Introduction
I Ching is an ancient divination text and the oldest of the Chinese classics. It uses a type of divination called cleromancy, which produces apparently random numbers.
The basic unit of the Zhou yi is the hexagram (卦 guà), a figure composed of six stacked horizontal lines (爻 yáo). Each line is either broken or unbroken. The received text of the Zhou yi contains all 64 possible hexagrams
The King Wen sequence present the 64 hexagrams, grouped into 32 pairs. For 28 of the pairs, the second hexagram is created by turning the first upside down (i.e. 180° rotation). The exception to this rule is for symmetrical hexagrams that are the same after rotation. Partners for these are given by inverting each line: solid becomes broken and broken becomes solid.
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Request
The goal of this is to create a little tool that compute pair for a given hexagram value.
For translating this into binary, I use:
broken line = 0, unbroken line = 1, sohexagram Number 1hasbinary value 63.The tool take exactly one argument, a number between 1 to 64, as hexagram pair request and produce two exagram containing requested number and his oposite (explanation: if arg is odd, the output must contain hexagram from arg and arg + 1, but if arg is even, the output must contain hexagram from arg - 1 and arg).
The tool have to rotate by 180° requested hexagram while not symetric, or invert them when symetric.
No map are authorized except this one, wich could be stored in any form you'll find usefull
{ 1:63, 3:34, 5:58, 7:16, 9:59, 11:56, 13:47, 15: 8, 17:38, 19:48, 21:37, 23: 1, 25:39, 27:33, 29:18, 31:14, 33:15, 35: 5, 37:43, 39:10, 41:49, 43:62, 45: 6, 47:22, 49:46, 51:36, 53:11, 55:44, 57:27, 59:19, 61:51, 63:42 }This map hold binary value of each 1st exagram from pairs. So for each pair, 1st has to be taken from this map, but second have to be computed conforming to previous rule.
Ouput must contain two hexagram and his numbers. Sample:
iChingHexaPair 1 ▄▄▄▄▄▄▄ ▄▄▄ ▄▄▄ ▄▄▄▄▄▄▄ ▄▄▄ ▄▄▄ ▄▄▄▄▄▄▄ ▄▄▄ ▄▄▄ ▄▄▄▄▄▄▄ ▄▄▄ ▄▄▄ ▄▄▄▄▄▄▄ ▄▄▄ ▄▄▄ ▄▄▄▄▄▄▄ ▄▄▄ ▄▄▄ 1 2 iChingHexaPair 14 ▄▄▄▄▄▄▄ ▄▄▄▄▄▄▄ ▄▄▄▄▄▄▄ ▄▄▄ ▄▄▄ ▄▄▄▄▄▄▄ ▄▄▄▄▄▄▄ ▄▄▄▄▄▄▄ ▄▄▄▄▄▄▄ ▄▄▄ ▄▄▄ ▄▄▄▄▄▄▄ ▄▄▄▄▄▄▄ ▄▄▄▄▄▄▄ 13 14Standard loophole applies
- Please avoid non-free language or post output for full test cases.
This is a code-golf, so the shortest answer in characters wins.
