problems/day16.html

   1 <!DOCTYPE html>
   2 <html lang="en-us">
   3 <head>
   4 <meta charset="utf-8"/>
   5 <title>Day 16 - Advent of Code 2022</title>
   6 <!--[if lt IE 9]><script src="/static/html5.js"></script><![endif]-->
   7 <link href='//fonts.googleapis.com/css?family=Source+Code+Pro:300&subset=latin,latin-ext' rel='stylesheet' type='text/css'/>
   8 <link rel="stylesheet" type="text/css" href="/static/style.css?30"/>
   9 <link rel="stylesheet alternate" type="text/css" href="/static/highcontrast.css?0" title="High Contrast"/>
  10 <link rel="shortcut icon" href="/favicon.png"/>
  11 <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>
  12 </head><!--
  13
  14
  15
  16
  17 Oh, hello!  Funny seeing you here.
  18
  19 I appreciate your enthusiasm, but you aren't going to find much down here.
  20 There certainly aren't clues to any of the puzzles.  The best surprises don't
  21 even appear in the source until you unlock them for real.
  22
  23 Please be careful with automated requests; I'm not a massive company, and I can
  24 only take so much traffic.  Please be considerate so that everyone gets to play.
  25
  26 If you're curious about how Advent of Code works, it's running on some custom
  27 Perl code. Other than a few integrations (auth, analytics, social media), I
  28 built the whole thing myself, including the design, animations, prose, and all
  29 of the puzzles.
  30
  31 The puzzles are most of the work; preparing a new calendar and a new set of
  32 puzzles each year takes all of my free time for 4-5 months. A lot of effort
  33 went into building this thing - I hope you're enjoying playing it as much as I
  34 enjoyed making it for you!
  35
  36 If you'd like to hang out, I'm @ericwastl on Twitter.
  37
  38 - Eric Wastl
  39
  40
  41
  42
  43
  44
  45
  46
  47
  48
  49
  50
  51
  52
  53
  54
  55
  56
  57
  58
  59
  60
  61
  62
  63
  64
  65
  66
  67
  68
  69
  70
  71
  72
  73
  74
  75
  76
  77
  78
  79
  80
  81
  82
  83
  84
  85
  86
  87
  88
  89 -->
  90 <body>
  91 <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/settings">[Settings]</a></li><li><a href="/2022/auth/logout">[Log Out]</a></li></ul></nav><div class="user">Neil Smith <a href="/2022/support" class="supporter-badge" title="Advent of Code Supporter">(AoC++)</a> <span class="star-count">32*</span></div></div><div><h1 class="title-event">&nbsp;<span class="title-event-wrap">{&apos;year&apos;:</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>
  92
  93 <div id="sidebar">
  94 <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://careers.bankofamerica.com/" target="_blank" onclick="if(ga)ga('send','event','sponsor','sidebar',this.href);" rel="noopener">Bank of America</a> - We use technology, models and data to make financial lives better for our clients and communities.</div></div>
  95 </div><!--/sidebar-->
  96
  97 <main>
  98 <article class="day-desc"><h2>--- Day 16: Proboscidea Volcanium ---</h2><p>The sensors have led you to the origin of the distress signal: yet another handheld device, just like the one the Elves gave you. However, you don't see any Elves around; instead, the device is surrounded by elephants! They must have gotten lost in these tunnels, and one of the elephants apparently figured out how to turn on the distress signal.</p>
