From a95dffbf5c0090ff2ebb7db3ffcf45dbdc2dd029 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Moritz=20H=C3=B6lting?=
 <87192362+moritz-hoelting@users.noreply.github.com>
Date: Sun, 24 Dec 2023 13:35:07 +0100
Subject: [PATCH] day 24

---
 Cargo.lock               | 193 +++++++++++++++++++++++++
 day-24/Cargo.toml        |  13 ++
 day-24/src/bin/input.txt | 300 +++++++++++++++++++++++++++++++++++++++
 day-24/src/bin/part1.rs  | 164 +++++++++++++++++++++
 day-24/src/bin/part2.rs  | 141 ++++++++++++++++++
 5 files changed, 811 insertions(+)
 create mode 100644 day-24/Cargo.toml
 create mode 100644 day-24/src/bin/input.txt
 create mode 100644 day-24/src/bin/part1.rs
 create mode 100644 day-24/src/bin/part2.rs

diff --git a/Cargo.lock b/Cargo.lock
index 6c80edf..1d4521c 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -2,18 +2,91 @@
 # It is not intended for manual editing.
 version = 3
 
+[[package]]
+name = "aho-corasick"
+version = "1.1.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "b2969dcb958b36655471fc61f7e416fa76033bdd4bfed0678d8fee1e2d07a1f0"
+dependencies = [
+ "memchr",
+]
+
 [[package]]
 name = "autocfg"
 version = "1.1.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "d468802bab17cbc0cc575e9b053f41e72aa36bfa6b7f55e3529ffa43161b97fa"
 
+[[package]]
+name = "bindgen"
+version = "0.66.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "f2b84e06fc203107bfbad243f4aba2af864eb7db3b1cf46ea0a023b0b433d2a7"
+dependencies = [
+ "bitflags",
+ "cexpr",
+ "clang-sys",
+ "lazy_static",
+ "lazycell",
+ "peeking_take_while",
+ "proc-macro2",
+ "quote",
+ "regex",
+ "rustc-hash",
+ "shlex",
+ "syn",
+]
+
+[[package]]
+name = "bitflags"
+version = "2.4.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "327762f6e5a765692301e5bb513e0d9fef63be86bbc14528052b1cd3e6f03e07"
+
+[[package]]
+name = "cc"
+version = "1.0.83"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "f1174fb0b6ec23863f8b971027804a42614e347eafb0a95bf0b12cdae21fc4d0"
+dependencies = [
+ "libc",
+]
+
+[[package]]
+name = "cexpr"
+version = "0.6.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "6fac387a98bb7c37292057cffc56d62ecb629900026402633ae9160df93a8766"
+dependencies = [
+ "nom",
+]
+
 [[package]]
 name = "cfg-if"
 version = "1.0.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "baf1de4339761588bc0619e3cbc0120ee582ebb74b53b4efbf79117bd2da40fd"
 
+[[package]]
+name = "clang-sys"
+version = "1.6.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "c688fc74432808e3eb684cae8830a86be1d66a2bd58e1f248ed0960a590baf6f"
+dependencies = [
+ "glob",
+ "libc",
+ "libloading",
+]
+
+[[package]]
+name = "cmake"
+version = "0.1.50"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "a31c789563b815f77f4250caee12365734369f942439b7defd71e18a48197130"
+dependencies = [
+ "cc",
+]
+
 [[package]]
 name = "console"
 version = "0.15.7"
@@ -229,6 +302,15 @@ dependencies = [
  "indoc",
 ]
 
+[[package]]
+name = "day-24"
+version = "0.0.0"
+dependencies = [
+ "indoc",
+ "itertools",
+ "z3",
+]
+
 [[package]]
 name = "deprecate-until"
 version = "0.1.1"
@@ -265,6 +347,12 @@ version = "0.4.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "0ce7134b9999ecaf8bcd65542e436736ef32ddca1b3e06094cb6ec5755203b80"
 
+[[package]]
+name = "glob"
+version = "0.3.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "d2fabcfbdc87f4758337ca535fb41a6d701b65693ce38287d856d1674551ec9b"
+
 [[package]]
 name = "hashbrown"
 version = "0.12.3"
@@ -350,12 +438,34 @@ version = "1.4.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "e2abad23fbc42b3700f2f279844dc832adb2b2eb069b2df918f455c4e18cc646"
 
