[WIP] Day 17 part 1 solved

2021-12-19 12:15:50 +01:00
parent da579fbfac
commit 2c3c1f8f08
3 changed files with 225 additions and 47 deletions
--- a/functions/package.json
+++ b/functions/package.json
@@ -7,7 +7,8 @@
    "shell": "npm run build && firebase functions:shell",
    "start": "npm run shell",
    "deploy": "firebase deploy --only functions",
-    "logs": "firebase functions:log"
+    "logs": "firebase functions:log",
+    "debug-day17": "ts-node src/day17.ts"
  },
  "engines": {
    "node": "16"
@@ -24,6 +25,7 @@
    "eslint-config-google": "^0.14.0",
    "eslint-plugin-import": "^2.22.0",
    "firebase-functions-test": "^0.2.0",
+    "ts-node": "^10.4.0",
    "typescript": "^3.8.0"
  },
  "private": true
--- a/functions/src/day17.ts
+++ b/functions/src/day17.ts
@@ -2,58 +2,74 @@ import Day from "./day";

 class Day17 implements Day {

+  // steps = 3
+  // y = 1 -> 1 + 0 + -1 = 0
+  // y = 2 -> 2 + 1 + 0 = 3
+  // y = 3 -> 3 + 2 + 1 = 6
+  // y = 4 -> 4 + 3 + 2 = 9
+  // y = 5 -> 5 + 4 + 3 = 12
+
+  // steps = 4
+  // y = 1 -> -2
+  // y = 2 -> 2
+  // y = 3 -> 6
+  // y = 4 -> 10
+
+  // y = 0
+  // steps = 1 -> 0            =  0
+  // steps = 2 -> 0 - 1       =  -1
+  // steps = 3 -> 0 - 1 - 2   =  -3
+  // steps = 4 -> 0 - 1- 2 - 3=  -6
+  // steps = 5 -> 0-1-2-3-4   = -10
+  // steps = 6 -> 0-1-2-3-4-5 = -15
+
+  // v = -1 * x
+
+  // Theoretically, the displacement should be:
+  // s(t) = s_0 + v_0 t + 1/2 a t^2
+  // Filling that in for s_0 = 0 and a = -1, we get:
+  // s(t) = v_0 t - 1/2 t ^ 2
+  // But that gives us non-integer values, for example when t = 3, we get: v_0 * 3 - 4.5
+
  part1(input: string[]): number | string {

    const targetArea = TargetArea.parse(input[0]);

-    // First we find all x-es between 1 and maxX + 1 (as all others will immediately overshoot), that overlap with the target at some points:
-    for (let x = 1; x <= targetArea.maxX + 1; x++) {
-      let curSpeed = x;
-      let curPosX = 0;
-      for (let step = 0; step < (targetArea.maxX + 1) / x; step++) {
+    // Assuming v_y0 > 0, the maximum height the probe reaches is triangle(y).
+    // After reaching the top, the probe starts falling back down, taking "v_y0" steps to get back to a height of 0.
+    // After that it has a speed of v_y0 - 1.

-        curPosX += curSpeed;
-        if (targetArea.isInX(curPosX)) {
-          // Find y's that given this position and step, match:
-          // TODO: find out which y's make sense to check
-          for (let y = 0; y < 100; y++) {
-            // steps = 3
-            // y = 1 -> 1 + 0 + -1 = 0
-            // y = 2 -> 2 + 1 + 0 = 3
-            // y = 3 -> 3 + 2 + 1 = 6
-            // y = 4 -> 4 + 3 + 2 = 9
-            // y = 5 -> 5 + 4 + 3 = 12
+    // Note that the triangle value of x must be at least the minimal x of the target area, otherwise the probe won't
+    // reach the target area before it's velocity reaches zero:
+    const vx0_min = this.triangleInvCeil(targetArea.minX);
+    // Calculate the x-position we reach after v_x0 steps:
+    const x_min = this.triangle(vx0_min);

