problems/day18.html

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   5 <title>Day 18 - Advent of Code 2020</title>
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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.
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  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">35*</span></div></div><div><h1 class="title-event">&nbsp;&nbsp;&nbsp;<span class="title-event-wrap">$year=</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 18: Operation Order ---</h2><p>As you look out the window and notice a heavily-forested continent slowly appear over the horizon, you are interrupted by the child sitting next to you. They're curious if you could help them with their <span title="Or &quot;maths&quot;, if you have more than one.">math</span> homework.</p>
  99 <p>Unfortunately, it seems like this "math" <a href="https://www.youtube.com/watch?v=3QtRK7Y2pPU&t=15" target="_blank">follows different rules</a> than you remember.</p>
 100 <p>The homework (your puzzle input) consists of a series of expressions that consist of addition (<code>+</code>), multiplication (<code>*</code>), and parentheses (<code>(...)</code>). Just like normal math, parentheses indicate that the expression inside must be evaluated before it can be used by the surrounding expression. Addition still finds the sum of the numbers on both sides of the operator, and multiplication still finds the product.</p>
 101 <p>However, the rules of <em>operator precedence</em> have changed. Rather than evaluating multiplication before addition, the operators have the <em>same precedence</em>, and are evaluated left-to-right regardless of the order in which they appear.</p>
 102 <p>For example, the steps to evaluate the expression <code>1 + 2 * 3 + 4 * 5 + 6</code> are as follows:</p>
 103 <pre><code><em>1 + 2</em> * 3 + 4 * 5 + 6
 104   <em>3   * 3</em> + 4 * 5 + 6
 105       <em>9   + 4</em> * 5 + 6
 106          <em>13   * 5</em> + 6
 107              <em>65   + 6</em>
 108                  <em>71</em>
 109 </code></pre>
 110 <p>Parentheses can override this order; for example, here is what happens if parentheses are added to form <code>1 + (2 * 3) + (4 * (5 + 6))</code>:</p>
 111 <pre><code>1 + <em>(2 * 3)</em> + (4 * (5 + 6))
 112 <em>1 +    6</em>    + (4 * (5 + 6))
 113      7      + (4 * <em>(5 + 6)</em>)
 114      7      + <em>(4 *   11   )</em>
 115      <em>7      +     44</em>
 116             <em>51</em>
 117 </code></pre>
 118 <p>Here are a few more examples:</p>
 119 <ul>
 120 <li><code>2 * 3 + (4 * 5)</code> becomes <em><code>26</code></em>.</li>
 121 <li><code>5 + (8 * 3 + 9 + 3 * 4 * 3)</code> becomes <em><code>437</code></em>.</li>
 122 <li><code>5 * 9 * (7 * 3 * 3 + 9 * 3 + (8 + 6 * 4))</code> becomes <em><code>12240</code></em>.</li>
 123 <li><code>((2 + 4 * 9) * (6 + 9 * 8 + 6) + 6) + 2 + 4 * 2</code> becomes <em><code>13632</code></em>.</li>
 124 </ul>
 125 <p>Before you can help with the homework, you need to understand it yourself. <em>Evaluate the expression on each line of the homework; what is the sum of the resulting values?</em></p>
 126 </article>
 127 <p>Your puzzle answer was <code>75592527415659</code>.</p><p class="day-success">The first half of this puzzle is complete! It provides one gold star: *</p>
 128 <article class="day-desc"><h2 id="part2">--- Part Two ---</h2><p>You manage to answer the child's questions and they finish part 1 of their homework, but get stuck when they reach the next section: <em>advanced</em> math.</p>
 129 <p>Now, addition and multiplication have <em>different</em> precedence levels, but they're not the ones you're familiar with. Instead, addition is evaluated <em>before</em> multiplication.</p>
 130 <p>For example, the steps to evaluate the expression <code>1 + 2 * 3 + 4 * 5 + 6</code> are now as follows:</p>
 131 <pre><code><em>1 + 2</em> * 3 + 4 * 5 + 6
 132   3   * <em>3 + 4</em> * 5 + 6
 133   3   *   7   * <em>5 + 6</em>
 134   <em>3   *   7</em>   *  11
 135      <em>21       *  11</em>
 136          <em>231</em>
 137 </code></pre>
 138 <p>Here are the other examples from above:</p>
 139 <ul>
 140 <li><code>1 + (2 * 3) + (4 * (5 + 6))</code> still becomes <em><code>51</code></em>.</li>
 141 <li><code>2 * 3 + (4 * 5)</code> becomes <em><code>46</code></em>.</li>
 142 <li><code>5 + (8 * 3 + 9 + 3 * 4 * 3)</code> becomes <em><code>1445</code></em>.</li>
 143 <li><code>5 * 9 * (7 * 3 * 3 + 9 * 3 + (8 + 6 * 4))</code> becomes <em><code>669060</code></em>.</li>
 144 <li><code>((2 + 4 * 9) * (6 + 9 * 8 + 6) + 6) + 2 + 4 * 2</code> becomes <em><code>23340</code></em>.</li>
 145 </ul>
 146 <p><em>What do you get if you add up the results of evaluating the homework problems using these new rules?</em></p>
 147 </article>
 148 <form method="post" action="18/answer"><input type="hidden" name="level" value="2"/><p>Answer: <input type="text" name="answer" autocomplete="off"/> <input type="submit" value="[Submit]"/></p></form>
 149 <p>Although it hasn't changed, you can still <a href="18/input" target="_blank">get your puzzle input</a>.</p>
 150 <p>You can also <span class="share">[Share<span class="share-content">on
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 153 ></span>]</span> this puzzle.</p>
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