simplify

src/2023/day24.js

@@ -1,37 +1,3 @@
-function parse(input) {
-  return input.split('\n').map(line => {
-    let [point, velocity] = line.split(' @ ');
-    point = point.split(', ').map(n => +n);
-    velocity = velocity.split(', ').map(n => +n);
-    return { point, velocity };
-  });
-}
-
-export function part1(input, min = 2e14, max = 4e14) {
-  let hails = parse(input);
-  hails = hails.map(({ point, velocity }) => {
-    let point2 = point.map((n, i) => n + velocity[i]);
-    let m = (point[1] - point2[1]) / (point[0] - point2[0]);
-    let n = point[1] - m * point[0];
-    return { point, velocity, m, n };
-  });
-  let result = 0;
-  for (let i = 0; i < hails.length; i++) {
-    for (let j = i + 1; j < hails.length; j++) {
-      let { m: m1, n: n1 } = hails[i];
-      let { m: m2, n: n2 } = hails[j];
-      let x = (n2 - n1) / (m1 - m2);
-      let y = m1 * x + n1;
-      if (x > min && x < max && y > min && y < max) {
-        if ((x - hails[i].point[0]) / hails[i].velocity[0] < 0) continue;
-        if ((x - hails[j].point[0]) / hails[j].velocity[0] < 0) continue;
-        result++;
-      }
-    }
-  }
-  return result;
-}
-
 // 1) px0 + vx0 t0 = pxr + vxr t0
 // 2) py0 + vy0 t0 = pyr + vyr t0
 // 1) t0 = (pxr - px0) / (vx0 - vxr)
@@ -70,6 +36,34 @@ function cramer(A, B) {
   return A.map((_, i) => det(A.map((r, j) => r.toSpliced(i, 1, B[j]))) / detA);
 }
 
+// 1) px1 + vx1 t1 = px2 + vx2 t2
+// 2) py1 + vy1 t1 = py2 + vy2 t2
+// 1) t1 vx1 - t2 vx2 = px2 - px1
+// 2) t1 vy1 - t2 vy2 = py2 - py1
+export function part1(input, min = 2e14, max = 4e14) {
+  let hails = input.split('\n').map(line => line.match(/-?\d+/g).map(BigInt));
+  let result = 0;
+  for (let i = 0; i < hails.length; i++) {
+    for (let j = i + 1; j < hails.length; j++) {
+      const [px1, py1, , vx1, vy1] = hails[i];
+      const [px2, py2, , vx2, vy2] = hails[j];
+      const A = [
+        [vx1, -vx2],
+        [vy1, -vy2],
+      ];
+      const B = [px2 - px1, py2 - py1];
+      if (det(A) === 0n) continue;
+      const [t1, t2] = cramer(A, B);
+      const x = px1 + vx1 * t1;
+      const y = py1 + vy1 * t1;
+      if (t1 > 0 && t2 > 0 && x > min && x < max && y > min && y < max) {
+        result++;
+      }
+    }
+  }
+  return result;
+}
+
 export function part2(input) {
   const hails = input.split('\n').map(line => line.match(/-?\d+/g).map(BigInt));
   const A = [];
@@ -82,7 +76,6 @@ export function part2(input) {
 // import { init } from 'z3-solver';
 // export async function part2(input) {
 //   const hails = parse(input);
-
 //   const { Context } = await init();
 //   const { Solver, Int } = Context('main');
 //   const solver = new Solver();