  99 <p>The ground rumbles again, much stronger this time. What kind of cave is this, exactly? You scan the cave with your handheld device; it reports mostly igneous rock, some ash, pockets of pressurized gas, magma... this isn't just a cave, it's a volcano!</p>
 100 <p>You need to get the elephants out of here, quickly. Your device estimates that you have <em>30 minutes</em> before the volcano erupts, so you don't have time to go back out the way you came in.</p>
 101 <p>You scan the cave for other options and discover a network of pipes and pressure-release <em>valves</em>. You aren't sure how such a system got into a volcano, but you don't have time to complain; your device produces a report (your puzzle input) of each valve's <em>flow rate</em> if it were opened (in pressure per minute) and the tunnels you could use to move between the valves.</p>
 102 <p>There's even a valve in the room you and the elephants are currently standing in labeled <code>AA</code>. You estimate it will take you one minute to open a single valve and one minute to follow any tunnel from one valve to another. What is the most pressure you could release?</p>
 103 <p>For example, suppose you had the following scan output:</p>
 104 <pre><code>Valve AA has flow rate=0; tunnels lead to valves DD, II, BB
 105 Valve BB has flow rate=13; tunnels lead to valves CC, AA
 106 Valve CC has flow rate=2; tunnels lead to valves DD, BB
 107 Valve DD has flow rate=20; tunnels lead to valves CC, AA, EE
 108 Valve EE has flow rate=3; tunnels lead to valves FF, DD
 109 Valve FF has flow rate=0; tunnels lead to valves EE, GG
 110 Valve GG has flow rate=0; tunnels lead to valves FF, HH
 111 Valve HH has flow rate=22; tunnel leads to valve GG
 112 Valve II has flow rate=0; tunnels lead to valves AA, JJ
 113 Valve JJ has flow rate=21; tunnel leads to valve II
 114 </code></pre>
 115 <p>All of the valves begin <em>closed</em>. You start at valve <code>AA</code>, but it must be damaged or <span title="Wait, sir! The valve, sir! it appears to be... jammed!">jammed</span> or something: its flow rate is <code>0</code>, so there's no point in opening it. However, you could spend one minute moving to valve <code>BB</code> and another minute opening it; doing so would release pressure during the remaining <em>28 minutes</em> at a flow rate of <code>13</code>, a total eventual pressure release of <code>28 * 13 = <em>364</em></code>. Then, you could spend your third minute moving to valve <code>CC</code> and your fourth minute opening it, providing an additional <em>26 minutes</em> of eventual pressure release at a flow rate of <code>2</code>, or <code><em>52</em></code> total pressure released by valve <code>CC</code>.</p>
 116 <p>Making your way through the tunnels like this, you could probably open many or all of the valves by the time 30 minutes have elapsed. However, you need to release as much pressure as possible, so you'll need to be methodical. Instead, consider this approach:</p>
