128 lines
9.1 KiB
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128 lines
9.1 KiB
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<title>Day 17 - Advent of Code 2021</title>
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</head><div id="readability-page-1" class="page"><article><h2>--- Day 17: Trick Shot ---</h2><p>You finally decode the Elves' message. <code><span title="Maybe you need to turn the message 90 degrees counterclockwise?">HI</span></code>, the message says. You continue searching for the sleigh keys.</p>
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<p>Ahead of you is what appears to be a large <a href="https://en.wikipedia.org/wiki/Oceanic_trench" target="_blank">ocean trench</a>. Could the keys have fallen into it? You'd better send a probe to investigate.</p>
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<p>The probe launcher on your submarine can fire the probe with any <a href="https://en.wikipedia.org/wiki/Integer" target="_blank">integer</a> velocity in the <code>x</code> (forward) and <code>y</code> (upward, or downward if negative) directions. For example, an initial <code>x,y</code> velocity like <code>0,10</code> would fire the probe straight up, while an initial velocity like <code>10,-1</code> would fire the probe forward at a slight downward angle.</p>
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<p>The probe's <code>x,y</code> position starts at <code>0,0</code>. Then, it will follow some trajectory by moving in <em>steps</em>. On each step, these changes occur in the following order:</p>
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<ul>
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<li>The probe's <code>x</code> position increases by its <code>x</code> velocity.</li>
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<li>The probe's <code>y</code> position increases by its <code>y</code> velocity.</li>
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<li>Due to drag, the probe's <code>x</code> velocity changes by <code>1</code> toward the value <code>0</code>; that is, it decreases by <code>1</code> if it is greater than <code>0</code>, increases by <code>1</code> if it is less than <code>0</code>, or does not change if it is already <code>0</code>.</li>
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<li>Due to gravity, the probe's <code>y</code> velocity decreases by <code>1</code>.</li>
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</ul>
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<p>For the probe to successfully make it into the trench, the probe must be on some trajectory that causes it to be within a <em>target area</em> after any step. The submarine computer has already calculated this target area (your puzzle input). For example:</p>
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<pre><code>target area: x=20..30, y=-10..-5</code></pre>
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<p>This target area means that you need to find initial <code>x,y</code> velocity values such that after any step, the probe's <code>x</code> position is at least <code>20</code> and at most <code>30</code>, <em>and</em> the probe's <code>y</code> position is at least <code>-10</code> and at most <code>-5</code>.</p>
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<p>Given this target area, one initial velocity that causes the probe to be within the target area after any step is <code>7,2</code>:</p>
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<pre><code>.............#....#............
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.......#..............#........
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...............................
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S........................#.....
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...............................
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...............................
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...........................#...
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...............................
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....................TTTTTTTTTTT
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....................TTTTTTTTTTT
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....................TTTTTTTT#TT
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....................TTTTTTTTTTT
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....................TTTTTTTTTTT
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....................TTTTTTTTTTT
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</code></pre>
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<p>In this diagram, <code>S</code> is the probe's initial position, <code>0,0</code>. The <code>x</code> coordinate increases to the right, and the <code>y</code> coordinate increases upward. In the bottom right, positions that are within the target area are shown as <code>T</code>. After each step (until the target area is reached), the position of the probe is marked with <code>#</code>. (The bottom-right <code>#</code> is both a position the probe reaches and a position in the target area.)</p>
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<p>Another initial velocity that causes the probe to be within the target area after any step is <code>6,3</code>:</p>
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<pre><code>...............#..#............
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...........#........#..........
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...............................
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......#..............#.........
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...............................
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...............................
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S....................#.........
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...............................
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...............................
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...............................
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.....................#.........
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....................TTTTTTTTTTT
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....................TTTTTTTTTTT
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....................TTTTTTTTTTT
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....................TTTTTTTTTTT
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....................T#TTTTTTTTT
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....................TTTTTTTTTTT
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</code></pre>
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<p>Another one is <code>9,0</code>:</p>
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<pre><code>S........#.....................
