Day 13

day13.peggy

@@ -0,0 +1,9 @@
+machines = machine|.., "\n"|
+
+machine = button button prize
+
+button = "Button" _ [AB] ":" _ "X+" @num _ "," _  "Y+" _ @num "\n"
+prize = "Prize:" _ "X=" @num _ "," _ "Y=" _ @num "\n"
+
+num = n:$[0-9]+ { return parseInt(n, 10) }
+_ = [ \t]*

day13.ts

@@ -0,0 +1,38 @@
+import { type MainArgs, parseFile } from './lib/utils.ts';
+
+type Parsed = number[][][];
+
+function cranmer(coeff: number[]): number {
+  const [x0, y0, c0, x1, y1, c1] = coeff;
+  // Cranmer's rule
+  const D = x0 * y1 - y0 * x1;
+  const Dx = c0 * y1 - y0 * c1;
+  const Dy = x0 * c1 - c0 * x1;
+  if ((Dx % D) || (Dy % D)) {
+    return 0;
+  }
+  const x = Dx / D;
+  const y = Dy / D;
+  return (3 * x) + y;
+}
+
+function part1(inp: Parsed): number {
+  return inp.reduce(
+    (t, [[x0, x1], [y0, y1], [c0, c1]]) =>
+      t + cranmer([x0, y0, c0, x1, y1, c1]),
+    0,
+  );
+}
+
+function part2(inp: Parsed): number {
+  return inp.reduce(
+    (t, [[x0, x1], [y0, y1], [c0, c1]]) =>
+      t + cranmer([x0, y0, c0 + 10000000000000, x1, y1, c1 + 10000000000000]),
+    0,
+  );
+}
+
+export default async function main(args: MainArgs): Promise<[number, number]> {
+  const inp = await parseFile<Parsed>(args);
+  return [part1(inp), part2(inp)];
+}

lib/utils.ts

@@ -211,6 +211,62 @@ export function divmod<T extends number | bigint>(x: T, y: T): [T, T] {
   return [Math.floor(q) as T, r];
 }
 
+export function abs<T extends number | bigint>(a: T): T {
+  if (typeof a === 'bigint') {
+    return (a < 0 ? -a : a) as T;
+  }
+  return Math.abs(a) as T;
+}
+
+export function sign<T extends number | bigint>(a: T): T {
+  if (typeof a === 'bigint') {
+    if (a === 0n) {
+      return 0n as T;
+    }
+    return ((a < 0n) ? -1n : 1n) as T;
+  }
+  return Math.sign(a) as T;
+}
+
+export function egcd<T extends number | bigint>(
+  a: T,
+  b: T,
+): [gcd: T, a: T, b: T] {
+  const bi = typeof a === 'bigint';
+  let s0 = (bi ? 1n : 1) as T;
+  let s1 = (bi ? 0n : 0) as T;
+  let t0 = s1;
+  let t1 = s0;
+  const sa = sign(a);
+  const sb = sign(b);
+
+  // Needs to work for both 0 and 0n
+  // deno-lint-ignore eqeqeq
+  if (a == 0) {
+    return [b, s1, t1];
+  }
+  if (!bi) {
+    if ((isNaN(a as number) || isNaN(b as number))) {
+      return [NaN as T, NaN as T, NaN as T];
+    }
+    if ((!isFinite(a as number) || !isFinite(b as number))) {
+      return [Infinity as T, Infinity as T, Infinity as T];
+    }
+  }
+
+  a = abs(a);
+  b = abs(b);
+
+  // deno-lint-ignore eqeqeq
+  while (b != 0) {
+    const [q, r] = divmod(a, b);
+    [s0, s1] = [s1, (s0 - (q * s1)) as T];
+    [t0, t1] = [t1, (t0 - (q * t1)) as T];
+    [a, b] = [b, r];
+  }
+  return [a, sa * s0 as T, sb * t0 as T];
+}
+
 export function gcd<T extends number | bigint>(...n: T[]): T {
   switch (n.length) {
     case 0:

test/day13.js

@@ -0,0 +1 @@
+export default [40069, 71493195288102];