-            // steps = 4
-            // y = 1 -> -2
-            // y = 2 -> 2
-            // y = 3 -> 6
-            // y = 4 -> 10
-
-            // y = 0
-            // steps = 1 -> 0            =  0
-            // steps = 2 -> 0 - 1       =  -1
-            // steps = 3 -> 0 - 1 - 2   =  -3
-            // steps = 4 -> 0 - 1- 2 - 3=  -6
-            // steps = 5 -> 0-1-2-3-4   = -10
-            // steps = 6 -> 0-1-2-3-4-5 = -15
-
-            // v = -1 * x
-            // pos = -.5 * steps^2 + y * steps
-
-            // f(s) = s * y +
-          }
-          const { maxY, finalY } = this.simulateY() 
-        } else if ( curPosX > targetArea.maxX || (curSpeed === 0 && curPosX < targetArea.minX)) {
-          break;
-        }
-        curSpeed--;
-      }
+    if (targetArea.isInX(x_min)) {
+      // We have an x-speed that reaches the target area in x_min steps and stays there (e.g. reaches velocity zero in the target area),
+      // so we can just find the biggest y that at some point ends up in the target area.
+      // We already know that the y speed when the "probe" comes down is:
+      // -v_y0 - 1
+      // So if we choose as starting y that is one higher than the minimal y value, we end up in the bottom of the target area, while reaching the maximum height:
+      const vy0_max = Math.abs(targetArea.minY) - 1;
+      return this.triangle(vy0_max);
+    } else {
+      throw Error("fuck :)");
    }
-
-    return 0;
  }

+  part2(input: string[]): number | string {
+
+    // So that means that the only y values that work are those for which two triangle numbers exists, between which the distance falls
+    // in the target area.
+    // Following this reasoning, we also know that y is inside the target area after (2 * v_y0) + { the number of triangle numbers between triangle(vy_0) and triangle(?) in y_range) }
+
+    const targetArea = TargetArea.parse(input[0]);
+
+
+    // TODO implement
+    return 0;
+  }
  simulateY(initialSpeedY: number, steps: number): { maxY: number, finalY: number} {

    let curSpeed = initialSpeedY;
@@ -69,9 +85,12 @@ class Day17 implements Day {
    return { finalY: y, maxY: maxY };
  }

-  part2(input: string[]): number | string {
-    // TODO implement
-    return 0;
+  triangle(n: number): number {
+    return (n*(n + 1)) / 2;
+  }
+
+  triangleInvCeil(x: number): number {
+    return Math.ceil((Math.sqrt(8 * x + 1) - 1) / 2);
  }

 }
@@ -121,3 +140,75 @@ class TargetArea {
 }

 export default Day17;
+
+const exampleInput = ["target area: x=20..30, y=-10..-5"];
+run(exampleInput);
+
+const input = ["target area: x=48..70, y=-189..-148"];
+run(input);
+
+
+function run(input: string[]) {
+  const day = new Day17();
+  console.log(`Part 1: ${day.part1(input)}`);
+  console.log(`Part 2: ${day.part2(input)}`);
+}
+
+
+// Archive:
+
+// const maxYs: number[] = [];
+// const yMinStepInTargets = [];
+// const yMaxStepInTargets = [];
+// // Array(100).fill([]);
+// // Let's first find the y values that reach the highest height and end up in the target area:
+// for (let vy0 = 0; vy0 < Math.abs(targetArea.minY) + 1; vy0++) {
+//
+//   let y = 0;
+//   const ys = [y];
+//   let vy = vy0;
+//   let yMinStepInTarget = -1;
+//   let yMaxStepInTarget = -1;
+//   let step = 0;
+//   while (y > targetArea.minY) {
+//     y += vy;
+//     ys.push(y);
+//     vy--;
+//     if (targetArea.isInY(y)) {
+//       if (yMinStepInTarget === -1) {
+//         yMinStepInTarget = step;
+//       }
+//       yMaxStepInTarget = step;
+//     }
+//     step++;
+//   }
+//   yMinStepInTargets.push(yMinStepInTarget)
+//   yMaxStepInTargets.push(yMaxStepInTarget)
+//   // yCache.push(ys);
+//   maxYs.push(Math.max(...ys));
+// }
+//
+// // Now we "greedily" go over the found y values
+//
+// // First we find all x-es between 1 and maxX + 1 (as all others will immediately overshoot), that overlap with the target at some points:
+// for (let x = 1; x <= targetArea.maxX + 1; x++) {
+//   let curSpeed = x;
+//   let curPosX = 0;
+//   for (let step = 0; step < (targetArea.maxX + 1) / x; step++) {
+//
+//     curPosX += curSpeed;
+//     if (targetArea.isInX(curPosX)) {
+//       // Find y's that given this position and step, match:
+//       // TODO: find out which y's make sense to check
+//       for (let y = 0; y < 100; y++) {
+//
+//
+//         // f(s) = s * y +
+//       }
+//       const { maxY, finalY } = this.simulateY()
+//     } else if ( curPosX > targetArea.maxX || (curSpeed === 0 && curPosX < targetArea.minX)) {
+//       break;
+//     }
+//     curSpeed--;
+//   }
+// }
--- a/functions/yarn.lock
+++ b/functions/yarn.lock
@@ -23,6 +23,18 @@
    chalk "^2.0.0"
    js-tokens "^4.0.0"