 117 <pre><code>== Minute 1 ==
 118 No valves are open.
 119 You move to valve DD.
 120
 121 == Minute 2 ==
 122 No valves are open.
 123 You open valve DD.
 124
 125 == Minute 3 ==
 126 Valve DD is open, releasing <em>20</em> pressure.
 127 You move to valve CC.
 128
 129 == Minute 4 ==
 130 Valve DD is open, releasing <em>20</em> pressure.
 131 You move to valve BB.
 132
 133 == Minute 5 ==
 134 Valve DD is open, releasing <em>20</em> pressure.
 135 You open valve BB.
 136
 137 == Minute 6 ==
 138 Valves BB and DD are open, releasing <em>33</em> pressure.
 139 You move to valve AA.
 140
 141 == Minute 7 ==
 142 Valves BB and DD are open, releasing <em>33</em> pressure.
 143 You move to valve II.
 144
 145 == Minute 8 ==
 146 Valves BB and DD are open, releasing <em>33</em> pressure.
 147 You move to valve JJ.
 148
 149 == Minute 9 ==
 150 Valves BB and DD are open, releasing <em>33</em> pressure.
 151 You open valve JJ.
 152
 153 == Minute 10 ==
 154 Valves BB, DD, and JJ are open, releasing <em>54</em> pressure.
 155 You move to valve II.
 156
 157 == Minute 11 ==
 158 Valves BB, DD, and JJ are open, releasing <em>54</em> pressure.
 159 You move to valve AA.
 160
 161 == Minute 12 ==
 162 Valves BB, DD, and JJ are open, releasing <em>54</em> pressure.
 163 You move to valve DD.
 164
 165 == Minute 13 ==
 166 Valves BB, DD, and JJ are open, releasing <em>54</em> pressure.
 167 You move to valve EE.
 168
 169 == Minute 14 ==
 170 Valves BB, DD, and JJ are open, releasing <em>54</em> pressure.
 171 You move to valve FF.
 172
 173 == Minute 15 ==
 174 Valves BB, DD, and JJ are open, releasing <em>54</em> pressure.
 175 You move to valve GG.
 176
 177 == Minute 16 ==
 178 Valves BB, DD, and JJ are open, releasing <em>54</em> pressure.
 179 You move to valve HH.
 180
 181 == Minute 17 ==
 182 Valves BB, DD, and JJ are open, releasing <em>54</em> pressure.
 183 You open valve HH.
 184
 185 == Minute 18 ==
 186 Valves BB, DD, HH, and JJ are open, releasing <em>76</em> pressure.
 187 You move to valve GG.
 188
 189 == Minute 19 ==
 190 Valves BB, DD, HH, and JJ are open, releasing <em>76</em> pressure.
 191 You move to valve FF.
 192
 193 == Minute 20 ==
 194 Valves BB, DD, HH, and JJ are open, releasing <em>76</em> pressure.
 195 You move to valve EE.
 196
 197 == Minute 21 ==
 198 Valves BB, DD, HH, and JJ are open, releasing <em>76</em> pressure.
 199 You open valve EE.
 200
 201 == Minute 22 ==
 202 Valves BB, DD, EE, HH, and JJ are open, releasing <em>79</em> pressure.
 203 You move to valve DD.
 204
 205 == Minute 23 ==
 206 Valves BB, DD, EE, HH, and JJ are open, releasing <em>79</em> pressure.
 207 You move to valve CC.
 208
 209 == Minute 24 ==
 210 Valves BB, DD, EE, HH, and JJ are open, releasing <em>79</em> pressure.
 211 You open valve CC.
 212
 213 == Minute 25 ==
 214 Valves BB, CC, DD, EE, HH, and JJ are open, releasing <em>81</em> pressure.
 215
 216 == Minute 26 ==
 217 Valves BB, CC, DD, EE, HH, and JJ are open, releasing <em>81</em> pressure.
 218
 219 == Minute 27 ==
 220 Valves BB, CC, DD, EE, HH, and JJ are open, releasing <em>81</em> pressure.
 221
 222 == Minute 28 ==
 223 Valves BB, CC, DD, EE, HH, and JJ are open, releasing <em>81</em> pressure.
 224
 225 == Minute 29 ==
 226 Valves BB, CC, DD, EE, HH, and JJ are open, releasing <em>81</em> pressure.
 227
 228 == Minute 30 ==
 229 Valves BB, CC, DD, EE, HH, and JJ are open, releasing <em>81</em> pressure.
 230 </code></pre>
 231 <p>This approach lets you release the most pressure possible in 30 minutes with this valve layout, <code><em>1651</em></code>.</p>
 232 <p>Work out the steps to release the most pressure in 30 minutes. <em>What is the most pressure you can release?</em></p>
 233 </article>
 234 <p>Your puzzle answer was <code>1792</code>.</p><article class="day-desc"><h2 id="part2">--- Part Two ---</h2><p>You're worried that even with an optimal approach, the pressure released won't be enough. What if you got one of the elephants to help you?</p>
 235 <p>It would take you 4 minutes to teach an elephant how to open the right valves in the right order, leaving you with only <em>26 minutes</em> to actually execute your plan. Would having two of you working together be better, even if it means having less time? (Assume that you teach the elephant before opening any valves yourself, giving you both the same full 26 minutes.)</p>
 236 <p>In the example above, you could teach the elephant to help you as follows:</p>
