13/2024

Author: breadadams

2024/13/index.ts

@@ -0,0 +1,127 @@
+import { getPuzzle } from "../../utils";
+
+const puzzleInput = getPuzzle(__dirname).trim();
+
+const configs = puzzleInput.split("\n\n").map((prizeConfig) => {
+  const [buttonA, buttonB, prize] = prizeConfig.split("\n");
+
+  const [buttonAX, buttonAY] = buttonA
+    .replace("Button A: X+", "")
+    .replace("Y+", "")
+    .split(", ")
+    .map(Number);
+
+  const [buttonBX, buttonBY] = buttonB
+    .replace("Button B: X+", "")
+    .replace("Y+", "")
+    .split(", ")
+    .map(Number);
+
+  const [prizeX, prizeY] = prize
+    .replace("Prize: X=", "")
+    .replace("Y=", "")
+    .split(", ")
+    .map(Number);
+
+  return {
+    buttonA: { x: buttonAX, y: buttonAY },
+    buttonB: { x: buttonBX, y: buttonBY },
+    prize: { x: prizeX, y: prizeY },
+  };
+});
+
+// Part 1
+(() => {
+  console.time("part 1");
+  let tokensSpent = 0;
+
+  for (const config of configs) {
+    let lowestTokenCount: number = undefined;
+    let currentTokenCount = 0;
+    let x = 0;
+    let y = 0;
+
+    while (true) {
+      if (x > config.prize.x || y > config.prize.y) {
+        break;
+      }
+
+      x += config.buttonA.x;
+      y += config.buttonA.y;
+      currentTokenCount += 3;
+
+      const remainingX = config.prize.x - x;
+      const remainingY = config.prize.y - y;
+
+      if (
+        remainingX % config.buttonB.x === 0 &&
+        remainingY % config.buttonB.y === 0 &&
+        remainingX / config.buttonB.x === remainingY / config.buttonB.y
+      ) {
+        const buttonBCost = remainingX / config.buttonB.x;
+
+        if (
+          typeof lowestTokenCount === "undefined" ||
+          buttonBCost + currentTokenCount < lowestTokenCount
+        ) {
+          lowestTokenCount = buttonBCost + currentTokenCount;
+        }
+      }
+    }
+
+    if (lowestTokenCount) {
+      tokensSpent += lowestTokenCount;
+    }
+  }
+
+  console.log("part 1 tokens spent ::", tokensSpent);
+  console.timeEnd("part 1");
+})();
+
+// Part 2
+(() => {
+  console.time("part 2");
+  let tokensSpent = 0;
+
+  const EXTRA_DISTANCE = 10000000000000;
+
+  for (const config of configs) {
+    /*
+     * [Cramer's Rule for a 2x2 system]
+     *
+     * a = a button presses
+     * ax & ay = a button distances
+     * b = b button presses
+     * bx & by = b button distances
+     * cx & cy = prize position
+     *
+     * (a*ax) + (b*bx) = cx
+     * (a*ay) + (b*by) = cy
+     *
+     * a = (by*cx - bx*cy) / (ax*by - ay*bx)
+     * b = (ax*cy - ay*cx) / (ax*by - ay*bx)
+     */
+
+    const prizeX = config.prize.x + EXTRA_DISTANCE;
+    const prizeY = config.prize.y + EXTRA_DISTANCE;
+
+    const divisor =
+      config.buttonA.x * config.buttonB.y - config.buttonA.y * config.buttonB.x;
+
+    const aPresses =
+      (config.buttonB.y * prizeX - config.buttonB.x * prizeY) / divisor;
+
+    const bPresses =
+      (config.buttonA.x * prizeY - config.buttonA.y * prizeX) / divisor;
+
+    if (
+      Math.floor(aPresses) === aPresses &&
+      Math.floor(bPresses) === bPresses
+    ) {
+      tokensSpent += aPresses * 3 + bPresses;
+    }
+  }
+
+  console.log("part 2 tokens spent ::", tokensSpent);
+  console.timeEnd("part 2");
+})();

README.md

@@ -6,6 +6,7 @@
 
 |                    Day                     | Part 1 | Part 2 |
 | :----------------------------------------: | :----: | :----: |
+| [13](https://adventofcode.com/2024/day/13) |   ✅   |   ✅   |
 | [12](https://adventofcode.com/2024/day/12) |   ✅   |   ✅   |
 | [11](https://adventofcode.com/2024/day/11) |   ✅   |   ✅   |
 | [10](https://adventofcode.com/2024/day/10) |   ✅   |   ✅   |