Output Distinct Factor Cuboids
Today's task is very simple: given a positive integer, output a representative of each cuboid formable by its factors.
Explanations
A cuboid's volume is the product of its three side lengths. For example, a cuboid of volume 4 whose side lengths are integers can have sides [1, 1, 4]
, [1, 2, 2]
, [1, 4, 1]
, [2, 1, 2]
, [2, 2, 1]
, or [4, 1, 1]
. However, some of these represent the same cuboid: e.g. [1, 1, 4]
and [4, 1, 1]
are the same cuboid rotated. There are only two distinct cuboids with volume 4 and integer sides: [1, 1, 4]
and [1, 2, 2]
. The output can be any representation of the first cuboid, and any representation of the second cuboid.
Input
Your program must take a single positive integer \$1 \le n \le 2^{31}−1\$.
Output
You will need to output all possible cuboids in a list or any other acceptable way. E.g.
Input Output
1 [[1, 1, 1]]
2 [[1, 1, 2]]
3 [[1, 1, 3]]
4 [[1, 1, 4], [1, 2, 2]]
8 [[1, 1, 8], [1, 2, 4], [2, 2, 2]]
12 [[1, 1, 12], [1, 2, 6], [1, 3, 4], [2, 2, 3]]
13 [[1, 1, 13]]
15 [[1, 1, 15], [1, 3, 5]]
18 [[1, 1, 18], [1, 2, 9], [1, 3, 6], [2, 3, 3]]
23 [[1, 1, 23]]
27 [[1, 1, 27], [1, 3, 9], [3, 3, 3]]
32 [[1, 1, 32], [1, 2, 16], [1, 4, 8], [2, 2, 8], [2, 4, 4]]
36 [[1, 1, 36], [1, 2, 18], [1, 3, 12],[1, 4, 9], [1, 6, 6], [2, 2, 9], [2, 3, 6], [3, 3, 4]]
Sub-lists don't need to be sorted, just as long as they are unique.
Scoring
This is code golf, so shortest answer in bytes wins. Standard loopholes are forbidden.
Here is a test case generator
Leaderboards
Here is a Stack Snippet to generate both a regular leaderboard and an overview of winners by language.
To make sure that your answer shows up, please start your answer with a headline, using the following Markdown template:
# Language Name, N bytes
where N
is the size of your submission. If you improve your score, you can keep old scores in the headline, by striking them through. For instance:
# Ruby, <s>104</s> <s>101</s> 96 bytes
If there you want to include multiple numbers in your header (e.g. because your score is the sum of two files or you want to list interpreter flag penalties separately), make sure that the actual score is the last number in the header:
# Perl, 43 + 2 (-p flag) = 45 bytes
You can also make the language name a link which will then show up in the leaderboard snippet:
# [><>](http://esolangs.org/wiki/Fish), 121 bytes
var QUESTION_ID=192852;
var OVERRIDE_USER=8478;
var ANSWER_FILTER="!t)IWYnsLAZle2tQ3KqrVveCRJfxcRLe",COMMENT_FILTER="!)Q2B_A2kjfAiU78X(md6BoYk",answers=[],answers_hash,answer_ids,answer_page=1,more_answers=!0,comment_page;function answersUrl(d){return"https://api.stackexchange.com/2.2/questions/"+QUESTION_ID+"/answers?page="+d+"&pagesize=100&order=desc&sort=creation&site=codegolf&filter="+ANSWER_FILTER}function commentUrl(d,e){return"https://api.stackexchange.com/2.2/answers/"+e.join(";")+"/comments?page="+d+"&pagesize=100&order=desc&sort=creation&site=codegolf&filter="+COMMENT_FILTER}function getAnswers(){jQuery.ajax({url:answersUrl(answer_page++),method:"get",dataType:"jsonp",crossDomain:!0,success:function(d){answers.push.apply(answers,d.items),answers_hash=[],answer_ids=[],d.items.forEach(function(e){e.comments=[];var