95 lines
2.5 KiB
Markdown
95 lines
2.5 KiB
Markdown
---
|
|
id: 5900f3c31000cf542c50fed5
|
|
title: 'Problem 86: Cuboid route'
|
|
challengeType: 5
|
|
forumTopicId: 302200
|
|
dashedName: problem-86-cuboid-route
|
|
---
|
|
|
|
# --description--
|
|
|
|
A spider, S, sits in one corner of a cuboid room, measuring 6 by 5 by 3, and a fly, F, sits in the opposite corner. By travelling on the surfaces of the room the shortest "straight line" distance from S to F is 10 and the path is shown on the diagram.
|
|
|
|
<img class="img-responsive center-block" alt="a diagram of a spider and fly's path from one corner of a cuboid room to the opposite corner" src="https://cdn-media-1.freecodecamp.org/project-euler/cuboid-route.png" style="background-color: white; padding: 10px;">
|
|
|
|
However, there are up to three "shortest" path candidates for any given cuboid and the shortest route doesn't always have integer length.
|
|
|
|
It can be shown that there are exactly `2060` distinct cuboids, ignoring rotations, with integer dimensions, up to a maximum size of M by M by M, for which the shortest route has integer length when M = 100. This is the least value of M for which the number of solutions first exceeds two thousand; the number of solutions when M = 99 is `1975`.
|
|
|
|
Find the least value of M such that the number of solutions first exceeds `n`.
|
|
|
|
# --hints--
|
|
|
|
`cuboidRoute(2000)` should return a number.
|
|
|
|
```js
|
|
assert(typeof cuboidRoute(2000) === 'number');
|
|
```
|
|
|
|
`cuboidRoute(2000)` should return `100`.
|
|
|
|
```js
|
|
assert.strictEqual(cuboidRoute(2000), 100);
|
|
```
|
|
|
|
`cuboidRoute(25000)` should return `320`.
|
|
|
|
```js
|
|
assert.strictEqual(cuboidRoute(25000), 320);
|
|
```
|
|
|
|
`cuboidRoute(500000)` should return `1309`.
|
|
|
|
```js
|
|
assert.strictEqual(cuboidRoute(500000), 1309);
|
|
```
|
|
|
|
`cuboidRoute(1000000)` should return `1818`.
|
|
|
|
```js
|
|
assert.strictEqual(cuboidRoute(1000000), 1818);
|
|
```
|
|
|
|
# --seed--
|
|
|
|
## --seed-contents--
|
|
|
|
```js
|
|
function cuboidRoute(n) {
|
|
|
|
return true;
|
|
}
|
|
|
|
cuboidRoute(2000);
|
|
```
|
|
|
|
# --solutions--
|
|
|
|
```js
|
|
function cuboidRoute(n) {
|
|
// Based on https://www.mathblog.dk/project-euler-86-shortest-path-cuboid/
|
|
function getLength(a, b) {
|
|
return Math.sqrt(a ** 2 + b ** 2);
|
|
}
|
|
|
|
let M = 2;
|
|
let counter = 0;
|
|
|
|
while (counter < n) {
|
|
M++;
|
|
for (let baseHeightWidth = 3; baseHeightWidth <= 2 * M; baseHeightWidth++) {
|
|
const pathLength = getLength(M, baseHeightWidth);
|
|
if (Number.isInteger(pathLength)) {
|
|
if (baseHeightWidth <= M) {
|
|
counter += Math.floor(baseHeightWidth / 2);
|
|
} else {
|
|
counter += 1 + M - Math.floor((baseHeightWidth + 1) / 2);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
return M;
|
|
}
|
|
```
|