day-24 done
This commit is contained in:
Dylan Thies
1
2023/Cargo.lock
generated
1
2023/Cargo.lock
generated
@@ -248,6 +248,7 @@ dependencies = [
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"glam",
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"itertools",
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"nom",
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"num",
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]
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[[package]]
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@@ -11,3 +11,4 @@ repository.workspace = true
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nom = { workspace = true }
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itertools = {workspace = true }
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glam.workspace = true
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num = "0.4.1"
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@@ -5,8 +5,9 @@ use nom::{
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bytes::complete::tag,
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character::complete,
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multi::separated_list1,
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number,
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sequence::{separated_pair, tuple},
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IResult, Parser, number,
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IResult, Parser,
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};
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use itertools::Itertools;
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@@ -23,34 +24,52 @@ impl Stones {
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// (y_n - y_1)/v_y1 = (x_n - x_1)/v_x1
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// y_n = v_y1 * (x_n -x_1)/v_x1 + y_1
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// (v_y1/v_x1) * x_n - x_1 * (v_y1/v_x1) + y_1 = (v_y2/v_x2) * x_n -x_2 * (v_y2/v_x2) + y_2
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// x_n * ((v_y1/v_x1) - (v_y2/v_x2)) = x_1 * (v_y1/v_x1) - x_2 * (v_y2/v_x2) + y_2 - y_1
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// x_n * ((v_y1/v_x1) - (v_y2/v_x2)) = x_1 * (v_y1/v_x1) - x_2 * (v_y2/v_x2) + y_2 - y_1
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// x1 + v1 *t == x2 + v2*t
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// (x1-x2)/(v2-v1) = t
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let slope1 = self.velocity.y / self.velocity.x;
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let slope2 = other.velocity.y / other.velocity.x;
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let denom = slope1 - slope2;
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let x = (self.start.x *slope1 -other.start.x *slope2 + other.start.y - self.start.y) / denom;
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let x =
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(self.start.x * slope1 - other.start.x * slope2 + other.start.y - self.start.y) / denom;
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let y = slope1 * (x - self.start.x) + self.start.y;
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if !x.is_finite() || !y.is_finite() {
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return None;
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}
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let t1 = (x - self.start.x) / self.velocity.x;
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let t2 = (x - other.start.x) / other.velocity.x;
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if t1 < 0.0 || t2 < 0.0{
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if t1 < 0.0 || t2 < 0.0 {
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return None;
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}
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Some(DVec3::new(x, y, 0.0))
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}
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}
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/// day 24 part 1 of aoc 2023
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///
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/// # Arguments
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/// - input the input for today's puzzle
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///
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/// # Panics
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/// panics whne it cannot parse the input OR when ever the number of game numbers is greater than
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#[must_use]
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pub fn part1(input: &str, min:f64, max:f64) -> String {
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pub fn part1(input: &str, min: f64, max: f64) -> String {
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let (_, stones) = parse_input(input).expect("Aoc should have valid input");
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stones.iter().combinations(2)
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stones
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.iter()
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.combinations(2)
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.filter_map(|pair| {
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let [a,b] = pair[..] else { return None};
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a.cross(b).and_then(|cross_position| (cross_position.x <= max && cross_position.y <= max && cross_position.x >= min && cross_position.y >= min).then_some(cross_position) )
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}).count().to_string()
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let [a, b] = pair[..] else { return None };
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a.cross(b).and_then(|cross_position| {
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(cross_position.x <= max
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&& cross_position.y <= max
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&& cross_position.x >= min
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&& cross_position.y >= min)
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.then_some(cross_position)
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})
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})
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.count()
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.to_string()
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}
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fn parse_tuple(input: &str) -> IResult<&str, DVec3> {
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@@ -90,4 +109,3 @@ mod test {
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assert_eq!(result, "2".to_string());
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}
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}
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@@ -1,20 +1,278 @@
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#![warn(clippy::all, clippy::pedantic)]
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#![allow(clippy::similar_names)]
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use glam::I64Vec3;
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use nom::{
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bytes::complete::tag,
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character::complete,
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multi::separated_list1,
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sequence::{separated_pair, tuple},
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IResult, Parser,
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};
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use itertools::Itertools;
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use num::rational::Ratio;
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type Cord = Ratio<i128>;
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#[derive(Debug, Clone, Copy)]
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struct Stones {
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pub start: I64Vec3,
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pub velocity: I64Vec3,
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}
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impl Stones {
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fn cross_xy(&self, other: &Self) -> Option<(Cord, Cord)> {
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let pax = Cord::from(i128::from(self.start.x));
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let pay = Cord::from(i128::from(self.start.y));
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let pbx = Cord::from(i128::from(other.start.x));
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let pby = Cord::from(i128::from(other.start.y));
