[rs] Optimize 2022_15

rs/src/y2022/d15.rs

@@ -1,5 +1,6 @@
 use std::collections::HashSet;
 
+#[derive(Clone, Copy)]
 struct Sensor {
     pos: (i32, i32),
     beac: (i32, i32),
@@ -14,6 +15,12 @@ fn parse_coord(coord: &str) -> i32 {
 fn line_ranges(sensors: &[Sensor], y: i32) -> Vec<(i32, i32)> {
     let mut raw_ranges = vec![];
     for sensor in sensors {
+        // A beacon exactly dist away has 1 field, i. e. x±0
+        // A beacon exactly dist-1 away has 3 fields, i. e. x±1
+        // ...
+        // A beacon exactly 0 away has 2dist+1 fields, i. e. x±dist
+        //
+        // Formula: Go from x-(dist-dy) to x+(dist-dy)
         let dy = (y - sensor.pos.1).abs();
         if dy > sensor.dist {
             continue;
@@ -39,16 +46,49 @@ fn line_ranges(sensors: &[Sensor], y: i32) -> Vec<(i32, i32)> {
     ranges
 }
 
+fn intersect_lines(tlbr: (i32, i32, i32, i32), trbl: (i32, i32, i32, i32)) -> Option<(i32, i32)> {
+    // For tlbr lines, x1 - y1 = x2 - y2 = x - y = c.
+    // For trbl lines, x1 + y1 = x2 + y2 = x + y = c.
+    assert_eq!(tlbr.0 - tlbr.1, tlbr.2 - tlbr.3);
+    assert_eq!(trbl.0 + trbl.1, trbl.2 + trbl.3);
+    let c_tlbr = tlbr.0 - tlbr.1;
+    let c_trbl = trbl.0 + trbl.1;
+
+    // Find x, y such that
+    // x - y = c_tlbr
+    // x + y = c_trbl
+    //
+    // 2x = c_tlbr + c_trbl
+    // y = c_trbl - x
+    let two_x = c_tlbr + c_trbl;
+    if two_x.rem_euclid(2) != 0 {
+        return None; // Intersection not at integer coordinates
+    }
+    let x = two_x / 2;
+    let y = c_trbl - x;
+    assert_eq!(x - y, c_tlbr);
+    assert_eq!(x + y, c_trbl);
+
+    // Finally, check if the result is on both line segments. We only need to
+    // check one dimension per line segment.
+    let on_tlbr = tlbr.1 <= y && y <= tlbr.3;
+    let on_trbl = trbl.1 <= y && y <= trbl.3;
+    if on_tlbr && on_trbl {
+        Some((x, y))
+    } else {
+        None
+    }
+}
+
+fn covered_by(sensor: Sensor, pos: (i32, i32)) -> bool {
+    let dist = (pos.0 - sensor.pos.0).abs() + (pos.1 - sensor.pos.1).abs();
+    dist <= sensor.dist
+}
+
 pub fn solve(input: String) {
     let sensors = input
         .lines()
         .map(|l| {
-            // A beacon exactly dist away has 1 field, i. e. x±0
-            // A beacon exactly dist-1 away has 3 fields, i. e. x±1
-            // ...
-            // A beacon exactly 0 away has 2dist+1 fields, i. e. x±dist
-            //
-            // Formula: Go from x-(dist-dy) to x+(dist-dy)
             let parts = l.split_whitespace().collect::<Vec<_>>();
             let pos = (parse_coord(parts[2]), parse_coord(parts[3]));
             let beac = (parse_coord(parts[8]), parse_coord(parts[9]));
@@ -75,16 +115,40 @@ pub fn solve(input: String) {
     }
     println!("Part 1: {part1}");
 
-    for y in 0..=4000000 {
-        let mut ranges = line_ranges(&sensors, y);
-        ranges.retain(|(s, e)| *s <= 4000000 && 0 <= *e);
-        if ranges.len() != 1 {
-            // Found our beacon!
-            assert_eq!(ranges.len(), 2);
-            let x = ranges[0].1 + 1;
-            let tuning_frequency = x as i64 * 4000000 + y as i64;
-            println!("Part 2: {tuning_frequency}");
+    let mut lines_tlbr = vec![];
+    let mut lines_trbl = vec![];
+    for sensor in &sensors {
+        let d = sensor.dist;
+        let p = sensor.pos;
+        lines_tlbr.push((p.0, p.1 - d - 1, p.0 + d + 1, p.1));
+        lines_tlbr.push((p.0 - d - 1, p.1, p.0, p.1 + d + 1));
+        lines_trbl.push((p.0, p.1 - d - 1, p.0 - d - 1, p.1));
+        lines_trbl.push((p.0 + d + 1, p.1, p.0, p.1 + d + 1));
+    }
+
+    for tlbr in &lines_tlbr {
+        for trbl in &lines_trbl {
+            if let Some(intersect) = intersect_lines(*tlbr, *trbl) {
+                let x_in_bounds = 0 <= intersect.0 && intersect.0 <= 4000000;
+                let y_in_bounds = 0 <= intersect.1 && intersect.1 <= 4000000;
+                if !x_in_bounds || !y_in_bounds {
+                    continue;
+                }
+                let mut covered = false;
+                for sensor in &sensors {
+                    if covered_by(*sensor, intersect) {
+                        covered = true;
                         break;
                     }
                 }
+                if covered {
+                    continue;
+                }
+                // We found our candidate :)
+                let tuning_frequency = intersect.0 as i64 * 4000000 + intersect.1 as i64;
+                println!("Part 2: {tuning_frequency}");
+                return;
+            }
+        }
+    }
 }