75 lines
3.7 KiB
Markdown
Executable File
75 lines
3.7 KiB
Markdown
Executable File
## \-\-\- Day 24: Never Tell Me The Odds ---
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It seems like something is going wrong with the snow-making process. Instead of forming snow, the water that's been absorbed into the air seems to be forming [hail](https://en.wikipedia.org/wiki/Hail)!
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Maybe there's something you can do to break up the hailstones?
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Due to strong, probably-magical winds, the hailstones are all flying through the air in perfectly linear trajectories. You make a note of each hailstone's _position_ and _velocity_ (your puzzle input). For example:
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```
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19, 13, 30 @ -2, 1, -2
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18, 19, 22 @ -1, -1, -2
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20, 25, 34 @ -2, -2, -4
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12, 31, 28 @ -1, -2, -1
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20, 19, 15 @ 1, -5, -3
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```
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Each line of text corresponds to the position and velocity of a single hailstone. The positions indicate where the hailstones are _right now_ (at time `0`). The velocities are constant and indicate exactly how far each hailstone will move in _one nanosecond_.
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Each line of text uses the format `px py pz @ vx vy vz`. For instance, the hailstone specified by `20, 19, 15 @ 1, -5, -3` has initial X position `20`, Y position `19`, Z position `15`, X velocity `1`, Y velocity `-5`, and Z velocity `-3`. After one nanosecond, the hailstone would be at `21, 14, 12`.
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Perhaps you won't have to do anything. How likely are the hailstones to collide with each other and smash into tiny ice crystals?
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To estimate this, consider only the X and Y axes; _ignore the Z axis_. Looking _forward in time_, how many of the hailstones' _paths_ will intersect within a test area? (The hailstones themselves don't have to collide, just test for intersections between the paths they will trace.)
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In this example, look for intersections that happen with an X and Y position each at least `7` and at most `27`; in your actual data, you'll need to check a much larger test area. Comparing all pairs of hailstones' future paths produces the following results:
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```
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Hailstone A: 19, 13, 30 @ -2, 1, -2
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Hailstone B: 18, 19, 22 @ -1, -1, -2
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Hailstones' paths will cross inside the test area (at x=14.333, y=15.333).
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Hailstone A: 19, 13, 30 @ -2, 1, -2
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Hailstone B: 20, 25, 34 @ -2, -2, -4
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Hailstones' paths will cross inside the test area (at x=11.667, y=16.667).
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Hailstone A: 19, 13, 30 @ -2, 1, -2
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Hailstone B: 12, 31, 28 @ -1, -2, -1
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Hailstones' paths will cross outside the test area (at x=6.2, y=19.4).
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Hailstone A: 19, 13, 30 @ -2, 1, -2
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Hailstone B: 20, 19, 15 @ 1, -5, -3
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Hailstones' paths crossed in the past for hailstone A.
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Hailstone A: 18, 19, 22 @ -1, -1, -2
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Hailstone B: 20, 25, 34 @ -2, -2, -4
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Hailstones' paths are parallel; they never intersect.
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Hailstone A: 18, 19, 22 @ -1, -1, -2
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Hailstone B: 12, 31, 28 @ -1, -2, -1
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Hailstones' paths will cross outside the test area (at x=-6, y=-5).
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Hailstone A: 18, 19, 22 @ -1, -1, -2
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Hailstone B: 20, 19, 15 @ 1, -5, -3
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Hailstones' paths crossed in the past for both hailstones.
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Hailstone A: 20, 25, 34 @ -2, -2, -4
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Hailstone B: 12, 31, 28 @ -1, -2, -1
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Hailstones' paths will cross outside the test area (at x=-2, y=3).
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Hailstone A: 20, 25, 34 @ -2, -2, -4
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Hailstone B: 20, 19, 15 @ 1, -5, -3
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Hailstones' paths crossed in the past for hailstone B.
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Hailstone A: 12, 31, 28 @ -1, -2, -1
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Hailstone B: 20, 19, 15 @ 1, -5, -3
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Hailstones' paths crossed in the past for both hailstones.
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```
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So, in this example, `2` hailstones' future paths cross inside the boundaries of the test area.
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However, you'll need to search a much larger test area if you want to see if any hailstones might collide. Look for intersections that happen with an X and Y position each at least `200000000000000` and at most `400000000000000`. Disregard the Z axis entirely.
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Considering only the X and Y axes, check all pairs of hailstones' future paths for intersections. _How many of these intersections occur within the test area?_ |