Shortest by language
<style>body { text-align: left !important} #answer-list { padding: 10px; width: 290px; float: left; } #language-list { padding: 10px; width: 290px; float: left; } table thead { font-weight: bold; } table td { padding: 5px; }</style><script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script> <link rel="stylesheet" type="text/css" href="//cdn.sstatic.net/codegolf/all.css?v=83c949450c8b"> <div id="language-list"> <h2>Shortest Solution 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>{{SIZE}}</td><td><a href="{{LINK}}">Link</a></td></tr> </tbody> </table> <table style="display: none"> <tbody id="language-template"> <tr><td>{{LANGUAGE}}</td><td>{{NAME}}</td><td>{{SIZE}}</td><td><a href="{{LINK}}">Link</a></td></tr> </tbody> </table><script>var QUESTION_ID = document.referrer.split("/")[4]; var ANSWER_FILTER = "!t)IWYnsLAZle2tQ3KqrVveCRJfxcRLe"; var COMMENT_FILTER = "!)Q2B_A2kjfAiU78X(md6BoYk"; var OVERRIDE_USER = 0; var answers = [], answers_hash, answer_ids, answer_page = 1, more_answers = true, comment_page; function answersUrl(index) { return "//api.stackexchange.com/2.2/questions/" + QUESTION_ID + "/answers?page=" + index + "&pagesize=100&order=desc&sort=creation&site=codegolf&filter=" + ANSWER_FILTER; } function commentUrl(index, answers) { return "//api.stackexchange.com/2.2/answers/" + answers.join(';') + "/comments?page=" + index + "&pagesize=100&order=desc&sort=creation&site=codegolf&filter=" + COMMENT_FILTER; } function getAnswers() { jQuery.ajax({ url: answersUrl(answer_page++), method: "get", dataType: "jsonp", crossDomain: true, success: function (data) { answers.push.apply(answers, data.items); answers_hash = []; answer_ids = []; data.items.forEach(function(a) { a.comments = []; var id = +a.share_link.match(/\d+/); answer_ids.push(id); answers_hash[id] = a; }); if (!data.has_more) more_answers = false; comment_page = 1; getComments(); } }); } function getComments() { jQuery.ajax({ url: commentUrl(comment_page++, answer_ids), method: "get", dataType: "jsonp", crossDomain: true, success: function (data) { data.items.forEach(function(c) { if (c.owner.user_id === OVERRIDE_USER) answers_hash[c.post_id].comments.push(c); }); if (data.has_more) getComments(); else if (more_answers) getAnswers(); else process(); } }); } getAnswers(); var SCORE_REG = /<h\d>\s*([^\n,<]*(?:<(?:[^\n>]*>[^\n<]*<\/[^\n>]*>)[^\n,<]*)*),.*?(\d+)(?=[^\n\d<>]*(?:<(?:s>[^\n<>]*<\/s>|[^\n<>]+>)[^\n\d<>]*)*<\/h\d>)/; var OVERRIDE_REG = /^Override\s*header:\s*/i; function getAuthorName(a) { return a.owner.display_name; } function process() { var valid = []; answers.forEach(function(a) { var body = a.body; a.comments.forEach(function(c) { if(OVERRIDE_REG.test(c.body)) body = '<h1>' + c.body.replace(OVERRIDE_REG, '') + '</h1>'; }); var match = body.match(SCORE_REG); if (match) valid.push({ user: getAuthorName(a), size: +match[2], language: match[1], link: a.share_link, }); else console.log(body); }); valid.sort(function (a, b) { var aB = a.size, bB = b.size; return aB - bB }); var languages = {}; var place = 1; var lastSize = null; var lastPlace = 1; valid.forEach(function (a) { if (a.size != lastSize) lastPlace = place; lastSize = a.size; ++place; var answer = jQuery("#answer-template").html(); answer = answer.replace("{{PLACE}}", lastPlace + ".") .replace("{{NAME}}", a.user) .replace("{{LANGUAGE}}", a.language) .replace("{{SIZE}}", a.size) .replace("{{LINK}}", a.link); answer = jQuery(answer); jQuery("#answers").append(answer); var lang = a.language; lang = jQuery('<a>'+lang+'</a>').text(); languages[lang] = languages[lang] || {lang: a.language, lang_raw: lang.toLowerCase(42), user: a.user, size: a.size, link: a.link}; }); var langs = []; for (var lang in languages) if (languages.hasOwnProperty(lang)) langs.push(languages[lang]); langs.sort(function (a, b) { if (a.lang_raw > b.lang_raw) return 1; if (a.lang_raw < b.lang_raw) return -1; return 0; }); for (var i = 0; i < langs.length; ++i) { var language = jQuery("#language-template").html(); var lang = langs[i]; language = language.replace("{{LANGUAGE}}", lang.lang) .replace("{{NAME}}", lang.user) .replace("{{SIZE}}", lang.size) .replace("{{LINK}}", lang.link); language = jQuery(language); jQuery("#languages").append(language); } }</script>
rotating binary by 180°\$\endgroup\$