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let vax = Cord::from(i128::from(self.velocity.x));
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let vay = Cord::from(i128::from(self.velocity.y));
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let vbx = Cord::from(i128::from(other.velocity.x));
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let vby = Cord::from(i128::from(other.velocity.y));
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let slope1 = vay / vax;
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let slope2 = vby / vbx;
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let denom = slope1 - slope2;
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if denom == num::Zero::zero() {
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return None;
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}
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let x = (pax * slope1 - pbx * slope2 + pby - pay) / denom;
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let y = slope1 * (x - pax) + pay;
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let t1 = (x - pax) / vax;
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let t2 = (x - pbx) / vbx;
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if t1 < num::zero() || t2 < num::zero() {
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return None;
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}
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Some((x, y))
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}
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fn cross_xz(&self, other: &Self) -> Option<(Cord, Cord)> {
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let pax = Cord::from(i128::from(self.start.x));
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let paz = Cord::from(i128::from(self.start.z));
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let pbx = Cord::from(i128::from(other.start.x));
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let pbz = Cord::from(i128::from(other.start.z));
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let vax = Cord::from(i128::from(self.velocity.x));
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let vaz = Cord::from(i128::from(self.velocity.z));
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let vbx = Cord::from(i128::from(other.velocity.x));
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let vbz = Cord::from(i128::from(other.velocity.z));
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let slope1 = vaz / vax;
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let slope2 = vbz / vbx;
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let denom = slope1 - slope2;
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if denom == num::Zero::zero() {
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return None;
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}
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let x = (pax * slope1 - pbx * slope2 + pbz - paz) / denom;
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let z = slope1 * (x - pax) + paz;
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let t1 = (x - pax) / vax;
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let t2 = (x - pbx) / vbx;
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if t1 < num::zero() || t2 < num::zero() {
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return None;
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}
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Some((x, z))
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}
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fn stone_to_tuples(&self) -> ((Cord, Cord, Cord), (Cord, Cord, Cord)) {
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let Stones {
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start:
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I64Vec3 {
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x: p_x,
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y: p_y,
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z: p_z,
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},
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velocity:
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I64Vec3 {
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x: v_x,
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y: v_y,
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z: v_z,
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},
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} = *self;
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(
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(
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Cord::from(i128::from(p_x)),
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Cord::from(i128::from(p_y)),
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Cord::from(i128::from(p_z)),
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),
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(
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Cord::from(i128::from(v_x)),
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Cord::from(i128::from(v_y)),
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Cord::from(i128::from(v_z)),
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),
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)
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}
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}
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/// day 24 part 2 of aoc 2023
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///
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/// # Arguments
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/// - input the input for today's puzzle
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///
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/// # Panics
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/// panics whne it cannot parse the input OR when ever the number of game numbers is greater than
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#[must_use]
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pub fn part2 (_input: &str) -> String {
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"Not Finished".to_string()
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pub fn part2(input: &str) -> String {
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let (_, stones) = parse_input(input).expect("Aoc should have valid input");
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let iteresting_stones = stones
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.iter()
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.combinations(2)
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.filter_map(|pair| {
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let [a, b] = pair[..] else {
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return None;
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};
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match (a.cross_xy(b), a.cross_xz(b)) {
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(None, None) => false,
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(None, Some(_)) | (Some(_), None) => true,
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(Some((x1, _)), Some((x2, _))) => x1 != x2,
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}
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.then_some(*b)
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})
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.skip(4)
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.take(3)
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.collect::<Vec<_>>();
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let ((p_ax, p_ay, p_az), (v_ax, v_ay, v_az)) = iteresting_stones[0].stone_to_tuples();
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let ((p_bx, p_by, p_bz), (v_bx, v_by, v_bz)) = iteresting_stones[1].stone_to_tuples();
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let ((p_cx, p_cy, p_cz), (v_cx, v_cy, v_cz)) = iteresting_stones[2].stone_to_tuples();
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//setting up the syystem of equations
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//println!("{v_az} - {v_cz} = {:?}", v_az - v_cz);
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let mut equations = [
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[
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Cord::default(),
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v_az - v_cz,
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v_cy - v_ay,
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Cord::default(),
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p_cz - p_az,
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p_ay - p_cy,
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p_ay * v_az - p_az * v_ay - p_cy * v_cz + p_cz * v_cy,
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],