f=+e.share_link.match(/\d+/);answer_ids.push(f),answers_hash[f]=e}),d.has_more||(more_answers=!1),comment_page=1,getComments()}})}function getComments(){jQuery.ajax({url:commentUrl(comment_page++,answer_ids),method:"get",dataType:"jsonp",crossDomain:!0,success:function(d){d.items.forEach(function(e){e.owner.user_id===OVERRIDE_USER&&answers_hash[e.post_id].comments.push(e)}),d.has_more?getComments():more_answers?getAnswers():process()}})}getAnswers();var SCORE_REG=function(){var d=String.raw`h\d`,e=String.raw`\-?\d+\.?\d*`,f=String.raw`[^\n<>]*`,g=String.raw`<s>${f}</s>|<strike>${f}</strike>|<del>${f}</del>`,h=String.raw`[^\n\d<>]*`,j=String.raw`<[^\n<>]+>`;return new RegExp(String.raw`<${d}>`+String.raw`\s*([^\n,]*[^\s,]),.*?`+String.raw`(${e})`+String.raw`(?=`+String.raw`${h}`+String.raw`(?:(?:${g}|${j})${h})*`+String.raw`</${d}>`+String.raw`)`)}(),OVERRIDE_REG=/^Override\s*header:\s*/i;function getAuthorName(d){return d.owner.display_name}function process(){var d=[];answers.forEach(function(n){var o=n.body;n.comments.forEach(function(q){OVERRIDE_REG.test(q.body)&&(o="<h1>"+q.body.replace(OVERRIDE_REG,"")+"</h1>")});var p=o.match(SCORE_REG);p&&d.push({user:getAuthorName(n),size:+p[2],language:p[1],link:n.share_link})}),d.sort(function(n,o){var p=n.size,q=o.size;return p-q});var e={},f=1,g=null,h=1;d.forEach(function(n){n.size!=g&&(h=f),g=n.size,++f;var o=jQuery("#answer-template").html();o=o.replace("{{PLACE}}",h+".").replace("{{NAME}}",n.user).replace("{{LANGUAGE}}",n.language).replace("{{SIZE}}",n.size).replace("{{LINK}}",n.link),o=jQuery(o),jQuery("#answers").append(o);var p=n.language;p=jQuery("<i>"+n.language+"</i>").text().toLowerCase(),e[p]=e[p]||{lang:n.language,user:n.user,size:n.size,link:n.link,uniq:p}});var j=[];for(var k in e)e.hasOwnProperty(k)&&j.push(e[k]);j.sort(function(n,o){return n.uniq>o.uniq?1:n.uniq<o.uniq?-1:0});for(var l=0;l<j.length;++l){var m=jQuery("#language-template").html(),k=j[l];m=m.replace("{{LANGUAGE}}",k.lang).replace("{{NAME}}",k.user).replace("{{SIZE}}",k.size).replace("{{LINK}}",k.link),m=jQuery(m),jQuery("#languages").append(m)}}
body{text-align:left!important}#answer-list{padding:10px;float:left}#language-list{padding:10px;float:left}table thead{font-weight:700}table td{padding:5px}
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script> <link rel="stylesheet" type="text/css" href="https://cdn.sstatic.net/Sites/codegolf/primary.css?v=f52df912b654"> <div id="language-list"> <h2>Winners by Language</h2> <table class="language-list"> <thead> <tr><td>Language</td><td>User</td><td>Score</td></tr></thead> <tbody id="languages"> </tbody> </table> </div><div id="answer-list"> <h2>Leaderboard</h2> <table class="answer-list"> <thead> <tr><td></td><td>Author</td><td>Language</td><td>Size</td></tr></thead> <tbody id="answers"> </tbody> </table> </div><table style="display: none"> <tbody id="answer-template"> <tr><td>{{PLACE}}</td><td>{{NAME}}</td><td>{{LANGUAGE}}</td><td><a href="{{LINK}}">{{SIZE}}</a></td></tr></tbody> </table> <table style="display: none"> <tbody id="language-template"> <tr><td>{{LANGUAGE}}</td><td>{{NAME}}</td><td><a href="{{LINK}}">{{SIZE}}</a></td></tr></tbody> </table>