178 lines
5.0 KiB
Markdown
178 lines
5.0 KiB
Markdown
## \-\-- Day 14: Restroom Redoubt \-\--
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One of The Historians needs to use the bathroom; fortunately, you know
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there\'s a bathroom near an unvisited location on their list, and so
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you\'re all quickly teleported directly to the lobby of Easter Bunny
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Headquarters.
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Unfortunately, EBHQ seems to have \"improved\" bathroom security *again*
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after your last [visit](/2016/day/2). The area outside the bathroom is
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swarming with robots!
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To get The Historian safely to the bathroom, you\'ll need a way to
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predict where the robots will be in the future. Fortunately, they all
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seem to be moving on the tile floor in predictable *straight lines*.
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You make a list (your puzzle input) of all of the robots\' current
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*positions* (`p`) and *velocities* (`v`), one robot per line. For
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example:
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p=0,4 v=3,-3
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p=6,3 v=-1,-3
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p=10,3 v=-1,2
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p=2,0 v=2,-1
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p=0,0 v=1,3
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p=3,0 v=-2,-2
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p=7,6 v=-1,-3
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p=3,0 v=-1,-2
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p=9,3 v=2,3
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p=7,3 v=-1,2
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p=2,4 v=2,-3
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p=9,5 v=-3,-3
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Each robot\'s position is given as `p=x,y` where `x` represents the
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number of tiles the robot is from the left wall and `y` represents the
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number of tiles from the top wall (when viewed from above). So, a
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position of `p=0,0` means the robot is all the way in the top-left
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corner.
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Each robot\'s velocity is given as `v=x,y` where `x` and `y` are given
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in *tiles per second*. Positive `x` means the robot is moving to the
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*right*, and positive `y` means the robot is moving *down*. So, a
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velocity of `v=1,-2` means that each second, the robot moves `1` tile to
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the right and `2` tiles up.
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The robots outside the actual bathroom are in a space which is `101`
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tiles wide and `103` tiles tall (when viewed from above). However, in
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this example, the robots are in a space which is only `11` tiles wide
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and `7` tiles tall.
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The robots are good at navigating over/under each other (due to a
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combination of springs, extendable legs, and quadcopters), so they can
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share the same tile and don\'t interact with each other. Visually, the
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number of robots on each tile in this example looks like this:
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1.12.......
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...........
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...........
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......11.11
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1.1........
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.........1.
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.......1...
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These robots have a unique feature for maximum bathroom security: they
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can *teleport*. When a robot would run into an edge of the space
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they\'re in, they instead *teleport to the other side*, effectively
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wrapping around the edges. Here is what robot `p=2,4 v=2,-3` does for
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the first few seconds:
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Initial state:
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...........
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...........
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...........
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...........
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..1........
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...........
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...........
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After 1 second:
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...........
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....1......
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...........
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...........
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...........
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...........
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...........
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After 2 seconds:
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...........
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...........
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...........
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...........
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...........
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......1....
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...........
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After 3 seconds:
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...........
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...........
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........1..
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...........
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...........
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...........
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...........
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After 4 seconds:
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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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..........1
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After 5 seconds:
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...........
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...........
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...........
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.1.........
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...........
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...........
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...........
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The Historian can\'t wait much longer, so you don\'t have to simulate
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the robots for very long. Where will the robots be after `100` seconds?
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In the above example, the number of robots on each tile after 100
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seconds has elapsed looks like this:
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......2..1.
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...........
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1..........
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.11........
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.....1.....
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...12......
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.1....1....
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To determine the safest area, count the *number of robots in each
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quadrant* after 100 seconds. Robots that are exactly in the middle
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(horizontally or vertically) don\'t count as being in any quadrant, so
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the only relevant robots are:
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..... 2..1.
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..... .....
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1.... .....
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..... .....
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...12 .....
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.1... 1....
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In this example, the quadrants contain `1`, `3`, `4`, and `1` robot.
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Multiplying these together gives a total *safety factor* of `12`.
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Predict the motion of the robots in your list within a space which is
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`101` tiles wide and `103` tiles tall. *What will the safety factor be
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after exactly 100 seconds have elapsed?*
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Your puzzle answer was `230686500`.
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The first half of this puzzle is complete! It provides one gold star: \*
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## \-\-- Part Two \-\-- {#part2}
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During the bathroom break, someone notices that these robots seem
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awfully similar to ones built and used at the North Pole. If they\'re
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the same type of robots, they should have a hard-coded [Easter
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egg]{title="This puzzle was originally going to be about the motion of space rocks in a fictitious arcade game called Meteoroids, but we just had an arcade puzzle."}:
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very rarely, most of the robots should arrange themselves into *a
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picture of a Christmas tree*.
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*What is the fewest number of seconds that must elapse for the robots to
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display the Easter egg?*
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Answer:
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Although it hasn\'t changed, you can still [get your puzzle
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input](14/input).
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