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title	id	challengeType
Fractran	5a7dad05be01840e1778a0d1	3

Description

FRACTRAN is a Turing-complete esoteric programming language invented by the mathematician 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:

$17/91$, $78/85$, $19/51$, $23/38$, $29/33$, $77/29$, $95/23$, $77/19$, $1/17$, $11/13$, $13/11$, $15/14$, $15/2$, $55/1$

Starting with $n=2$, this FRACTRAN program will change $n$ to $15=2\times (15/2)$, then $825=15\times (55/1)$, 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.

Task:

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.

Instructions

Tests

tests:
  - text: <code>fractran</code> should be a function.
    testString: assert(typeof fractran=='function','<code>fractran</code> should be a function.');
  - text: <code>fractran("3/2, 1/3")</code> should return an array.
    testString: assert(Array.isArray(fractran('3/2, 1/3')),'<code>fractran("3/2, 1/3")</code> should return an array.');
  - text: <code>fractran("3/2, 1/3")</code> should return <code>[ 2, 3, 1 ]</code>.
    testString: assert.deepEqual(fractran('3/2, 1/3'), [ 2, 3, 1 ],'<code>fractran("3/2, 1/3")</code> should return <code>[ 2, 3, 1 ]</code>.');
  - text: <code>fractran("3/2, 5/3, 1/5")</code> should return <code>[ 2, 3, 5, 1 ]</code>.
    testString: assert.deepEqual(fractran('3/2, 5/3, 1/5'), [ 2, 3, 5, 1 ],'<code>fractran("3/2, 5/3, 1/5")</code> should return <code>[ 2, 3, 5, 1 ]</code>.');
  - text: <code>fractran("3/2, 6/3")</code> should return <code>[ 2, 3, 6, 9, 18, 27, 54, 81, 162, 243 ]</code>.
    testString: assert.deepEqual(fractran('3/2, 6/3'), [ 2, 3, 6, 9, 18, 27, 54, 81, 162, 243 ],'<code>fractran("3/2, 6/3")</code> should return <code>[ 2, 3, 6, 9, 18, 27, 54, 81, 162, 243 ]</code>.');
  - text: <code>fractran("2/7, 7/2")</code> should return <code>[ 2, 7, 2, 7, 2, 7, 2, 7, 2, 7 ]</code>.
    testString: assert.deepEqual(fractran('2/7, 7/2'), [ 2, 7, 2, 7, 2, 7, 2, 7, 2, 7 ],'<code>fractran("2/7, 7/2")</code> should return <code>[ 2, 7, 2, 7, 2, 7, 2, 7, 2, 7 ]</code>.');
  - text: <code>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")</code> should return <code>[ 2, 15, 825, 725, 1925, 2275, 425, 390, 330, 290 ]</code>.
    testString: 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 ],'<code>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")</code> should return <code>[ 2, 15, 825, 725, 1925, 2275, 425, 390, 330, 290 ]</code>.');

Challenge Seed

function fractran (progStr) {
  // Good luck!
}

Solution

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;
}

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