CINXE.COM
Day 15 - Advent of Code 2022
<!DOCTYPE html> <html lang="en-us"> <head> <meta charset="utf-8"/> <title>Day 15 - Advent of Code 2022</title> <link rel="stylesheet" type="text/css" href="/static/style.css?31"/> <link rel="stylesheet alternate" type="text/css" href="/static/highcontrast.css?1" title="High Contrast"/> <link rel="shortcut icon" href="/favicon.png"/> <script>window.addEventListener('click', function(e,s,r){if(e.target.nodeName==='CODE'&&e.detail===3){s=window.getSelection();s.removeAllRanges();r=document.createRange();r.selectNodeContents(e.target);s.addRange(r);}});</script> </head><!-- Oh, hello! Funny seeing you here. I appreciate your enthusiasm, but you aren't going to find much down here. There certainly aren't clues to any of the puzzles. The best surprises don't even appear in the source until you unlock them for real. Please be careful with automated requests; I'm not a massive company, and I can only take so much traffic. Please be considerate so that everyone gets to play. If you're curious about how Advent of Code works, it's running on some custom Perl code. Other than a few integrations (auth, analytics, social media), I built the whole thing myself, including the design, animations, prose, and all of the puzzles. The puzzles are most of the work; preparing a new calendar and a new set of puzzles each year takes all of my free time for 4-5 months. A lot of effort went into building this thing - I hope you're enjoying playing it as much as I enjoyed making it for you! If you'd like to hang out, I'm @ericwastl@hachyderm.io on Mastodon and @ericwastl on Twitter. - Eric Wastl --> <body> <header><div><h1 class="title-global"><a href="/">Advent of Code</a></h1><nav><ul><li><a href="/2022/about">[About]</a></li><li><a href="/2022/events">[Events]</a></li><li><a href="https://teespring.com/stores/advent-of-code" target="_blank">[Shop]</a></li><li><a href="/2022/auth/login">[Log In]</a></li></ul></nav></div><div><h1 class="title-event"> <span class="title-event-wrap"></span><a href="/2022">2022</a><span class="title-event-wrap"></span></h1><nav><ul><li><a href="/2022">[Calendar]</a></li><li><a href="/2022/support">[AoC++]</a></li><li><a href="/2022/sponsors">[Sponsors]</a></li><li><a href="/2022/leaderboard">[Leaderboard]</a></li><li><a href="/2022/stats">[Stats]</a></li></ul></nav></div></header> <div id="sidebar"> <div id="sponsor"><div class="quiet">Our <a href="/2022/sponsors">sponsors</a> help make Advent of Code possible:</div><div class="sponsor"><a href="https://www.retool.com" target="_blank" onclick="if(ga)ga('send','event','sponsor','sidebar',this.href);" rel="noopener">Retool</a> - Quickly build CRUD apps, admin panels, recurring jobs, and dashboards with JavaScript. Run in our cloud or yours. Free for small teams.</div></div> </div><!--/sidebar--> <main> <article class="day-desc"><h2>--- Day 15: Beacon Exclusion Zone ---</h2><p>You feel the ground rumble again as the distress signal leads you to a large network of subterranean tunnels. You don't have time to search them all, but you don't need to: your pack contains a set of deployable <em>sensors</em> that you imagine were originally built to locate lost Elves.</p> <p>The sensors aren't very powerful, but that's okay; your handheld device indicates that you're close enough to the source of the distress signal to use them. You pull the emergency sensor system out of your pack, hit the big button on top, and the sensors zoom off down the tunnels.</p> <p>Once a sensor finds a spot it thinks will give it a good reading, it attaches itself to a hard surface and begins monitoring for the nearest signal source <em>beacon</em>. Sensors and beacons always exist at integer coordinates. Each sensor knows its own position and can <em>determine the position of a beacon precisely</em>; however, sensors can only lock on to the one beacon <em>closest to the sensor</em> as measured by the <a href="https://en.wikipedia.org/wiki/Taxicab_geometry" target="_blank">Manhattan distance</a>. (There is never a tie where two beacons are the same distance to a sensor.)</p> <p>It doesn't take long for the sensors to report back their positions and closest beacons (your puzzle input). For example:</p> <pre><code>Sensor at x=2, y=18: closest beacon is at x=-2, y=15 Sensor at x=9, y=16: closest beacon is at x=10, y=16 Sensor at x=13, y=2: closest beacon is at x=15, y=3 Sensor at x=12, y=14: closest beacon is at x=10, y=16 Sensor at x=10, y=20: closest beacon is at x=10, y=16 Sensor at x=14, y=17: closest beacon is at x=10, y=16 Sensor at x=8, y=7: closest beacon is at x=2, y=10 Sensor at x=2, y=0: closest beacon is at x=2, y=10 Sensor at x=0, y=11: closest beacon is at x=2, y=10 Sensor at x=20, y=14: closest beacon is at x=25, y=17 Sensor at x=17, y=20: closest beacon is at x=21, y=22 Sensor at x=16, y=7: closest beacon is at x=15, y=3 Sensor at x=14, y=3: closest beacon is at x=15, y=3 Sensor at x=20, y=1: closest beacon is at x=15, y=3 </code></pre> <p>So, consider the sensor at <code>2,18</code>; the closest beacon to it is at <code>-2,15</code>. For the sensor at <code>9,16</code>, the closest beacon to it is at <code>10,16</code>.