140 lines
3.7 KiB
Markdown
140 lines
3.7 KiB
Markdown
---
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id: 5a7dad05be01840e1778a0d1
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title: Fractran
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challengeType: 5
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forumTopicId: 302270
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dashedName: fractran
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---
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# --description--
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[FRACTRAN](https://en.wikipedia.org/wiki/FRACTRAN "wp: 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").
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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 $n$.
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The program is run by updating the integer $n$ as follows:
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<ul>
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<li>for the first fraction, $f_i$, in the list for which $nf_i$ is an integer, replace $n$ with $nf_i$ ;</li>
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<li>repeat this rule until no fraction in the list produces an integer when multiplied by $n$, then halt.</li>
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</ul>
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Conway gave a program for primes in FRACTRAN:
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$\\dfrac{17}{91}$, $\\dfrac{78}{85}$, $\\dfrac{19}{51}$, $\\dfrac{23}{38}$, $\\dfrac{29}{33}$, $\\dfrac{77}{29}$, $\\dfrac{95}{23}$, $\\dfrac{77}{19}$, $\\dfrac{1}{17}$, $\\dfrac{11}{13}$, $\\dfrac{13}{11}$, $\\dfrac{15}{14}$, $\\dfrac{15}{2}$, $\\dfrac{55}{1}$
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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:
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$2$, $15$, $825$, $725$, $1925$, $2275$, $425$, $390$, $330$, $290$, $770$, $\\ldots$
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After 2, this sequence contains the following powers of 2:
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$2^2=4$, $2^3=8$, $2^5=32$, $2^7=128$, $2^{11}=2048$, $2^{13}=8192$, $2^{17}=131072$, $2^{19}=524288$, $\\ldots$
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which are the prime powers of 2.
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# --instructions--
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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.
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# --hints--
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`fractran` should be a function.
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```js
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assert(typeof fractran == 'function');
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```
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`fractran("3/2, 1/3")` should return an array.
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```js
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assert(Array.isArray(fractran('3/2, 1/3')));
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```
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`fractran("3/2, 1/3")` should return `[ 2, 3, 1 ]`.
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```js
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assert.deepEqual(fractran('3/2, 1/3'), [2, 3, 1]);
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```
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`fractran("3/2, 5/3, 1/5")` should return `[ 2, 3, 5, 1 ]`.
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```js
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assert.deepEqual(fractran('3/2, 5/3, 1/5'), [2, 3, 5, 1]);
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```
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`fractran("3/2, 6/3")` should return `[ 2, 3, 6, 9, 18, 27, 54, 81, 162, 243 ]`.
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```js
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assert.deepEqual(fractran('3/2, 6/3'), [2, 3, 6, 9, 18, 27, 54, 81, 162, 243]);
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```
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`fractran("2/7, 7/2")` should return `[ 2, 7, 2, 7, 2, 7, 2, 7, 2, 7 ]`.
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```js
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assert.deepEqual(fractran('2/7, 7/2'), [2, 7, 2, 7, 2, 7, 2, 7, 2, 7]);
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```
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`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 ]`.
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```js
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assert.deepEqual(
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fractran(
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'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'
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),
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[2, 15, 825, 725, 1925, 2275, 425, 390, 330, 290]
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);
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```
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# --seed--
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## --seed-contents--
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```js
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function fractran(progStr) {
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}
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```
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# --solutions--
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```js
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function fractran(progStr){
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var num = new Array();
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var den = new Array();
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var val ;
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var out="";
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function compile(prog){
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var regex = /\s*(\d*)\s*\/\s*(\d*)\s*(.*)/m;
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while(regex.test(prog)){
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num.push(regex.exec(prog)[1]);
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den.push(regex.exec(prog)[2]);
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prog = regex.exec(prog)[3];
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}
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}
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function step(val){
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var i=0;
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while(i<den.length && val%den[i] != 0) i++;
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return num[i]*val/den[i];
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}
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var seq=[]
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function exec(val){
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var i = 0;
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while(val && i<limit){
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seq.push(val)
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val = step(val);
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i ++;
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}
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}
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// Main
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compile(progStr);
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var limit = 10;
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exec(2);
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return seq;
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}
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```
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