Find the Formula

Question

Introduction

What you have to do is, given an an ASCII diagram of a chemical, output the chemical formula.

Rules

Your code must not access the internet and may not use a stored library of molecules. You may have a library of elements.

You must verify all of the elements included in the formula are real, with all elements needed to be required found here:

If there are invalid elements in the formula, you must output: Invalid elements in diagram.

Order the formulae using the Hill system: carbon then hydrogen then the other elements alphabetically.

Any library/text file of elements is not needed to be included in the byte count.

Examples

H2O

H-O-H

or

H   H
 \ /
  O

CO2

O=C=O

H4N

  H
  |
H-N-H
  |
  H

Winning

The winning code is the shortest program in bytes

Leaderboard

/* Configuration */

var QUESTION_ID = 52630; // Obtain this from the url
// It will be like http://XYZ.stackexchange.com/questions/QUESTION_ID/... on any question page
var ANSWER_FILTER = "!t)IWYnsLAZle2tQ3KqrVveCRJfxcRLe";

/* App */

var answers = [], page = 1;

function answersUrl(index) {
  return "http://api.stackexchange.com/2.2/questions/" +  QUESTION_ID + "/answers?page=" + index + "&pagesize=100&order=desc&sort=creation&site=codegolf&filter=" + ANSWER_FILTER;
}

function getAnswers() {
  jQuery.ajax({
    url: answersUrl(page++),
    method: "get",
    dataType: "jsonp",
    crossDomain: true,
    success: function (data) {
      answers.push.apply(answers, data.items);
      if (data.has_more) getAnswers();
      else process();
    }
  });
}

getAnswers();

var SIZE_REG = /\d+(?=[^\d&]*(?:<(?:s>[^&]*<\/s>|[^&]+>)[^\d&]*)*$)/;
var NUMBER_REG = /\d+/;
var LANGUAGE_REG = /^#*\s*([^,]+)/;

function shouldHaveHeading(a) {
  var pass = false;
  var lines = a.body_markdown.split("\n");
  try {
    pass |= /^#/.test(a.body_markdown);
    pass |= ["-", "="]
              .indexOf(lines[1][0]) > -1;
    pass &= LANGUAGE_REG.test(a.body_markdown);
  } catch (ex) {}
  return pass;
}

function shouldHaveScore(a) {
  var pass = false;
  try {
    pass |= SIZE_REG.test(a.body_markdown.split("\n")[0]);
  } catch (ex) {}
  return pass;
}

function getAuthorName(a) {
  return a.owner.display_name;
}

function process() {
  answers = answers.filter(shouldHaveScore)
                   .filter(shouldHaveHeading);
  answers.sort(function (a, b) {
    var aB = +(a.body_markdown.split("\n")[0].match(SIZE_REG) || [Infinity])[0],
        bB = +(b.body_markdown.split("\n")[0].match(SIZE_REG) || [Infinity])[0];
    return aB - bB
  });

  var languages = {};
  var place = 1;
  var lastSize = null;
  var lastPlace = 1;
  answers.forEach(function (a) {
    var headline = a.body_markdown.split("\n")[0];
    //console.log(a);
    var answer = jQuery("#answer-template").html();
    var num = headline.match(NUMBER_REG)[0];
    var size = (headline.match(SIZE_REG)||[0])[0];
    var language = headline.match(LANGUAGE_REG)[1];
    var user = getAuthorName(a);
    if (size != lastSize)
      lastPlace = place;
    lastSize = size;
    ++place;
    answer = answer.replace("{{PLACE}}", lastPlace + ".")
                   .replace("{{NAME}}", user)
                   .replace("{{LANGUAGE}}", language)
                   .replace("{{SIZE}}", size)
                   .replace("{{LINK}}", a.share_link);
    answer = jQuery(answer)
    jQuery("#answers").append(answer);

    languages[language] = languages[language] || {lang: language, user: user, size: size, link: a.share_link};
  });

  var langs = [];
  for (var lang in languages)
    if (languages.hasOwnProperty(lang))
      langs.push(languages[lang]);

  langs.sort(function (a, b) {
    if (a.lang > b.lang) return 1;
    if (a.lang < b.lang) 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);
  }

}

body { text-align: left !important}

#answer-list {
  padding: 10px;
  width: 50%;
  float: left;
}

#language-list {
  padding: 10px;
  width: 50%px;
  float: left;
}

table thead {
  font-weight: bold;
}

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="//cdn.sstatic.net/codegolf/all.css?v=83c949450c8b">
<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>
<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>
<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>

Answer 1

PHP, 205 bytes

function($f)use($l){for($a=preg_split('#(?=[A-Z])#',eregi_replace('[^a-z]','',$f));++$i<count($a);)if($l[$a[$i]]++===null)die('Invalid elements in diagram');foreach($l as$k=>$v)echo$v?$k.($v>1?$v:''):'';};

The array of elements is stored in the $l variable in the following form:

$l = ['C' => 0, 'H' => 0, 'Ac' => 0, …, 'Zr' => 0];

Here is the ungolfed version:

function ($formula) use ($elementsList)
{
    $linearFormula = preg_replace('#[^a-z]#i', '', $formula);       // Remove everything except the letters in the formula
    $elementsInFormula = preg_split('#(?=[A-Z])#', $linearFormula); // Split the formula before each uppercase letter, with an additional empty element in the first position

    for ($i = 1; $i < count($elementsInFormula); ++$i)
    {
        // Check if the element is valid
        if (!isset($elementsList[$elementsInFormula[$i]])) {
            die('Invalid elements in diagram');
        }

        // Increment the associated counter
        ++$elementsList[$elementsInFormula[$i]];
    }

    // Print the raw formula
    foreach ($elementsList as $element => $number)
    {
        if ($number > 0) {
            echo $element;
            if ($number > 1) {
                echo $number;
            }
        }
    }
};