</p> <p>Drawing sensors as <code>S</code> and beacons as <code>B</code>, the above arrangement of sensors and beacons looks like this:</p> <pre><code> 1 1 2 2 0 5 0 5 0 5 0 ....S....................... 1 ......................S..... 2 ...............S............ 3 ................SB.......... 4 ............................ 5 ............................ 6 ............................ 7 ..........S.......S......... 8 ............................ 9 ............................ 10 ....B....................... 11 ..S......................... 12 ............................ 13 ............................ 14 ..............S.......S..... 15 B........................... 16 ...........SB............... 17 ................S..........B 18 ....S....................... 19 ............................ 20 ............S......S........ 21 ............................ 22 .......................B.... </code></pre> <p>This isn't necessarily a comprehensive map of all beacons in the area, though. Because each sensor only identifies its closest beacon, if a sensor detects a beacon, you know there are no other beacons that close or closer to that sensor. There could still be beacons that just happen to not be the closest beacon to any sensor. Consider the sensor at <code>8,7</code>:</p> <pre><code> 1 1 2 2 0 5 0 5 0 5 -2 ..........#................. -1 .........###................ 0 ....S...#####............... 1 .......#######........S..... 2 ......#########S............ 3 .....###########SB.......... 4 ....#############........... 5 ...###############.......... 6 ..#################......... 7 .#########<em>S</em>#######S#........ 8 ..#################......... 9 ...###############.......... 10 ....<em>B</em>############........... 11 ..S..###########............ 12 ......#########............. 13 .......#######.............. 14 ........#####.S.......S..... 15 B........###................ 16 ..........#SB............... 17 ................S..........B 18 ....S....................... 19 ............................ 20 ............S......S........ 21 ............................ 22 .......................B.... </code></pre> <p>This sensor's closest beacon is at <code>2,10</code>, and so you know there are no beacons that close or closer (in any positions marked <code>#</code>).</p> <p>None of the detected beacons seem to be producing the distress signal, so you'll need to <span title=""When you have eliminated all which is impossible, then whatever remains, however improbable, must be where the missing beacon is." - Sherlock Holmes">work out</span> where the distress beacon is by working out where it <em>isn't</em>. For now, keep things simple by counting the positions where a beacon cannot possibly be along just a single row.</p> <p>So, suppose you have an arrangement of beacons and sensors like in the example above and, just in the row where <code>y=10</code>, you'd like to count the number of positions a beacon cannot possibly exist. The coverage from all sensors near that row looks like this:</p> <pre><code> 1 1 2 2 0 5 0 5 0 5 9 ...#########################... <em>10 ..####B######################..</em> 11 .###S#############.###########. </code></pre> <p>In this example, in the row where <code>y=10</code>, there are <code><em>26</em></code> positions where a beacon cannot be present.</p> <p>Consult the report from the sensors you just deployed. <em>In the row where <code>y=2000000</code>, how many positions cannot contain a beacon?</em></p> </article> <p>To play, please identify yourself via one of these services:</p> <p><a href="/auth/github">[GitHub]</a> <a href="/auth/google">[Google]</a> <a href="/auth/twitter">[Twitter]</a> <a href="/auth/reddit">[Reddit]</a> <span class="quiet">- <a href="/about#faq_auth">[How Does Auth Work?]</a></span></p> </main> <!-- ga --> <script> (function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){ (i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o), m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m) })(window,document,'script','//www.google-analytics.com/analytics.js','ga'); ga('create', 'UA-69522494-1', 'auto'); ga('set', 'anonymizeIp', true); ga('send', 'pageview'); </script> <!-- /ga --> </body> </html>