108 lines
5.4 KiB
Markdown
108 lines
5.4 KiB
Markdown
---
|
|
title: Fractran
|
|
id: 5a7dad05be01840e1778a0d1
|
|
challengeType: 5
|
|
---
|
|
|
|
## Description
|
|
<section id='description'>
|
|
<div class="rosetta"><p class="rosetta__paragraph"><span class="rosetta__text--bold"><a class="rosetta__link--wiki" href="https://en.wikipedia.org/wiki/FRACTRAN" title="wp: FRACTRAN">FRACTRAN</a></span> is a Turing-complete esoteric programming language invented by the mathematician <a class="rosetta__link--wiki" href="https://en.wikipedia.org/wiki/John Horton Conway" title="wp: John Horton Conway">John Horton Conway</a>.</p><br/><p class="rosetta__paragraph">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 $n$.</p>
|
|
<br/><p class="rosetta__paragraph">The program is run by updating the integer $n$ as follows:</p><br/><ul class="rosetta__unordered-list"><li class="rosetta__list-item--unordered">for the first fraction, $f_i$, in the list for which $nf_i$ is an integer, replace $n$ with $nf_i$ ;</li>
|
|
<li class="rosetta__list-item--unordered">repeat this rule until no fraction in the list produces an integer when multiplied by $n$, then halt.</li></ul>
|
|
<br>
|
|
<p class="rosetta__paragraph">Conway gave a program for primes in FRACTRAN:</p><br/><p class="rosetta__paragraph"><span class="rosetta__text--indented"> $17/91$, $78/85$, $19/51$, $23/38$, $29/33$, $77/29$, $95/23$, $77/19$, $1/17$, $11/13$, $13/11$, $15/14$, $15/2$, $55/1$</span></p><br/><p class="rosetta__paragraph">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:</p><br/><p class="rosetta__paragraph"><span class="rosetta__text--indented"> $2$, $15$, $825$, $725$, $1925$, $2275$, $425$, $390$, $330$, $290$, $770$, $\ldots$</span></p><br/><p class="rosetta__paragraph">After 2, this sequence contains the following powers of 2:</p><br/><p class="rosetta__paragraph"><span class="rosetta__text--indented">$2^2=4$, $2^3=8$, $2^5=32$, $2^7=128$, $2^{11}=2048$, $2^{13}=8192$, $2^{17}=131072$, $2^{19}=524288$, $\ldots$</span></p><br/><p class="rosetta__paragraph">which are the prime powers of 2.</p>
|
|
<br/><dl class="rosetta__description-list"><dt class="rosetta__description-title">Task:</dt></dl>
|
|
<p class="rosetta__paragraph">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.</p></div>
|
|
</section>
|
|
|
|
## Instructions
|
|
<section id='instructions'>
|
|
|
|
</section>
|
|
|
|
## Tests
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
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>.');
|
|
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
<section id='challengeSeed'>
|
|
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function fractran (progStr) {
|
|
// Good luck!
|
|
}
|
|
```
|
|
|
|
</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>
|