+[[package]]
+name = "lazycell"
+version = "1.3.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "830d08ce1d1d941e6b30645f1a0eb5643013d835ce3779a5fc208261dbe10f55"
+
 [[package]]
 name = "libc"
 version = "0.2.151"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "302d7ab3130588088d277783b1e2d2e10c9e9e4a16dd9050e6ec93fb3e7048f4"
 
+[[package]]
+name = "libloading"
+version = "0.7.4"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "b67380fd3b2fbe7527a606e18729d21c6f3951633d0500574c4dc22d2d638b9f"
+dependencies = [
+ "cfg-if",
+ "winapi",
+]
+
+[[package]]
+name = "log"
+version = "0.4.20"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "b5e6163cb8c49088c2c36f57875e58ccd8c87c7427f7fbd50ea6710b2f3f2e8f"
+
 [[package]]
 name = "memchr"
 version = "2.6.4"
@@ -484,6 +594,12 @@ dependencies = [
  "thiserror",
 ]
 
+[[package]]
+name = "peeking_take_while"
+version = "0.1.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "19b17cddbe7ec3f8bc800887bab5e717348c95ea2ca0b1bf0837fb964dc67099"
+
 [[package]]
 name = "portable-atomic"
 version = "1.6.0"
@@ -544,6 +660,35 @@ dependencies = [
  "crossbeam-utils",
 ]
 
+[[package]]
+name = "regex"
+version = "1.10.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "380b951a9c5e80ddfd6136919eef32310721aa4aacd4889a8d39124b026ab343"
+dependencies = [
+ "aho-corasick",
+ "memchr",
+ "regex-automata",
+ "regex-syntax",
+]
+
+[[package]]
+name = "regex-automata"
+version = "0.4.3"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "5f804c7828047e88b2d32e2d7fe5a105da8ee3264f01902f796c8e067dc2483f"
+dependencies = [
+ "aho-corasick",
+ "memchr",
+ "regex-syntax",
+]
+
+[[package]]
+name = "regex-syntax"
+version = "0.8.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "c08c74e62047bb2de4ff487b251e4a92e24f48745648451635cec7d591162d9f"
+
 [[package]]
 name = "rustc-hash"
 version = "1.1.0"
@@ -562,6 +707,12 @@ version = "1.0.20"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "836fa6a3e1e547f9a2c4040802ec865b5d85f4014efe00555d7090a3dcaa1090"
 
+[[package]]
+name = "shlex"
+version = "1.2.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "a7cee0529a6d40f580e7a5e6c495c8fbfe21b7b52795ed4bb5e62cdf92bc6380"
+
 [[package]]
 name = "syn"
 version = "2.0.40"
@@ -605,6 +756,28 @@ version = "0.1.11"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "e51733f11c9c4f72aa0c160008246859e340b00807569a0da0e7a1079b27ba85"
 