+"@cspotcode/source-map-consumer@0.8.0":
+  version "0.8.0"
+  resolved "https://registry.yarnpkg.com/@cspotcode/source-map-consumer/-/source-map-consumer-0.8.0.tgz#33bf4b7b39c178821606f669bbc447a6a629786b"
+  integrity sha512-41qniHzTU8yAGbCp04ohlmSrZf8bkf/iJsl3V0dRGsQN/5GFfx+LbCSsCpp2gqrqjTVg/K6O8ycoV35JIwAzAg==
+
+"@cspotcode/source-map-support@0.7.0":
+  version "0.7.0"
+  resolved "https://registry.yarnpkg.com/@cspotcode/source-map-support/-/source-map-support-0.7.0.tgz#4789840aa859e46d2f3173727ab707c66bf344f5"
+  integrity sha512-X4xqRHqN8ACt2aHVe51OxeA2HjbcL4MqFqXkrmQszJ1NOUuUu5u6Vqx/0lZSVNku7velL5FC/s5uEAj1lsBMhA==
+  dependencies:
+    "@cspotcode/source-map-consumer" "0.8.0"
+
 "@eslint/eslintrc@^0.4.3":
  version "0.4.3"
  resolved "https://registry.yarnpkg.com/@eslint/eslintrc/-/eslintrc-0.4.3.tgz#9e42981ef035beb3dd49add17acb96e8ff6f394c"
@@ -278,6 +290,26 @@
  resolved "https://registry.yarnpkg.com/@tootallnate/once/-/once-2.0.0.tgz#f544a148d3ab35801c1f633a7441fd87c2e484bf"
  integrity sha512-XCuKFP5PS55gnMVu3dty8KPatLqUoy/ZYzDzAGCQ8JNFCkLXzmI7vNHCR+XpbZaMWQK/vQubr7PkYq8g470J/A==

+"@tsconfig/node10@^1.0.7":
+  version "1.0.8"
+  resolved "https://registry.yarnpkg.com/@tsconfig/node10/-/node10-1.0.8.tgz#c1e4e80d6f964fbecb3359c43bd48b40f7cadad9"
+  integrity sha512-6XFfSQmMgq0CFLY1MslA/CPUfhIL919M1rMsa5lP2P097N2Wd1sSX0tx1u4olM16fLNhtHZpRhedZJphNJqmZg==
+
+"@tsconfig/node12@^1.0.7":
+  version "1.0.9"
+  resolved "https://registry.yarnpkg.com/@tsconfig/node12/-/node12-1.0.9.tgz#62c1f6dee2ebd9aead80dc3afa56810e58e1a04c"
+  integrity sha512-/yBMcem+fbvhSREH+s14YJi18sp7J9jpuhYByADT2rypfajMZZN4WQ6zBGgBKp53NKmqI36wFYDb3yaMPurITw==
+
+"@tsconfig/node14@^1.0.0":
+  version "1.0.1"
+  resolved "https://registry.yarnpkg.com/@tsconfig/node14/-/node14-1.0.1.tgz#95f2d167ffb9b8d2068b0b235302fafd4df711f2"
+  integrity sha512-509r2+yARFfHHE7T6Puu2jjkoycftovhXRqW328PDXTVGKihlb1P8Z9mMZH04ebyajfRY7dedfGynlrFHJUQCg==
+
+"@tsconfig/node16@^1.0.2":
+  version "1.0.2"
+  resolved "https://registry.yarnpkg.com/@tsconfig/node16/-/node16-1.0.2.tgz#423c77877d0569db20e1fc80885ac4118314010e"
+  integrity sha512-eZxlbI8GZscaGS7kkc/trHTT5xgrjH3/1n2JDwusC9iahPKWMRvRjJSAN5mCXviuTGQ/lHnhvv8Q1YTpnfz9gA==
+
 "@types/body-parser@*":
  version "1.19.2"
  resolved "https://registry.yarnpkg.com/@types/body-parser/-/body-parser-1.19.2.tgz#aea2059e28b7658639081347ac4fab3de166e6f0"
@@ -474,11 +506,21 @@ acorn-jsx@^5.3.1:
  resolved "https://registry.yarnpkg.com/acorn-jsx/-/acorn-jsx-5.3.2.tgz#7ed5bb55908b3b2f1bc55c6af1653bada7f07937"
  integrity sha512-rq9s+JNhf0IChjtDXxllJ7g41oZk5SlXtp0LHwyA5cejwn7vKmKp4pPri6YEePv2PU65sAsegbXtIinmDFDXgQ==

