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curriculum/challenges/english/10-coding-interview-prep/rosetta-code/fractran.md

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+---
+title: Fractran
+id: 5a7dad05be01840e1778a0d1
+challengeType: 5
+forumTopicId: 302270
+---
+
+## Description
+<section id='description'>
+<a href="https://en.wikipedia.org/wiki/FRACTRAN" title="wp: FRACTRAN" target="_blank">FRACTRAN</a> is a Turing-complete esoteric programming language invented by the mathematician <a href="https://en.wikipedia.org/wiki/John Horton Conway" title="wp: John Horton Conway" target="_blank">John Horton Conway</a>.
+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:
+<ul>
+  <li>for the first fraction, $f_i$, in the list for which $nf_i$ is an integer, replace $n$ with $nf_i$ ;</li>
+  <li>repeat this rule until no fraction in the list produces an integer when multiplied by $n$, then halt.</li>
+</ul>
+Conway gave a program for primes in FRACTRAN:
+<span style="margin-left: 1em;">$\dfrac{17}{91}$, $\dfrac{78}{85}$, $\dfrac{19}{51}$, $\dfrac{23}{38}$, $\dfrac{29}{33}$, $\dfrac{77}{29}$, $\dfrac{95}{23}$, $\dfrac{77}{19}$, $\dfrac{1}{17}$, $\dfrac{11}{13}$, $\dfrac{13}{11}$, $\dfrac{15}{14}$, $\dfrac{15}{2}$, $\dfrac{55}{1}$</span>
+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:
+<span style="margin-left: 1em;">$2$, $15$, $825$, $725$, $1925$, $2275$, $425$, $390$, $330$, $290$, $770$, $\ldots$</span>
+After 2, this sequence contains the following powers of 2:
+<span style="margin-left: 1em;">$2^2=4$, $2^3=8$, $2^5=32$, $2^7=128$, $2^{11}=2048$, $2^{13}=8192$, $2^{17}=131072$, $2^{19}=524288$, $\ldots$</span>
+which are the prime powers of 2.
+</section>
+
+## Instructions
+<section id='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.
+</section>
+
+## Tests
+<section id='tests'>
+
+```yml
+tests:
+  - text: <code>fractran</code> should be a function.
+    testString: assert(typeof fractran=='function');
+  - text: <code>fractran("3/2, 1/3")</code> should return an array.
+    testString: assert(Array.isArray(fractran('3/2, 1/3')));
+  - 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 ]);
+  - 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 ]);
+  - 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 ]);
+  - 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 ]);
+  - 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 ]);
+
+```
+
+</section>
+
+## Challenge Seed
+<section id='challengeSeed'>
+
+<div id='js-seed'>
+
+```js
+function fractran(progStr) {
+
+}
+```
+
+</div>
+
+</section>
+
+## Solution
+<section id='solution'>
+
+
+```js
+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;
+}
+
+```
+
+</section>