7d9496e52c
* fix: clean-up Project Euler 361-380 * fix: improve wording Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> * fix: remove unnecessary paragraph * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
51 lines
1.3 KiB
Markdown
51 lines
1.3 KiB
Markdown
---
|
|
id: 5900f4d91000cf542c50ffea
|
|
title: 'Problem 364: Comfortable distance'
|
|
challengeType: 5
|
|
forumTopicId: 302025
|
|
dashedName: problem-364-comfortable-distance
|
|
---
|
|
|
|
# --description--
|
|
|
|
There are $N$ seats in a row. $N$ people come after each other to fill the seats according to the following rules:
|
|
|
|
1. If there is any seat whose adjacent seat(s) are not occupied take such a seat.
|
|
2. If there is no such seat and there is any seat for which only one adjacent seat is occupied take such a seat.
|
|
3. Otherwise take one of the remaining available seats.
|
|
|
|
Let $T(N)$ be the number of possibilities that $N$ seats are occupied by $N$ people with the given rules. The following figure shows $T(4) = 8$.
|
|
|
|
<img class="img-responsive center-block" alt="eight ways for N seats to be occupied by N people" src="https://cdn.freecodecamp.org/curriculum/project-euler/comfortable-distance.gif" style="background-color: white; padding: 10px;">
|
|
|
|
We can verify that $T(10) = 61\\,632$ and $T(1\\,000)\bmod 100\\,000\\,007 = 47\\,255\\,094$.
|
|
|
|
Find $T(1\\,000\\,000)\bmod 100\\,000\\,007$.
|
|
|
|
# --hints--
|
|
|
|
`comfortableDistance()` should return `44855254`.
|
|
|
|
```js
|
|
assert.strictEqual(comfortableDistance(), 44855254);
|
|
```
|
|
|
|
# --seed--
|
|
|
|
## --seed-contents--
|
|
|
|
```js
|
|
function comfortableDistance() {
|
|
|
|
return true;
|
|
}
|
|
|
|
comfortableDistance();
|
|
```
|
|
|
|
# --solutions--
|
|
|
|
```js
|
|
// solution required
|
|
```
|