problems/day19.html

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  16 Oh, hello!  Funny seeing you here.
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  18 I appreciate your enthusiasm, but you aren't going to find much down here.
  19 There certainly aren't clues to any of the puzzles.  The best surprises don't
  20 even appear in the source until you unlock them for real.
  21
  22 Please be careful with automated requests; I'm not a massive company, and I can
  23 only take so much traffic.  Please be considerate so that everyone gets to play.
  24
  25 If you're curious about how Advent of Code works, it's running on some custom
  26 Perl code. Other than a few integrations (auth, analytics, social media), I
  27 built the whole thing myself, including the design, animations, prose, and all
  28 of the puzzles.
  29
  30 The puzzles are most of the work; preparing a new calendar and a new set of
  31 puzzles each year takes all of my free time for 4-5 months. A lot of effort
  32 went into building this thing - I hope you're enjoying playing it as much as I
  33 enjoyed making it for you!
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  35 If you'd like to hang out, I'm @ericwastl on Twitter.
  36
  37 - Eric Wastl
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  90 <header><div><h1 class="title-global"><a href="/">Advent of Code</a></h1><nav><ul><li><a href="/2020/about">[About]</a></li><li><a href="/2020/events">[Events]</a></li><li><a href="https://teespring.com/stores/advent-of-code" target="_blank">[Shop]</a></li><li><a href="/2020/settings">[Settings]</a></li><li><a href="/2020/auth/logout">[Log Out]</a></li></ul></nav><div class="user">Neil Smith <a href="/2020/support" class="supporter-badge" title="Advent of Code Supporter">(AoC++)</a> <span class="star-count">38*</span></div></div><div><h1 class="title-event">&nbsp;<span class="title-event-wrap">{&apos;year&apos;:</span><a href="/2020">2020</a><span class="title-event-wrap">}</span></h1><nav><ul><li><a href="/2020">[Calendar]</a></li><li><a href="/2020/support">[AoC++]</a></li><li><a href="/2020/sponsors">[Sponsors]</a></li><li><a href="/2020/leaderboard">[Leaderboard]</a></li><li><a href="/2020/stats">[Stats]</a></li></ul></nav></div></header>
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  98 <article class="day-desc"><h2>--- Day 19: Monster Messages ---</h2><p>You land in an airport surrounded by dense forest. As you walk to your high-speed train, the Elves at the <span title="This is a purely fictional organization. Any resemblance to actual organizations, past or present, is purely coincidental.">Mythical Information Bureau</span> contact you again. They think their satellite has collected an image of a <em>sea monster</em>! Unfortunately, the connection to the satellite is having problems, and many of the messages sent back from the satellite have been corrupted.</p>
  99 <p>They sent you a list of <em>the rules valid messages should obey</em> and a list of <em>received messages</em> they've collected so far (your puzzle input).</p>
 100 <p>The <em>rules for valid messages</em> (the top part of your puzzle input) are numbered and build upon each other. For example:</p>
 101 <pre><code>0: 1 2
 102 1: "a"
 103 2: 1 3 | 3 1
 104 3: "b"
 105 </code></pre>
 106 <p>Some rules, like <code>3: "b"</code>, simply match a single character (in this case, <code>b</code>).</p>
 107 <p>The remaining rules list the sub-rules that must be followed; for example, the rule <code>0: 1 2</code> means that to match rule <code>0</code>, the text being checked must match rule <code>1</code>, and the text after the part that matched rule <code>1</code> must then match rule <code>2</code>.</p>
