Complete day 13

day-13/src/main.rs

@@ -9,7 +9,7 @@ fn main() -> Result<(), Box<dyn std::error::Error>> {
     println!("{}", (arrival - time) * earliest);
 
     // Part 2
-    let timestamp = find_incrementing(&ids);
+    let timestamp = find_gauss(&ids);
     println!("{}", timestamp);
 
     Ok(())
@@ -28,7 +28,7 @@ fn parse_notes(input: &str) -> Result<(u32, Vec<u32>), &str> {
         .next()
         .ok_or("Input too short")?
         .split(',')
-        .map(|id| id.parse().unwrap_or(0))
+        .map(|id| id.parse().unwrap_or(1))
         .collect();
 
     Ok((estimate, ids))
@@ -36,7 +36,7 @@ fn parse_notes(input: &str) -> Result<(u32, Vec<u32>), &str> {
 
 fn find_closest_bus(time: u32, ids: &Vec<u32>) -> (u32, u32) {
     ids.iter()
-        .filter(|id| **id != 0)
+        .filter(|id| **id != 1)
         .map(|id| {
             let mut arrival = *id;
 
@@ -50,48 +50,39 @@ fn find_closest_bus(time: u32, ids: &Vec<u32>) -> (u32, u32) {
         .expect("Must have at least one bus ID")
 }
 
-fn find_incrementing(ids: &Vec<u32>) -> u128 {
+fn find_gauss(ids: &Vec<u32>) -> u128 {
     let ids: Vec<u128> = ids.iter().map(|id| *id as u128).collect();
-    let (largest, increment) = ids
-        .iter()
-        .enumerate()
-        .max_by_key(|id| id.1)
-        .expect("Must have at least one bus ID");
+    let product: u128 = ids.iter().product();
 
-    let mut iterations = (14166999999493 - largest as u128) / increment;
+    let gauss = |mut n: u128, mut d: u128, m: u128| -> u128 {
+        while d != 1 {
+            if m == 1 {
+                return 0;
+            };
 
-    loop {
-        iterations += 1;
-        let max = increment * iterations;
-
-        if ids.iter().enumerate().rev().all(|(i, number)| {
-            if *number == 0 {
-                true
+            let multiplier = if m > d {
+                m / d + (m % d != 0) as u128
             } else {
-                let target = max - largest as u128 + i as u128;
-                target % number == 0
-            }
-        }) {
-            break max - largest as u128;
-        } else {
-            if iterations % 100000000 == 0 {
-                let fun = ids
-                    .iter()
-                    .enumerate()
-                    .filter(|(i, number)| {
-                        if **number == 0 {
-                            true
-                        } else {
-                            let target = max - largest as u128 + *i as u128;
-                            target % **number == 0
+                1
+            };
+
+            n = (n * multiplier) % m;
+            d = (d * multiplier) % m;
         }
+
+        n / d
+    };
+
+    (0..ids.len())
+        .map(|a| {
+            let b = product / ids[a];
+            let bi = gauss(1, b, ids[a]);
+            let a = (ids[a] * a as u128 - a as u128) % ids[a] as u128;
+
+            a * b * bi
         })
-                    .count();
-
-                println!("{} - {}/{}", max - largest as u128, fun, ids.len());
-            }
-        }
-    }
+        .sum::<u128>()
+        % product
 }
 
 #[cfg(test)]
@@ -124,7 +115,7 @@ mod tests {
         );
 
         let (time, ids) = parse_notes(input)?;
-        let timestamp = find_incrementing(&ids);
+        let timestamp = find_gauss(&ids);
 
         assert_eq!(timestamp, 3417);
 
@@ -140,7 +131,7 @@ mod tests {
         );
 
         let (time, ids) = parse_notes(input)?;
-        let timestamp = find_incrementing(&ids);
+        let timestamp = find_gauss(&ids);
 
         assert_eq!(timestamp, 1068781);
 
@@ -156,7 +147,7 @@ mod tests {
         );
 
         let (time, ids) = parse_notes(input)?;
-        let timestamp = find_incrementing(&ids);
+        let timestamp = find_gauss(&ids);
 
         assert_eq!(timestamp, 754018);
 
@@ -172,7 +163,7 @@ mod tests {
         );
 
         let (time, ids) = parse_notes(input)?;
-        let timestamp = find_incrementing(&ids);
+        let timestamp = find_gauss(&ids);
 
         assert_eq!(timestamp, 779210);