+[[package]]
+name = "winapi"
+version = "0.3.9"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "5c839a674fcd7a98952e593242ea400abe93992746761e38641405d28b00f419"
+dependencies = [
+ "winapi-i686-pc-windows-gnu",
+ "winapi-x86_64-pc-windows-gnu",
+]
+
+[[package]]
+name = "winapi-i686-pc-windows-gnu"
+version = "0.4.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "ac3b87c63620426dd9b991e5ce0329eff545bccbbb34f3be09ff6fb6ab51b7b6"
+
+[[package]]
+name = "winapi-x86_64-pc-windows-gnu"
+version = "0.4.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "712e227841d057c1ee1cd2fb22fa7e5a5461ae8e48fa2ca79ec42cfc1931183f"
+
 [[package]]
 name = "windows-sys"
 version = "0.45.0"
@@ -670,3 +843,23 @@ name = "windows_x86_64_msvc"
 version = "0.42.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "9aec5da331524158c6d1a4ac0ab1541149c0b9505fde06423b02f5ef0106b9f0"
+
+[[package]]
+name = "z3"
+version = "0.12.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "4a7ff5718c079e7b813378d67a5bed32ccc2086f151d6185074a7e24f4a565e8"
+dependencies = [
+ "log",
+ "z3-sys",
+]
+
+[[package]]
+name = "z3-sys"
+version = "0.8.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "d7cf70fdbc0de3f42b404f49b0d4686a82562254ea29ff0a155eef2f5430f4b0"
+dependencies = [
+ "bindgen",
+ "cmake",
+]
diff --git a/day-24/Cargo.toml b/day-24/Cargo.toml
new file mode 100644
index 0000000..f4f516d
--- /dev/null
+++ b/day-24/Cargo.toml
@@ -0,0 +1,13 @@
+[package]
+name = "day-24"
+version = "0.0.0"
+edition = "2021"
+
+# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
+
+[dependencies]
+itertools.workspace = true
+z3 = { version = "0.12.1", features = ["static-link-z3"] }
+
+[dev-dependencies]
+indoc.workspace = true
diff --git a/day-24/src/bin/input.txt b/day-24/src/bin/input.txt
new file mode 100644
index 0000000..401ed3c
--- /dev/null
+++ b/day-24/src/bin/input.txt
@@ -0,0 +1,300 @@
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+140281527306384, 277203155310618, 215785023894705 @ 15, 74, 161
+125895940497717, 289148791789134, 219122385224471 @ -20, -21, 147
+222155415164452, 279343831751648, 313610122440516 @ 53, -7, -62
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+372818488317164, 160016949117932, 387528673761549 @ -13, 115, -62
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+402092593050376, 247922330486591, 225079592544760 @ -55, 20, 116
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+133444165348728, 201763049380494, 288604925265459 @ 239, 106, 18
+106473419377620, 50451563918772, 246653752724433 @ 280, 350, 80
+174121409676891, 270674148087029, 278685236891477 @ 64, 34, -67
+171823955955694, 316694853209238, 231791964383255 @ 32, -132, 78
+260440517718208, 293039127874936, 237454004720008 @ 105, -31, 102
+477479812815169, 295719226979516, 484856995674445 @ -198, -35, -219
+210885150412920, 265959892267716, 277060875790365 @ 68, 21, 6
+247691524224231, 206017588288228, 354754164228682 @ 10, 133, -136
+349531458052309, 279152703128938, 304491414426810 @ 44, -17, 40
+258699283396533, 244044053202236, 479977269589363 @ -14, 61, -381
+368419720280954, 213077580485903, 375491525877885 @ 15, 50, -35
+368359482108805, 276938463575491, 319237362482943 @ 8, -14, 19
+231773269756038, 323018130216816, 296319685745647 @ 34, -93, -28
+387341264732292, 289502736377988, 203220796273077 @ 5, -27, 138
+236067436014778, 62693609266136, 349240847094177 @ 134, 227, -23
+424411221646508, 230847941181580, 269681048557249 @ -84, 40, 65
+157391625464718, 273639971939388, 153080768601069 @ -32, 73, 547
\ No newline at end of file
diff --git a/day-24/src/bin/part1.rs b/day-24/src/bin/part1.rs
new file mode 100644
index 0000000..37f12ed
--- /dev/null
+++ b/day-24/src/bin/part1.rs
@@ -0,0 +1,164 @@
+use itertools::Itertools;
+
+fn main() {
+    println!(
+        "{}",
+        part1(
+            include_str!("./input.txt"),
+            200_000_000_000_000,
+            400_000_000_000_000
+        )
+    );
+}
+
+fn part1(input: &str, min: i128, max: i128) -> usize {
+    let hailstones = input.lines().map(Hailstone::from).collect::<Vec<_>>();
+
+    let combinations = hailstones
