3.7 KiB

Raw Blame History

id	title	challengeType	forumTopicId	dashedName
5a7dad05be01840e1778a0d1	Fractran	5	302270	fractran

--description--

FRACTRAN is a Turing-complete esoteric programming language invented by the mathematician [John Horton Conway](https://en.wikipedia.org/wiki/John Horton Conway "wp: John Horton Conway").

A FRACTRAN program is an ordered list of positive fractions P = (f_1, f_2, \\ldots, f_m), together with an initial positive integer input n.

The program is run by updating the integer n as follows:

for the first fraction, $f_i$, in the list for which $nf_i$ is an integer, replace $n$ with $nf_i$ ;
repeat this rule until no fraction in the list produces an integer when multiplied by $n$, then halt.

Conway gave a program for primes in FRACTRAN:

\\dfrac{17}{91}, \\dfrac{78}{85}, \\dfrac{19}{51}, \\dfrac{23}{38}, \\dfrac{29}{33}, \\dfrac{77}{29}, \\dfrac{95}{23}, \\dfrac{77}{19}, \\dfrac{1}{17}, \\dfrac{11}{13}, \\dfrac{13}{11}, \\dfrac{15}{14}, \\dfrac{15}{2}, \\dfrac{55}{1}

Starting with n=2, this FRACTRAN program will change n to 15=2\\times (\\frac{15}{2}), then 825=15\\times (\\frac{55}{1}), generating the following sequence of integers:

2, 15, 825, 725, 1925, 2275, 425, 390, 330, 290, 770, \\ldots

After 2, this sequence contains the following powers of 2:

2^2=4, 2^3=8, 2^5=32, 2^7=128, 2^{11}=2048, 2^{13}=8192, 2^{17}=131072, 2^{19}=524288, \\ldots

which are the prime powers of 2.

--instructions--

Write a function that takes a fractran program as a string parameter and returns the first 10 numbers of the program as an array. If the result does not have 10 numbers then return the numbers as is.

--hints--

fractran should be a function.

assert(typeof fractran == 'function');

fractran("3/2, 1/3") should return an array.

assert(Array.isArray(fractran('3/2, 1/3')));

fractran("3/2, 1/3") should return [ 2, 3, 1 ].

assert.deepEqual(fractran('3/2, 1/3'), [2, 3, 1]);

fractran("3/2, 5/3, 1/5") should return [ 2, 3, 5, 1 ].

assert.deepEqual(fractran('3/2, 5/3, 1/5'), [2, 3, 5, 1]);

fractran("3/2, 6/3") should return [ 2, 3, 6, 9, 18, 27, 54, 81, 162, 243 ].

assert.deepEqual(fractran('3/2, 6/3'), [2, 3, 6, 9, 18, 27, 54, 81, 162, 243]);

fractran("2/7, 7/2") should return [ 2, 7, 2, 7, 2, 7, 2, 7, 2, 7 ].

assert.deepEqual(fractran('2/7, 7/2'), [2, 7, 2, 7, 2, 7, 2, 7, 2, 7]);

fractran("17/91, 78/85, 19/51, 23/38, 29/33, 77/29, 95/23, 77/19, 1/17, 11/13, 13/11, 15/14, 15/2, 55/1") should return [ 2, 15, 825, 725, 1925, 2275, 425, 390, 330, 290 ].

assert.deepEqual(
  fractran(
    '17/91, 78/85, 19/51, 23/38, 29/33, 77/29, 95/23, 77/19, 1/17, 11/13, 13/11, 15/14, 15/2, 55/1'
  ),
  [2, 15, 825, 725, 1925, 2275, 425, 390, 330, 290]
);

--seed--

--seed-contents--

function fractran(progStr) {

}

--solutions--

function fractran(progStr){
  var num = new Array();
  var den = new Array();
  var val ;
  var out="";
  function compile(prog){
    var regex = /\s*(\d*)\s*\/\s*(\d*)\s*(.*)/m;
    while(regex.test(prog)){
      num.push(regex.exec(prog)[1]);
      den.push(regex.exec(prog)[2]);
      prog = regex.exec(prog)[3];
    }
  }

  function step(val){
    var i=0;
    while(i<den.length && val%den[i] != 0) i++;
    return num[i]*val/den[i];
  }

  var seq=[]

  function exec(val){
    var i = 0;
    while(val && i<limit){
      seq.push(val)
      val = step(val);
      i ++;
    }
  }

  // Main
  compile(progStr);
  var limit = 10;
  exec(2);
  return seq;
}

3.7 KiB Raw Blame History