problems/day05.html

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   5 <title>Day 5 - Advent of Code 2021</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.
  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="/2021/about">[About]</a></li><li><a href="/2021/events">[Events]</a></li><li><a href="https://teespring.com/stores/advent-of-code" target="_blank">[Shop]</a></li><li><a href="/2021/settings">[Settings]</a></li><li><a href="/2021/auth/logout">[Log Out]</a></li></ul></nav><div class="user">Neil Smith <a href="/2021/support" class="supporter-badge" title="Advent of Code Supporter">(AoC++)</a> <span class="star-count">10*</span></div></div><div><h1 class="title-event">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<span class="title-event-wrap">/*</span><a href="/2021">2021</a><span class="title-event-wrap">*/</span></h1><nav><ul><li><a href="/2021">[Calendar]</a></li><li><a href="/2021/support">[AoC++]</a></li><li><a href="/2021/sponsors">[Sponsors]</a></li><li><a href="/2021/leaderboard">[Leaderboard]</a></li><li><a href="/2021/stats">[Stats]</a></li></ul></nav></div></header>
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  98 <article class="day-desc"><h2>--- Day 5: Hydrothermal Venture ---</h2><p>You come across a field of <a href="https://en.wikipedia.org/wiki/Hydrothermal_vent" target="_blank">hydrothermal vents</a> on the ocean floor! These vents constantly produce large, opaque clouds, so it would be best to avoid them if possible.</p>
  99 <p>They tend to form in <em>lines</em>; the submarine helpfully produces a list of nearby <span title="Maybe they're Bresenham vents.">lines of vents</span> (your puzzle input) for you to review. For example:</p>
 100 <pre><code>0,9 -&gt; 5,9
 101 8,0 -&gt; 0,8
 102 9,4 -&gt; 3,4
 103 2,2 -&gt; 2,1
 104 7,0 -&gt; 7,4
 105 6,4 -&gt; 2,0
 106 0,9 -&gt; 2,9
 107 3,4 -&gt; 1,4
 108 0,0 -&gt; 8,8
 109 5,5 -&gt; 8,2
 110 </code></pre>
 111 <p>Each line of vents is given as a line segment in the format <code>x1,y1 -&gt; x2,y2</code> where <code>x1</code>,<code>y1</code> are the coordinates of one end the line segment and <code>x2</code>,<code>y2</code> are the coordinates of the other end. These line segments include the points at both ends. In other words:</p>
 112 <ul>
 113 <li>An entry like <code>1,1 -&gt; 1,3</code> covers points <code>1,1</code>, <code>1,2</code>, and <code>1,3</code>.</li>
 114 <li>An entry like <code>9,7 -&gt; 7,7</code> covers points <code>9,7</code>, <code>8,7</code>, and <code>7,7</code>.</li>
 115 </ul>
 116 <p>For now, <em>only consider horizontal and vertical lines</em>: lines where either <code>x1 = x2</code> or <code>y1 = y2</code>.</p>
 117 <p>So, the horizontal and vertical lines from the above list would produce the following diagram:</p>
 118 <pre><code>.......1..
 119 ..1....1..
 120 ..1....1..
 121 .......1..
 122 .112111211
 123 ..........
 124 ..........
 125 ..........
 126 ..........
 127 222111....
 128 </code></pre>
 129 <p>In this diagram, the top left corner is <code>0,0</code> and the bottom right corner is <code>9,9</code>. Each position is shown as <em>the number of lines which cover that point</em> or <code>.</code> if no line covers that point. The top-left pair of <code>1</code>s, for example, comes from <code>2,2 -&gt; 2,1</code>; the very bottom row is formed by the overlapping lines <code>0,9 -&gt; 5,9</code> and <code>0,9 -&gt; 2,9</code>.</p>
 130 <p>To avoid the most dangerous areas, you need to determine <em>the number of points where at least two lines overlap</em>. In the above example, this is anywhere in the diagram with a <code>2</code> or larger - a total of <code><em>5</em></code> points.</p>
 131 <p>Consider only horizontal and vertical lines. <em>At how many points do at least two lines overlap?</em></p>
 132 </article>
 133 <p>Your puzzle answer was <code>5092</code>.</p><article class="day-desc"><h2 id="part2">--- Part Two ---</h2><p>Unfortunately, considering only horizontal and vertical lines doesn't give you the full picture; you need to also consider <em>diagonal lines</em>.</p>
 134 <p>Because of the limits of the hydrothermal vent mapping system, the lines in your list will only ever be horizontal, vertical, or a diagonal line at exactly 45 degrees. In other words:</p>
 135 <ul>
 136 <li>An entry like <code>1,1 -&gt; 3,3</code> covers points <code>1,1</code>, <code>2,2</code>, and <code>3,3</code>.</li>
 137 <li>An entry like <code>9,7 -&gt; 7,9</code> covers points <code>9,7</code>, <code>8,8</code>, and <code>7,9</code>.</li>
 138 </ul>
 139 <p>Considering all lines from the above example would now produce the following diagram:</p>
 140 <pre><code>1.1....11.
 141 .111...2..
 142 ..2.1.111.
 143 ...1.2.2..
 144 .112313211
 145 ...1.2....
 146 ..1...1...
 147 .1.....1..
 148 1.......1.
 149 222111....
 150 </code></pre>
 151 <p>You still need to determine <em>the number of points where at least two lines overlap</em>. In the above example, this is still anywhere in the diagram with a <code>2</code> or larger - now a total of <code><em>12</em></code> points.</p>
 152 <p>Consider all of the lines. <em>At how many points do at least two lines overlap?</em></p>
 153 </article>
 154 <p>Your puzzle answer was <code>20484</code>.</p><p class="day-success">Both parts of this puzzle are complete! They provide two gold stars: **</p>
 155 <p>At this point, you should <a href="/2021">return to your Advent calendar</a> and try another puzzle.</p>
 156 <p>If you still want to see it, you can <a href="5/input" target="_blank">get your puzzle input</a>.</p>
 157 <p>You can also <span class="share">[Share<span class="share-content">on
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