
    let p0 = Array.get a (Array.length a - 1) + 1 in
    let b = Array.init p0 [_ → True] in
    let () =
      Array.fold [(), di →
        let rec loop i =
          if i >= Array.length b then () else
            let () = Array.Unsafe.set b i False in