2017 day 13

Author: ictrobot

crates/utils/src/number.rs

@@ -255,6 +255,23 @@ pub fn egcd<T: SignedInteger>(mut a: T, mut b: T) -> (T, T, T) {
     (a, x0, y0)
 }
 
+/// Computes the lowest common multiple (LCM).
+///
+/// # Examples
+/// ```
+/// # use utils::number::lcm;
+/// assert_eq!(lcm(6, 4), 12);
+/// assert_eq!(lcm(21, 6), 42);
+/// ```
+pub fn lcm<T: SignedInteger>(a: T, b: T) -> T {
+    if a == T::ZERO || b == T::ZERO {
+        return T::ZERO;
+    }
+
+    let (gcd, ..) = egcd(a, b);
+    (a / gcd).abs() * b.abs()
+}
+
 /// Computes the modular inverse of `a` modulo `b` if it exists.
 ///
 /// # Examples

crates/year2017/src/day13.rs

@@ -0,0 +1,76 @@
+use std::collections::BTreeMap;
+use utils::number;
+use utils::prelude::*;
+
+/// Finding the gap in the firewall.
+///
+/// Similar to [2016 day 15](../year2016/struct.Day15.html), but instead of a system of linear
+/// simultaneous congruences, it is a system of simultaneous modular inequalities.
+#[derive(Clone, Debug)]
+pub struct Day13 {
+    layers: Vec<(u32, u32)>,
+}
+
+impl Day13 {
+    pub fn new(input: &str, _: InputType) -> Result<Self, InputError> {
+        Ok(Self {
+            layers: parser::u32()
+                .with_suffix(": ")
+                .then(parser::u32())
+                .parse_lines(input)?,
+        })
+    }
+
+    #[must_use]
+    pub fn part1(&self) -> u32 {
+        self.layers
+            .iter()
+            .map(|&(depth, range)| {
+                let period = (range - 1) * 2;
+                if depth % period == 0 {
+                    depth * range
+                } else {
+                    0
+                }
+            })
+            .sum()
+    }
+
+    #[must_use]
+    pub fn part2(&self) -> u32 {
+        // Each key represents a modulus and maps to a list of values where
+        // delay % modulus can't equal the value
+        let mut constraints = BTreeMap::new();
+        for &(depth, range) in &self.layers {
+            let modulus = (range as i32 - 1) * 2;
+            let disallowed_value = (-(depth as i32)).rem_euclid(modulus);
+
+            constraints
+                .entry(modulus)
+                .or_insert_with(Vec::new)
+                .push(disallowed_value);
+        }
+
+        // Find all the possible delays % lcm which meet the above constraints
+        let mut lcm = 1;
+        let mut possible_delays = vec![0];
+        for (modulus, disallowed_values) in constraints {
+            let new_lcm = number::lcm(modulus, lcm);
+            possible_delays = possible_delays
+                .into_iter()
+                .flat_map(|delay| {
+                    (delay..new_lcm)
+                        .step_by(lcm as usize)
+                        .filter(|&i| !disallowed_values.contains(&(i % modulus)))
+                })
+                .collect();
+            lcm = new_lcm;
+        }
+
+        *possible_delays.iter().min().unwrap() as u32
+    }
+}
+
+examples!(Day13 -> (u32, u32) [
+    {input: "0: 3\n1: 2\n4: 4\n6: 4", part1: 24, part2: 10},
+]);

crates/year2017/src/lib.rs

@@ -14,4 +14,5 @@ utils::year!(2017 => year2017, ${
     10 => day10::Day10<'_>,
     11 => day11::Day11,
     12 => day12::Day12,
+    13 => day13::Day13,
 });