 237 <pre><code>== Minute 1 ==
 238 No valves are open.
 239 You move to valve II.
 240 The elephant moves to valve DD.
 241
 242 == Minute 2 ==
 243 No valves are open.
 244 You move to valve JJ.
 245 The elephant opens valve DD.
 246
 247 == Minute 3 ==
 248 Valve DD is open, releasing <em>20</em> pressure.
 249 You open valve JJ.
 250 The elephant moves to valve EE.
 251
 252 == Minute 4 ==
 253 Valves DD and JJ are open, releasing <em>41</em> pressure.
 254 You move to valve II.
 255 The elephant moves to valve FF.
 256
 257 == Minute 5 ==
 258 Valves DD and JJ are open, releasing <em>41</em> pressure.
 259 You move to valve AA.
 260 The elephant moves to valve GG.
 261
 262 == Minute 6 ==
 263 Valves DD and JJ are open, releasing <em>41</em> pressure.
 264 You move to valve BB.
 265 The elephant moves to valve HH.
 266
 267 == Minute 7 ==
 268 Valves DD and JJ are open, releasing <em>41</em> pressure.
 269 You open valve BB.
 270 The elephant opens valve HH.
 271
 272 == Minute 8 ==
 273 Valves BB, DD, HH, and JJ are open, releasing <em>76</em> pressure.
 274 You move to valve CC.
 275 The elephant moves to valve GG.
 276
 277 == Minute 9 ==
 278 Valves BB, DD, HH, and JJ are open, releasing <em>76</em> pressure.
 279 You open valve CC.
 280 The elephant moves to valve FF.
 281
 282 == Minute 10 ==
 283 Valves BB, CC, DD, HH, and JJ are open, releasing <em>78</em> pressure.
 284 The elephant moves to valve EE.
 285
 286 == Minute 11 ==
 287 Valves BB, CC, DD, HH, and JJ are open, releasing <em>78</em> pressure.
 288 The elephant opens valve EE.
 289
 290 (At this point, all valves are open.)
 291
 292 == Minute 12 ==
 293 Valves BB, CC, DD, EE, HH, and JJ are open, releasing <em>81</em> pressure.
 294
 295 ...
 296
 297 == Minute 20 ==
 298 Valves BB, CC, DD, EE, HH, and JJ are open, releasing <em>81</em> pressure.
 299
 300 ...
 301
 302 == Minute 26 ==
 303 Valves BB, CC, DD, EE, HH, and JJ are open, releasing <em>81</em> pressure.
 304 </code></pre>
 305 <p>With the elephant helping, after 26 minutes, the best you could do would release a total of <code><em>1707</em></code> pressure.</p>
 306 <p><em>With you and an elephant working together for 26 minutes, what is the most pressure you could release?</em></p>
 307 </article>
 308 <p>Your puzzle answer was <code>2587</code>.</p><p class="day-success">Both parts of this puzzle are complete! They provide two gold stars: **</p>
 309 <p>At this point, you should <a href="/2022">return to your Advent calendar</a> and try another puzzle.</p>
 310 <p>If you still want to see it, you can <a href="16/input" target="_blank">get your puzzle input</a>.</p>
 311 <p>You can also <span class="share">[Share<span class="share-content">on
 312   <a href="https://twitter.com/intent/tweet?text=I%27ve+completed+%22Proboscidea+Volcanium%22+%2D+Day+16+%2D+Advent+of+Code+2022&amp;url=https%3A%2F%2Fadventofcode%2Ecom%2F2022%2Fday%2F16&amp;related=ericwastl&amp;hashtags=AdventOfCode" target="_blank">Twitter</a>
 313   <a href="javascript:void(0);" onclick="var mastodon_instance=prompt('Mastodon Instance / Server Name?'); if(typeof mastodon_instance==='string' && mastodon_instance.length){this.href='https://'+mastodon_instance+'/share?text=I%27ve+completed+%22Proboscidea+Volcanium%22+%2D+Day+16+%2D+Advent+of+Code+2022+%23AdventOfCode+https%3A%2F%2Fadventofcode%2Ecom%2F2022%2Fday%2F16'}else{return false;}" target="_blank">Mastodon</a
 314 ></span>]</span> this puzzle.</p>
 315 </main>
 316
 317 <!-- ga -->
 318 <script>
 319 (function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
 320 (i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
 321 m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
 322 })(window,document,'script','//www.google-analytics.com/analytics.js','ga');
 323 ga('create', 'UA-69522494-1', 'auto');
 324 ga('set', 'anonymizeIp', true);
 325 ga('send', 'pageview');
 326 </script>
 327 <!-- /ga -->
 328 </body>
 329 </html>