adventofcode/2017/day20/problem

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2017-12-20 15:02:11 +00:00
Advent of Code
--- Day 20: Particle Swarm ---
Suddenly, the GPU contacts you, asking for help. Someone has
asked it to simulate too many particles, and it won't be able
to finish them all in time to render the next frame at this
rate.
It transmits to you a buffer (your puzzle input) listing each
particle in order (starting with particle 0, then particle 1,
particle 2, and so on). For each particle, it provides the X,
Y, and Z coordinates for the particle's position (p), velocity
(v), and acceleration (a), each in the format <X,Y,Z>.
Each tick, all particles are updated simultaneously. A
particle's properties are updated in the following order:
* Increase the X velocity by the X acceleration.
* Increase the Y velocity by the Y acceleration.
* Increase the Z velocity by the Z acceleration.
* Increase the X position by the X velocity.
* Increase the Y position by the Y velocity.
* Increase the Z position by the Z velocity.
Because of seemingly tenuous rationale involving z-buffering,
the GPU would like to know which particle will stay closest to
position <0,0,0> in the long term. Measure this using the
Manhattan distance, which in this situation is simply the sum
of the absolute values of a particle's X, Y, and Z position.
For example, suppose you are only given two particles, both of
which stay entirely on the X-axis (for simplicity). Drawing
the current states of particles 0 and 1 (in that order) with
an adjacent a number line and diagram of current X positions
(marked in parenthesis), the following would take place:
p=< 3,0,0>, v=< 2,0,0>, a=<-1,0,0> -4 -3 -2 -1 0 1 2 3 4
p=< 4,0,0>, v=< 0,0,0>, a=<-2,0,0> (0)(1)
p=< 4,0,0>, v=< 1,0,0>, a=<-1,0,0> -4 -3 -2 -1 0 1 2 3 4
p=< 2,0,0>, v=<-2,0,0>, a=<-2,0,0> (1) (0)
p=< 4,0,0>, v=< 0,0,0>, a=<-1,0,0> -4 -3 -2 -1 0 1 2 3 4
p=<-2,0,0>, v=<-4,0,0>, a=<-2,0,0> (1) (0)
p=< 3,0,0>, v=<-1,0,0>, a=<-1,0,0> -4 -3 -2 -1 0 1 2 3 4
p=<-8,0,0>, v=<-6,0,0>, a=<-2,0,0> (0)
At this point, particle 1 will never be closer to <0,0,0> than
particle 0, and so, in the long run, particle 0 will stay
closest.
Which particle will stay closest to position <0,0,0> in the
long term?
Your puzzle answer was _______.
The first half of this puzzle is complete! It provides one
gold star: *
--- Part Two ---
To simplify the problem further, the GPU would like to remove
any particles that collide. Particles collide if their
positions ever exactly match. Because particles are updated
simultaneously, more than two particles can collide at the
same time and place. Once particles collide, they are removed
and cannot collide with anything else after that tick.
For example:
p=<-6,0,0>, v=< 3,0,0>, a=< 0,0,0>
p=<-4,0,0>, v=< 2,0,0>, a=< 0,0,0> -6 -5 -4 -3 -2 -1 0 1 2 3
p=<-2,0,0>, v=< 1,0,0>, a=< 0,0,0> (0) (1) (2) (3)
p=< 3,0,0>, v=<-1,0,0>, a=< 0,0,0>
p=<-3,0,0>, v=< 3,0,0>, a=< 0,0,0>
p=<-2,0,0>, v=< 2,0,0>, a=< 0,0,0> -6 -5 -4 -3 -2 -1 0 1 2 3
p=<-1,0,0>, v=< 1,0,0>, a=< 0,0,0> (0)(1)(2) (3)
p=< 2,0,0>, v=<-1,0,0>, a=< 0,0,0>
p=< 0,0,0>, v=< 3,0,0>, a=< 0,0,0>
p=< 0,0,0>, v=< 2,0,0>, a=< 0,0,0> -6 -5 -4 -3 -2 -1 0 1 2 3
p=< 0,0,0>, v=< 1,0,0>, a=< 0,0,0> X (3)
p=< 1,0,0>, v=<-1,0,0>, a=< 0,0,0>
------destroyed by collision------
------destroyed by collision------ -6 -5 -4 -3 -2 -1 0 1 2 3
------destroyed by collision------ (3)
p=< 0,0,0>, v=<-1,0,0>, a=< 0,0,0>
In this example, particles 0, 1, and 2 are simultaneously
destroyed at the time and place marked X. On the next tick,
particle 3 passes through unharmed.
How many particles are left after all collisions are resolved?
Although it hasn't changed, you can still get your puzzle
input.
Answer: _____________________
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. https://en.wikipedia.org/wiki/Z-buffering
. https://en.wikipedia.org/wiki/Taxicab_geometry
. http://adventofcode.com/2017/day/20/input