+        .into_iter()
+        .combinations(2)
+        .map(|v| (v[0], v[1]))
+        .collect::<Vec<_>>();
+
+    let intersections = combinations
+        .into_iter()
+        .filter_map(|(a, b)| {
+            if let Some((x, y)) = a.intersection(&b) {
+                // intersection is in past
+                if i128::signum(x - a.x) != i128::signum(a.dx)
+                    || i128::signum(x - b.x) != i128::signum(b.dx)
+                    || i128::signum(y - a.y) != i128::signum(a.dy)
+                    || i128::signum(y - b.y) != i128::signum(b.dy)
+                {
+                    None
+                } else if x >= min && x <= max && y >= min && y <= max {
+                    // intersection is in the specified area
+                    Some((x, y))
+                } else {
+                    // intersection is not in the specified area
+                    None
+                }
+            } else {
+                // no intersection
+                None
+            }
+        })
+        .collect::<Vec<_>>();
+
+    intersections.len()
+}
+
+#[derive(Debug, PartialEq, Clone, Copy)]
+struct Hailstone {
+    x: i128,
+    y: i128,
+    z: i128,
+    dx: i128,
+    dy: i128,
+    dz: i128,
+}
+impl Hailstone {
+    fn new(x: i128, y: i128, z: i128, dx: i128, dy: i128, dz: i128) -> Self {
+        Self {
+            x,
+            y,
+            z,
+            dx,
+            dy,
+            dz,
+        }
+    }
+
+    fn to_line(self) -> (i128, i128, i128) {
+        let a = self.dy;
+        let b = -self.dx;
+        let c = self.dx * self.y - self.dy * self.x;
+        (a, b, c)
+    }
+
+    fn intersection(&self, other: &Self) -> Option<(i128, i128)> {
+        let (a1, b1, c1) = self.to_line();
+        let (a2, b2, c2) = other.to_line();
+
+        if (a1 * b2 - a2 * b1) == 0 {
+            return None;
+        }
+
+        let x = (b1 * c2 - b2 * c1) / (a1 * b2 - a2 * b1);
+        let y = (c1 * a2 - c2 * a1) / (a1 * b2 - a2 * b1);
+
+        Some((x, y))
+    }
+}
+impl From<&str> for Hailstone {
+    fn from(value: &str) -> Self {
+        let (pos, vel) = value.split_once(" @ ").expect("no @ symbol");
+        let mut pos = pos.split(", ");
+        let mut vel = vel.split(", ");
+
+        let x = pos
+            .next()
+            .expect("no x")
+            .trim()
+            .parse::<i128>()
+            .expect("x not a number");
+        let y = pos
+            .next()
+            .expect("no y")
+            .trim()
+            .parse::<i128>()
+            .expect("y not a number");
+        let z = pos
+            .next()
+            .expect("no z")
+            .trim()
+            .parse::<i128>()
+            .expect("z not a number");
+        let dx = vel
+            .next()
+            .expect("no dx")
+            .trim()
+            .parse::<i128>()
+            .expect("dx not a number");
+        let dy = vel
+            .next()
+            .expect("no dy")
+            .trim()
+            .parse::<i128>()
+            .expect("dy not a number");
+        let dz = vel
+            .next()
+            .expect("no dz")
+            .trim()
+            .parse::<i128>()
+            .expect("dz not a number");
+
+        Hailstone::new(x, y, z, dx, dy, dz)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use indoc::indoc;
+
+    #[test]
+    fn test_part1() {
+        assert_eq!(
+            part1(
+                indoc!(
+                    "
+                    19, 13, 30 @ -2,  1, -2
+                    18, 19, 22 @ -1, -1, -2
+                    20, 25, 34 @ -2, -2, -4
+                    12, 31, 28 @ -1, -2, -1
+                    20, 19, 15 @  1, -5, -3
+                    "
+                ),
+                7,
+                27
+            ),
+            2
+        );
+    }
+}
diff --git a/day-24/src/bin/part2.rs b/day-24/src/bin/part2.rs
new file mode 100644
index 0000000..e32ddc5
--- /dev/null
+++ b/day-24/src/bin/part2.rs
@@ -0,0 +1,141 @@
+use z3::{
+    ast::{Ast, Int},
+    Config, Context, SatResult, Solver,
+};
+