+acorn-walk@^8.1.1:
+  version "8.2.0"
+  resolved "https://registry.yarnpkg.com/acorn-walk/-/acorn-walk-8.2.0.tgz#741210f2e2426454508853a2f44d0ab83b7f69c1"
+  integrity sha512-k+iyHEuPgSw6SbuDpGQM+06HQUa04DZ3o+F6CSzXMvvI5KMvnaEqXe+YVe555R9nn6GPt404fos4wcgpw12SDA==
+
 acorn@^7.4.0:
  version "7.4.1"
  resolved "https://registry.yarnpkg.com/acorn/-/acorn-7.4.1.tgz#feaed255973d2e77555b83dbc08851a6c63520fa"
  integrity sha512-nQyp0o1/mNdbTO1PO6kHkwSrmgZ0MT/jCCpNiwbUjGoRN4dlBhqJtoQuCnEOKzgTVwg0ZWiCoQy6SxMebQVh8A==

+acorn@^8.4.1:
+  version "8.6.0"
+  resolved "https://registry.yarnpkg.com/acorn/-/acorn-8.6.0.tgz#e3692ba0eb1a0c83eaa4f37f5fa7368dd7142895"
+  integrity sha512-U1riIR+lBSNi3IbxtaHOIKdH8sLFv3NYfNv8sg7ZsNhcfl4HF2++BfqqrNAxoCLQW1iiylOj76ecnaUxz+z9yw==
+
 agent-base@6:
  version "6.0.2"
  resolved "https://registry.yarnpkg.com/agent-base/-/agent-base-6.0.2.tgz#49fff58577cfee3f37176feab4c22e00f86d7f77"
@@ -530,6 +572,11 @@ ansi-styles@^4.0.0, ansi-styles@^4.1.0:
  dependencies:
    color-convert "^2.0.1"

+arg@^4.1.0:
+  version "4.1.3"
+  resolved "https://registry.yarnpkg.com/arg/-/arg-4.1.3.tgz#269fc7ad5b8e42cb63c896d5666017261c144089"
+  integrity sha512-58S9QDqG0Xx27YwPSt9fJxivjYl432YCwfDMfZ+71RAqUrZef7LrKQZ3LHLOwCS4FLNBplP533Zx895SeOCHvA==
+
 argparse@^1.0.7:
  version "1.0.10"
  resolved "https://registry.yarnpkg.com/argparse/-/argparse-1.0.10.tgz#bcd6791ea5ae09725e17e5ad988134cd40b3d911"
@@ -745,6 +792,11 @@ cors@^2.8.5:
    object-assign "^4"
    vary "^1"

+create-require@^1.1.0:
+  version "1.1.1"
+  resolved "https://registry.yarnpkg.com/create-require/-/create-require-1.1.1.tgz#c1d7e8f1e5f6cfc9ff65f9cd352d37348756c333"
+  integrity sha512-dcKFX3jn0MpIaXjisoRvexIJVEKzaq7z2rZKxf+MSr9TkdmHmsU4m2lcLojrj/FHl8mk5VxMmYA+ftRkP/3oKQ==
+
 cross-spawn@^7.0.2:
  version "7.0.3"
  resolved "https://registry.yarnpkg.com/cross-spawn/-/cross-spawn-7.0.3.tgz#f73a85b9d5d41d045551c177e2882d4ac85728a6"
@@ -814,6 +866,11 @@ dicer@^0.3.0:
  dependencies:
    streamsearch "0.1.2"