 108 <p>Some of the rules have multiple lists of sub-rules separated by a pipe (<code>|</code>). This means that <em>at least one</em> list of sub-rules must match. (The ones that match might be different each time the rule is encountered.) For example, the rule <code>2: 1 3 | 3 1</code> means that to match rule <code>2</code>, the text being checked must match rule <code>1</code> followed by rule <code>3</code> <em>or</em> it must match rule <code>3</code> followed by rule <code>1</code>.</p>
 109 <p>Fortunately, there are no loops in the rules, so the list of possible matches will be finite. Since rule <code>1</code> matches <code>a</code> and rule <code>3</code> matches <code>b</code>, rule <code>2</code> matches either <code>ab</code> or <code>ba</code>. Therefore, rule <code>0</code> matches <code>aab</code> or <code>aba</code>.</p>
 110 <p>Here's a more interesting example:</p>
 111 <pre><code>0: 4 1 5
 112 1: 2 3 | 3 2
 113 2: 4 4 | 5 5
 114 3: 4 5 | 5 4
 115 4: "a"
 116 5: "b"
 117 </code></pre>
 118 <p>Here, because rule <code>4</code> matches <code>a</code> and rule <code>5</code> matches <code>b</code>, rule <code>2</code> matches two letters that are the same (<code>aa</code> or <code>bb</code>), and rule <code>3</code> matches two letters that are different (<code>ab</code> or <code>ba</code>).</p>
 119 <p>Since rule <code>1</code> matches rules <code>2</code> and <code>3</code> once each in either order, it must match two pairs of letters, one pair with matching letters and one pair with different letters. This leaves eight possibilities: <code>aaab</code>, <code>aaba</code>, <code>bbab</code>, <code>bbba</code>, <code>abaa</code>, <code>abbb</code>, <code>baaa</code>, or <code>babb</code>.</p>
 120 <p>Rule <code>0</code>, therefore, matches <code>a</code> (rule <code>4</code>), then any of the eight options from rule <code>1</code>, then <code>b</code> (rule <code>5</code>): <code>aaaabb</code>, <code>aaabab</code>, <code>abbabb</code>, <code>abbbab</code>, <code>aabaab</code>, <code>aabbbb</code>, <code>abaaab</code>, or <code>ababbb</code>.</p>
 121 <p>The <em>received messages</em> (the bottom part of your puzzle input) need to be checked against the rules so you can determine which are valid and which are corrupted. Including the rules and the messages together, this might look like:</p>
 122 <pre><code>0: 4 1 5
 123 1: 2 3 | 3 2
 124 2: 4 4 | 5 5
 125 3: 4 5 | 5 4
 126 4: "a"
 127 5: "b"
 128
 129 ababbb
 130 bababa
 131 abbbab
 132 aaabbb
 133 aaaabbb
 134 </code></pre>
 135 <p>Your goal is to determine <em>the number of messages that completely match rule <code>0</code></em>. In the above example, <code>ababbb</code> and <code>abbbab</code> match, but <code>bababa</code>, <code>aaabbb</code>, and <code>aaaabbb</code> do not, producing the answer <em><code>2</code></em>. The whole message must match all of rule <code>0</code>; there can't be extra unmatched characters in the message. (For example, <code>aaaabbb</code> might appear to match rule <code>0</code> above, but it has an extra unmatched <code>b</code> on the end.)</p>
 136 <p><em>How many messages completely match rule <code>0</code>?</em></p>
 137 </article>
 138 <p>Your puzzle answer was <code>235</code>.</p><article class="day-desc"><h2 id="part2">--- Part Two ---</h2><p>As you look over the list of messages, you realize your matching rules aren't quite right. To fix them, completely replace rules <code>8: 42</code> and <code>11: 42 31</code> with the following:</p>