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.................#.............
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...............................
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........................#......
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...............................
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....................TTTTTTTTTTT
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....................TTTTTTTTTT#
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....................TTTTTTTTTTT
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....................TTTTTTTTTTT
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....................TTTTTTTTTTT
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....................TTTTTTTTTTT
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</code></pre>
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<p>One initial velocity that <em>doesn't</em> cause the probe to be within the target area after any step is <code>17,-4</code>:</p>
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<pre><code>S..............................................................
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...............................................................
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...............................................................
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...............................................................
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.................#.............................................
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....................TTTTTTTTTTT................................
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....................TTTTTTTTTTT................................
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....................TTTTTTTTTTT................................
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....................TTTTTTTTTTT................................
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....................TTTTTTTTTTT..#.............................
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....................TTTTTTTTTTT................................
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...............................................................
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...............................................................
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...............................................................
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...............................................................
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................................................#..............
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...............................................................
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...............................................................
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...............................................................
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...............................................................
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...............................................................
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...............................................................
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..............................................................#
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</code></pre>
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<p>The probe appears to pass through the target area, but is never within it after any step. Instead, it continues down and to the right - only the first few steps are shown.</p>
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<p>If you're going to fire a highly scientific probe out of a super cool probe launcher, you might as well do it with <em>style</em>. How high can you make the probe go while still reaching the target area?</p>
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<p>In the above example, using an initial velocity of <code>6,9</code> is the best you can do, causing the probe to reach a maximum <code>y</code> position of <code><em>45</em></code>. (Any higher initial <code>y</code> velocity causes the probe to overshoot the target area entirely.)</p>
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<p>Find the initial velocity that causes the probe to reach the highest <code>y</code> position and still eventually be within the target area after any step. <em>What is the highest <code>y</code> position it reaches on this trajectory?</em></p>
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</article><p>Your puzzle answer was <code>6441</code>.</p><article><h2 id="part2">--- Part Two ---</h2><p>Maybe a fancy trick shot isn't the best idea; after all, you only have one probe, so you had better not miss.</p>
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<p>To get the best idea of what your options are for launching the probe, you need to find <em>every initial velocity</em> that causes the probe to eventually be within the target area after any step.</p>
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<p>In the above example, there are <code><em>112</em></code> different initial velocity values that meet these criteria:</p>
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<pre><code>23,-10 25,-9 27,-5 29,-6 22,-6 21,-7 9,0 27,-7 24,-5
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25,-7 26,-6 25,-5 6,8 11,-2 20,-5 29,-10 6,3 28,-7
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8,0 30,-6 29,-8 20,-10 6,7 6,4 6,1 14,-4 21,-6
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26,-10 7,-1 7,7 8,-1 21,-9 6,2 20,-7 30,-10 14,-3
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20,-8 13,-2 7,3 28,-8 29,-9 15,-3 22,-5 26,-8 25,-8
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25,-6 15,-4 9,-2 15,-2 12,-2 28,-9 12,-3 24,-6 23,-7
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25,-10 7,8 11,-3 26,-7 7,1 23,-9 6,0 22,-10 27,-6
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8,1 22,-8 13,-4 7,6 28,-6 11,-4 12,-4 26,-9 7,4
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24,-10 23,-8 30,-8 7,0 9,-1 10,-1 26,-5 22,-9 6,5
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7,5 23,-6 28,-10 10,-2 11,-1 20,-9 14,-2 29,-7 13,-3
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23,-5 24,-8 27,-9 30,-7 28,-5 21,-10 7,9 6,6 21,-5
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27,-10 7,2 30,-9 21,-8 22,-7 24,-9 20,-6 6,9 29,-5
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8,-2 27,-8 30,-5 24,-7
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</code></pre>
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<p><em>How many distinct initial velocity values cause the probe to be within the target area after any step?</em></p>
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</article><p>Your puzzle answer was <code>3186</code>.</p></div> |