+diff@^4.0.1:
+  version "4.0.2"
+  resolved "https://registry.yarnpkg.com/diff/-/diff-4.0.2.tgz#60f3aecb89d5fae520c11aa19efc2bb982aade7d"
+  integrity sha512-58lmxKSA4BNyLz+HHMUzlOEpg09FV+ev6ZMe3vJihgdxzgcwZ8VoEEPmALCZG9LmqfVoNMMKpttIYTVG6uDY7A==
+
 doctrine@^2.1.0:
  version "2.1.0"
  resolved "https://registry.yarnpkg.com/doctrine/-/doctrine-2.1.0.tgz#5cd01fc101621b42c4cd7f5d1a66243716d3f39d"
@@ -1903,6 +1960,11 @@ make-dir@^3.0.0:
  dependencies:
    semver "^6.0.0"

+make-error@^1.1.1:
+  version "1.3.6"
+  resolved "https://registry.yarnpkg.com/make-error/-/make-error-1.3.6.tgz#2eb2e37ea9b67c4891f684a1394799af484cf7a2"
+  integrity sha512-s8UhlNe7vPKomQhC1qFelMokr/Sc3AgNbso3n74mVPA5LTZwkB9NlXf4XPamLxJE8h0gh73rM94xvwRT2CVInw==
+
 media-typer@0.3.0:
  version "0.3.0"
  resolved "https://registry.yarnpkg.com/media-typer/-/media-typer-0.3.0.tgz#8710d7af0aa626f8fffa1ce00168545263255748"
@@ -2515,6 +2577,24 @@ tr46@~0.0.3:
  resolved "https://registry.yarnpkg.com/tr46/-/tr46-0.0.3.tgz#8184fd347dac9cdc185992f3a6622e14b9d9ab6a"
  integrity sha1-gYT9NH2snNwYWZLzpmIuFLnZq2o=

+ts-node@^10.4.0:
+  version "10.4.0"
+  resolved "https://registry.yarnpkg.com/ts-node/-/ts-node-10.4.0.tgz#680f88945885f4e6cf450e7f0d6223dd404895f7"
+  integrity sha512-g0FlPvvCXSIO1JDF6S232P5jPYqBkRL9qly81ZgAOSU7rwI0stphCgd2kLiCrU9DjQCrJMWEqcNSjQL02s6d8A==
+  dependencies:
+    "@cspotcode/source-map-support" "0.7.0"
+    "@tsconfig/node10" "^1.0.7"
+    "@tsconfig/node12" "^1.0.7"
+    "@tsconfig/node14" "^1.0.0"
+    "@tsconfig/node16" "^1.0.2"
+    acorn "^8.4.1"
+    acorn-walk "^8.1.1"
+    arg "^4.1.0"
+    create-require "^1.1.0"
+    diff "^4.0.1"
+    make-error "^1.1.1"
+    yn "3.1.1"
+
 tsconfig-paths@^3.11.0:
  version "3.12.0"
  resolved "https://registry.yarnpkg.com/tsconfig-paths/-/tsconfig-paths-3.12.0.tgz#19769aca6ee8f6a1a341e38c8fa45dd9fb18899b"
@@ -2740,6 +2820,11 @@ yargs@^16.1.1:
    y18n "^5.0.5"
    yargs-parser "^20.2.2"

+yn@3.1.1:
+  version "3.1.1"
+  resolved "https://registry.yarnpkg.com/yn/-/yn-3.1.1.tgz#1e87401a09d767c1d5eab26a6e4c185182d2eb50"
+  integrity sha512-Ux4ygGWsu2c7isFWe8Yu1YluJmqVhxqK2cLXNQA5AcC3QfbGNpM7fu0Y8b/z16pXLnFxZYvWhd3fhBY9DLmC6Q==
+
 yocto-queue@^0.1.0:
  version "0.1.0"
  resolved "https://registry.yarnpkg.com/yocto-queue/-/yocto-queue-0.1.0.tgz#0294eb3dee05028d31ee1a5fa2c556a6aaf10a1b"