+fn main() {
+    println!("{}", part2(include_str!("./input.txt"),));
+}
+
+fn part2(input: &str) -> i64 {
+    let hailstones = input.lines().map(Hailstone::from).collect::<Vec<_>>();
+
+    let cfg = Config::new();
+    let context = Context::new(&cfg);
+    let solver = Solver::new(&context);
+
+    let x = Int::new_const(&context, "x");
+    let y = Int::new_const(&context, "y");
+    let z = Int::new_const(&context, "z");
+    let dx = Int::new_const(&context, "dx");
+    let dy = Int::new_const(&context, "dy");
+    let dz = Int::new_const(&context, "dz");
+
+    // add assertions for every hailstone
+    for (i, hailstone) in hailstones.iter().take(3).enumerate() {
+        let a = Int::from_i64(&context, hailstone.x.try_into().unwrap());
+        let da = Int::from_i64(&context, hailstone.dx.try_into().unwrap());
+        let b = Int::from_i64(&context, hailstone.y.try_into().unwrap());
+        let db = Int::from_i64(&context, hailstone.dy.try_into().unwrap());
+        let c = Int::from_i64(&context, hailstone.z.try_into().unwrap());
+        let dc = Int::from_i64(&context, hailstone.dz.try_into().unwrap());
+
+        // add assertions that the hailstone is at the given position at time t
+        let t = Int::new_const(&context, "t".to_string() + &i.to_string());
+        solver.assert(&t.gt(&z3::ast::Int::from_i64(&context, 0)));
+        solver.assert(&(x.clone() + dx.clone() * t.clone())._eq(&(a + da * t.clone())));
+        solver.assert(&(y.clone() + dy.clone() * t.clone())._eq(&(b + db * t.clone())));
+        solver.assert(&(z.clone() + dz.clone() * t.clone())._eq(&(c + dc * t.clone())));
+    }
+
+    if solver.check() == SatResult::Sat {
+        if let Some(m) = solver.get_model() {
+            // get the sum of the x,y,z coordinates of the starting position
+            m.eval(&(x + y + z), true).unwrap().as_i64().unwrap()
+        } else {
+            panic!("Failed to solve!");
+        }
+    } else {
+        panic!("Failed to check")
+    }
+}
+
+#[derive(Debug, PartialEq, Clone, Copy)]
+struct Hailstone {
+    x: i128,
+    y: i128,
+    z: i128,
+    dx: i128,
+    dy: i128,
+    dz: i128,
+}
+impl Hailstone {
+    fn new(x: i128, y: i128, z: i128, dx: i128, dy: i128, dz: i128) -> Self {
+        Self {
+            x,
+            y,
+            z,
+            dx,
+            dy,
+            dz,
+        }
+    }
+}
+impl From<&str> for Hailstone {
+    fn from(value: &str) -> Self {
+        let (pos, vel) = value.split_once(" @ ").expect("no @ symbol");
+        let mut pos = pos.split(", ");
+        let mut vel = vel.split(", ");
+
+        let x = pos
+            .next()
+            .expect("no x")
+            .trim()
+            .parse::<i128>()
+            .expect("x not a number");
+        let y = pos
+            .next()
+            .expect("no y")
+            .trim()
+            .parse::<i128>()
+            .expect("y not a number");
+        let z = pos
+            .next()
+            .expect("no z")
+            .trim()
+            .parse::<i128>()
+            .expect("z not a number");
+        let dx = vel
+            .next()
+            .expect("no dx")
+            .trim()
+            .parse::<i128>()
+            .expect("dx not a number");
+        let dy = vel
+            .next()
+            .expect("no dy")
+            .trim()
+            .parse::<i128>()
+            .expect("dy not a number");
+        let dz = vel
+            .next()
+            .expect("no dz")
+            .trim()
+            .parse::<i128>()
+            .expect("dz not a number");
+
+        Hailstone::new(x, y, z, dx, dy, dz)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use indoc::indoc;
+
+    #[test]
+    fn test_part2() {
+        assert_eq!(
+            part2(indoc!(
+                "
+                    19, 13, 30 @ -2,  1, -2
+                    18, 19, 22 @ -1, -1, -2
+                    20, 25, 34 @ -2, -2, -4
+                    12, 31, 28 @ -1, -2, -1
+                    20, 19, 15 @  1, -5, -3
+                    "
+            )),
+            47
+        );
+    }
+}