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[
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v_az - v_cz,
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Cord::default(),
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v_cx - v_ax,
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p_cz - p_az,
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Cord::default(),
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p_ax - p_cx,
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p_ax * v_az - p_az * v_ax - p_cx * v_cz + p_cz * v_cx,
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],
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[
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v_cy - v_ay,
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v_ax - v_cx,
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Cord::default(),
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p_ay - p_cy,
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p_cx - p_ax,
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Cord::default(),
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p_ay * v_ax - p_ax * v_ay - p_cy * v_cx + p_cx * v_cy,
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],
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[
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Cord::default(),
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v_bz - v_cz,
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v_cy - v_by,
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Cord::default(),
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p_cz - p_bz,
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p_by - p_cy,
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p_by * v_bz - p_bz * v_by - p_cy * v_cz + p_cz * v_cy,
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],
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[
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v_bz - v_cz,
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Cord::default(),
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v_cx - v_bx,
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p_cz - p_bz,
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Cord::default(),
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p_bx - p_cx,
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p_bx * v_bz - p_bz * v_bx - p_cx * v_cz + p_cz * v_cx,
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],
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[
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v_cy - v_by,
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v_bx - v_cx,
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Cord::default(),
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p_by - p_cy,
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p_cx - p_bx,
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Cord::default(),
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p_by * v_bx - p_bx * v_by - p_cy * v_cx + p_cx * v_cy,
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],
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];
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//println!("{equations:?}");
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//gausian elimination
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for i in 0..6 {
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//need to make sure i,i is not zero
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let none_zero_index = (i..6)
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.find(|&row| equations[row][i] != Cord::default())
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.unwrap();
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//perform swap if need be
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if i != none_zero_index {
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(equations[i], equations[none_zero_index]) = (equations[none_zero_index], equations[i]);
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}
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// make i,i 1 and adjust the row
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let current_leader = equations[i][i];
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equations[i][i] = Cord::from_integer(1);
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for pos in &mut equations[i][(i + 1)..] {
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*pos /= current_leader;
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}
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//gausean elimination
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for row in (i + 1)..6 {
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let mult = equations[row][i];
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if mult != Cord::default() {
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equations[row][i] = Cord::default();
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for col in (i + 1)..7 {
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equations[row][col] -= equations[i][col] * mult;
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}
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}
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}
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}
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//upper triangle done now to make it identity
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//but doing a trick to turn col 6
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for i in (0..6).rev() {
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for row in 0..i {
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//equality row
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equations[row][6] -= equations[i][6] * equations[row][i];
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equations[row][i] = Cord::default();
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}
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}
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equations
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.iter()
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.take(3)
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.map(|x| x[6].to_integer())
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.sum::<i128>()
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.to_string()
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}
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fn parse_tuple(input: &str) -> IResult<&str, I64Vec3> {
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let (input, x) = complete::i64(input)?;
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let (input, _) = tuple((tag(","), complete::space0))(input)?;
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let (input, y) = complete::i64(input)?;
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let (input, _) = tuple((tag(","), complete::space0))(input)?;
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let (input, z) = complete::i64(input)?;
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Ok((input, I64Vec3::new(x, y, z)))
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}
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fn parse_input(input: &str) -> IResult<&str, Vec<Stones>> {
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separated_list1(
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complete::line_ending,
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separated_pair(
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parse_tuple,
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tuple((complete::space0, tag("@"), complete::space0)),
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parse_tuple,
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)
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.map(|(start, velocity)| Stones { start, velocity }),
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)(input)
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}
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#[cfg(test)]
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mod test {
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use super::*;
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const INPUT: &str = "";
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const INPUT: &str = "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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#[test]
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fn part2_works() {
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let result = part2(INPUT);
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assert_eq!(result, "Not Finished".to_string());
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assert_eq!(result, "47".to_string());
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}
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}
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Reference in New Issue
Block a user