 139 <pre><code>8: 42 | 42 8
 140 11: 42 31 | 42 11 31
 141 </code></pre>
 142 <p>This small change has a big impact: now, the rules <em>do</em> contain loops, and the list of messages they could hypothetically match is infinite. You'll need to determine how these changes affect which messages are valid.</p>
 143 <p>Fortunately, many of the rules are unaffected by this change; it might help to start by looking at which rules always match the same set of values and how <em>those</em> rules (especially rules <code>42</code> and <code>31</code>) are used by the new versions of rules <code>8</code> and <code>11</code>.</p>
 144 <p>(Remember, <em>you only need to handle the rules you have</em>; building a solution that could handle any hypothetical combination of rules would be <a href="https://en.wikipedia.org/wiki/Formal_grammar" target="_blank">significantly more difficult</a>.)</p>
 145 <p>For example:</p>
 146 <pre><code>42: 9 14 | 10 1
 147 9: 14 27 | 1 26
 148 10: 23 14 | 28 1
 149 1: "a"
 150 11: 42 31
 151 5: 1 14 | 15 1
 152 19: 14 1 | 14 14
 153 12: 24 14 | 19 1
 154 16: 15 1 | 14 14
 155 31: 14 17 | 1 13
 156 6: 14 14 | 1 14
 157 2: 1 24 | 14 4
 158 0: 8 11
 159 13: 14 3 | 1 12
 160 15: 1 | 14
 161 17: 14 2 | 1 7
 162 23: 25 1 | 22 14
 163 28: 16 1
 164 4: 1 1
 165 20: 14 14 | 1 15
 166 3: 5 14 | 16 1
 167 27: 1 6 | 14 18
 168 14: "b"
 169 21: 14 1 | 1 14
 170 25: 1 1 | 1 14
 171 22: 14 14
 172 8: 42
 173 26: 14 22 | 1 20
 174 18: 15 15
 175 7: 14 5 | 1 21
 176 24: 14 1
 177
 178 abbbbbabbbaaaababbaabbbbabababbbabbbbbbabaaaa
 179 bbabbbbaabaabba
 180 babbbbaabbbbbabbbbbbaabaaabaaa
 181 aaabbbbbbaaaabaababaabababbabaaabbababababaaa
 182 bbbbbbbaaaabbbbaaabbabaaa
 183 bbbababbbbaaaaaaaabbababaaababaabab
 184 ababaaaaaabaaab
 185 ababaaaaabbbaba
 186 baabbaaaabbaaaababbaababb
 187 abbbbabbbbaaaababbbbbbaaaababb
 188 aaaaabbaabaaaaababaa
 189 aaaabbaaaabbaaa
 190 aaaabbaabbaaaaaaabbbabbbaaabbaabaaa
 191 babaaabbbaaabaababbaabababaaab
 192 aabbbbbaabbbaaaaaabbbbbababaaaaabbaaabba
 193 </code></pre>
 194 <p>Without updating rules <code>8</code> and <code>11</code>, these rules only match three messages: <code>bbabbbbaabaabba</code>, <code>ababaaaaaabaaab</code>, and <code>ababaaaaabbbaba</code>.</p>
 195 <p>However, after updating rules <code>8</code> and <code>11</code>, a total of <em><code>12</code></em> messages match:</p>
 196 <ul>
 197 <li><code>bbabbbbaabaabba</code></li>
 198 <li><code>babbbbaabbbbbabbbbbbaabaaabaaa</code></li>
 199 <li><code>aaabbbbbbaaaabaababaabababbabaaabbababababaaa</code></li>
 200 <li><code>bbbbbbbaaaabbbbaaabbabaaa</code></li>
 201 <li><code>bbbababbbbaaaaaaaabbababaaababaabab</code></li>
 202 <li><code>ababaaaaaabaaab</code></li>
 203 <li><code>ababaaaaabbbaba</code></li>
 204 <li><code>baabbaaaabbaaaababbaababb</code></li>
 205 <li><code>abbbbabbbbaaaababbbbbbaaaababb</code></li>
 206 <li><code>aaaaabbaabaaaaababaa</code></li>
 207 <li><code>aaaabbaabbaaaaaaabbbabbbaaabbaabaaa</code></li>
 208 <li><code>aabbbbbaabbbaaaaaabbbbbababaaaaabbaaabba</code></li>
 209 </ul>
 210 <p><em>After updating rules <code>8</code> and <code>11</code>, how many messages completely match rule <code>0</code>?</em></p>
 211 </article>
 212 <p>Your puzzle answer was <code>379</code>.</p><p class="day-success">Both parts of this puzzle are complete! They provide two gold stars: **</p>
 213 <p>At this point, you should <a href="/2020">return to your Advent calendar</a> and try another puzzle.</p>
 214 <p>If you still want to see it, you can <a href="19/input" target="_blank">get your puzzle input</a>.</p>
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