freeCodeCamp/curriculum/challenges/en/08-coding-interview-prep/rosetta-code/fractran.en.md

title, id, challengeType

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

- text: <code>fractran</code> should be a function.
  testString: 'assert(typeof fractran==''function'',''<code>fractran</code> should be a function.'');'
- text: '<code>fractran("''+tests[0]+''")</code> should return an array.'
  testString: 'assert(Array.isArray(fractran(tests[0])),''<code>fractran("''+tests[0]+''")</code> should return an array.'');'
- text: '<code>fractran("''+tests[0]+''")</code> should return <code>''+JSON.stringify(results[0])+''</code>.'
  testString: 'assert.deepEqual(fractran(tests[0]),results[0],''<code>fractran("''+tests[0]+''")</code> should return <code>''+JSON.stringify(results[0])+''</code>.'');'
- text: '<code>fractran("''+tests[1]+''")</code> should return <code>''+JSON.stringify(results[1])+''</code>.'
  testString: 'assert.deepEqual(fractran(tests[1]),results[1],''<code>fractran("''+tests[1]+''")</code> should return <code>''+JSON.stringify(results[1])+''</code>.'');'
- text: '<code>fractran("''+tests[2]+''")</code> should return <code>''+JSON.stringify(results[2])+''</code>.'
  testString: 'assert.deepEqual(fractran(tests[2]),results[2],''<code>fractran("''+tests[2]+''")</code> should return <code>''+JSON.stringify(results[2])+''</code>.'');'
- text: '<code>fractran("''+tests[3]+''")</code> should return <code>''+JSON.stringify(results[3])+''</code>.'
  testString: 'assert.deepEqual(fractran(tests[3]),results[3],''<code>fractran("''+tests[3]+''")</code> should return <code>''+JSON.stringify(results[3])+''</code>.'');'
- text: '<code>fractran("''+tests[4]+''")</code> should return <code>''+JSON.stringify(results[4])+''</code>.'
  testString: 'assert.deepEqual(fractran(tests[4]),results[4],''<code>fractran("''+tests[4]+''")</code> should return <code>''+JSON.stringify(results[4])+''</code>.'');'

Challenge Seed

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

After Test

console.info('after the test');

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;
}