problems/day06.html

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   5 <title>Day 6 - Advent of Code 2018</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.
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  22 Please be careful with automated requests; I'm not Google, and I can only take
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  25 If you're curious about how Advent of Code works, it's running on some custom
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  30 The puzzles are most of the work; the easiest ones take 3-4 hours each, but the
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  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="/2018/about">[About]</a></li><li><a href="/2018/events">[Events]</a></li><li><a href="https://teespring.com/adventofcode" target="_blank">[Shop]</a></li><li><a href="/2018/settings">[Settings]</a></li><li><a href="/2018/auth/logout">[Log Out]</a></li></ul></nav><div class="user">Neil Smith <a href="/2018/support" class="supporter-badge" title="Advent of Code Supporter">(AoC++)</a> <span class="star-count">12*</span></div></div><div><h1 class="title-event">&nbsp;&nbsp;&nbsp;<span class="title-event-wrap">&lt;y&gt;</span><a href="/2018">2018</a><span class="title-event-wrap">&lt;/y&gt;</span></h1><nav><ul><li><a href="/2018">[Calendar]</a></li><li><a href="/2018/support">[AoC++]</a></li><li><a href="/2018/sponsors">[Sponsors]</a></li><li><a href="/2018/leaderboard">[Leaderboard]</a></li><li><a href="/2018/stats">[Stats]</a></li></ul></nav></div></header>
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  97 <article class="day-desc"><h2>--- Day 6: Chronal Coordinates ---</h2><p>The device on your wrist beeps several times, and once again you feel like you're falling.</p>
  98 <p>"<span title="Why is the situation always critical? Why can't the situation just be boring for once?">Situation critical</span>," the device announces. "Destination indeterminate. Chronal interference detected. Please specify new target coordinates."</p>
  99 <p>The device then produces a list of coordinates (your puzzle input). Are they places it thinks are safe or dangerous? It recommends you check manual page 729. The Elves did not give you a manual.</p>
 100 <p><em>If they're dangerous,</em> maybe you can minimize the danger by finding the coordinate that gives the largest distance from the other points.</p>
 101 <p>Using only the <a href="https://en.wikipedia.org/wiki/Taxicab_geometry">Manhattan distance</a>, determine the <em>area</em> around each coordinate by counting the number of <a href="https://en.wikipedia.org/wiki/Integer">integer</a> X,Y locations that are <em>closest</em> to that coordinate (and aren't <em>tied in distance</em> to any other coordinate).</p>
 102 <p>Your goal is to find the size of the <em>largest area</em> that isn't infinite. For example, consider the following list of coordinates:</p>
 103 <pre><code>1, 1
 104 1, 6
 105 8, 3
 106 3, 4
 107 5, 5
 108 8, 9
 109 </code></pre>
 110 <p>If we name these coordinates <code>A</code> through <code>F</code>, we can draw them on a grid, putting <code>0,0</code> at the top left:</p>
 111 <pre><code>..........
 112 .A........
 113 ..........
 114 ........C.
 115 ...D......
 116 .....E....
 117 .B........
 118 ..........
 119 ..........
 120 ........F.
 121 </code></pre>
 122 <p>This view is partial - the actual grid extends infinitely in all directions.  Using the Manhattan distance, each location's closest coordinate can be determined, shown here in lowercase:</p>
 123 <pre><code>aaaaa.cccc
 124 a<em>A</em>aaa.cccc
 125 aaaddecccc
 126 aadddecc<em>C</em>c
 127 ..d<em>D</em>deeccc
 128 bb.de<em>E</em>eecc
 129 b<em>B</em>b.eeee..
 130 bbb.eeefff
 131 bbb.eeffff
 132 bbb.ffff<em>F</em>f
 133 </code></pre>
 134 <p>Locations shown as <code>.</code> are equally far from two or more coordinates, and so they don't count as being closest to any.</p>
 135 <p>In this example, the areas of coordinates A, B, C, and F are infinite - while not shown here, their areas extend forever outside the visible grid. However, the areas of coordinates D and E are finite: D is closest to 9 locations, and E is closest to 17 (both including the coordinate's location itself).  Therefore, in this example, the size of the largest area is <em>17</em>.</p>
 136 <p><em>What is the size of the largest area</em> that isn't infinite?</p>
 137 </article>
 138 <p>Your puzzle answer was <code>3006</code>.</p><article class="day-desc"><h2 id="part2">--- Part Two ---</h2><p>On the other hand, <em>if the coordinates are safe</em>, maybe the best you can do is try to find a <em>region</em> near as many coordinates as possible.</p>
 139 <p>For example, suppose you want the sum of the <a href="https://en.wikipedia.org/wiki/Taxicab_geometry">Manhattan distance</a> to all of the coordinates to be <em>less than 32</em>.  For each location, add up the distances to all of the given coordinates; if the total of those distances is less than 32, that location is within the desired region. Using the same coordinates as above, the resulting region looks like this:</p>
 140 <pre><code>..........
 141 .A........
 142 ..........
 143 ...#<em>#</em>#..C.
 144 ..#D###...
 145 ..###E#...
 146 .B.###....
 147 ..........
 148 ..........
 149 ........F.
 150 </code></pre>
 151 <p>In particular, consider the highlighted location <code>4,3</code> located at the top middle of the region. Its calculation is as follows, where <code>abs()</code> is the <a href="https://en.wikipedia.org/wiki/Absolute_value">absolute value</a> function:</p>
 152 <ul>
 153 <li>Distance to coordinate A: <code>abs(4-1) + abs(3-1) = &nbsp;5</code></li>
 154 <li>Distance to coordinate B: <code>abs(4-1) + abs(3-6) = &nbsp;6</code></li>
 155 <li>Distance to coordinate C: <code>abs(4-8) + abs(3-3) = &nbsp;4</code></li>
 156 <li>Distance to coordinate D: <code>abs(4-3) + abs(3-4) = &nbsp;2</code></li>
 157 <li>Distance to coordinate E: <code>abs(4-5) + abs(3-5) = &nbsp;3</code></li>
 158 <li>Distance to coordinate F: <code>abs(4-8) + abs(3-9) = 10</code></li>
 159 <li>Total distance: <code>5 + 6 + 4 + 2 + 3 + 10 = 30</code></li>
 160 </ul>
 161 <p>Because the total distance to all coordinates (<code>30</code>) is less than 32, the location is <em>within</em> the region.</p>
 162 <p>This region, which also includes coordinates D and E, has a total size of <em>16</em>.</p>
 163 <p>Your actual region will need to be much larger than this example, though, instead including all locations with a total distance of less than <em>10000</em>.</p>
 164 <p><em>What is the size of the region containing all locations which have a total distance to all given coordinates of less than 10000?</em></p>
 165 </article>
 166 <p>Your puzzle answer was <code>42998</code>.</p><p class="day-success">Both parts of this puzzle are complete! They provide two gold stars: **</p>
 167 <p>At this point, you should <a href="/2018">return to your advent calendar</a> and try another puzzle.</p>
 168 <p>If you still want to see it, you can <a href="6/input" target="_blank">get your puzzle input</a>.</p>
 169 <p>You can also <span class="share">[Share<span class="share-content">on
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